**Magnetization Statics and Ultrafast Photoinduced Dynamics in Co/garnet Heterostructures**

Andrzej Stupakiewicz

[17] Chen Yuan-Tsung, Hsieh W.H. Thermal, magnetic, electric, and adhesive properties of

[18] Varga M, Varga R, Komova E, Csach K, Vojtanik P. Temperature evolution of magnetic susceptibility during devitrification of Cu-free HITPERM alloy. J. Magn. Magn. Mater.

[19] Nikolo M. Superconductivity: A guide to alternating current susceptibility measure‐ ments and alternating current susceptometer design. Am. J. Phys. 1995; 63:57–61. [20] Vázquez M, Kurlyandskaya G, Garcia-Benitez J, Sinnecker J. IEEE Trans. Magn. 1999;

[21] Coisson M, Kane S, Tiberto P, Vinai F. Influence of DC Joule-heating treatment on magnetoimpedance effect in amorphous Co64Fe21B15 alloy. J. Magn. Magn. Mater. 2004;

[22] Pal S, Manik N, Mitra A. Dependence of frequency and amplitude of the ac current on the GMI properties of Co based amorphous wires. Mater. Sci. Eng. A. 2006; 415:195–

[23] Rahman Z, Kamruzzaman M, Rahman M. A. J. Mater. Process. Technol. 2004; 153–

[24] Orozco A, Caamaño Z, Rosales A. AC magnetic susceptibility and influence of heat treatment on obtaining the nanocrystalline structure for the amorphous alloy of Fe37Co35Nb6B11Si10Cu1 composition. JPCS. 2016; 687:1–4. DOI:10.1088/1742-6596/012109.

amorphous Co60Fe20B20 thin films. J. Alloys Compd. 2013; 552:283–288.

2010; 322:2758-2761.

35:3358–3360.

271:312–317.

154:791–796.

201.

194 Magnetic Materials

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62542

#### **Abstract**

We demonstrate experimental studies of the magnetization behavior from statics to ultrafast photoinduced dynamics with high temporal resolution in ultrathin Co/garnet heterostructures with a sub-nanometer roughness at the interface. We report on modulation of spin precession in Co/garnet heterostructures with distinct frequencies and show that the excitation efficiency of these precessions strongly depends on the amplitude and the direction of external magnetic field. Furthermore, it is shown that the magnetization precession in the garnet film can be manipulated by the strong magneto‐ static coupling between Co and garnet layers. These findings could provide new possibilities in all-optical excitation and local spin manipulation by polarized femtosec‐ ond pulses for the application in nanodevices with high-speed switching.

**Keywords:** ultrafast magnetization dynamics, magneto-optical effect, magnetization reversal, magnetic anisotropy, magnetic domain structure, photomagnetism, ferro‐ magnetic resonance, garnet, cobalt

## **1. Introduction**

Control of magnetization with the help of femtosecond laser pulses is a hot topic in fundamen‐ tal science [1–5]. Understanding ultrafast magnetization dynamics on an ultrashort timescale promises to enable technologies based on the quantum-level interplay of nonlinear optics and magnetism. All-optical control of the magnetism in novel magnetic materials is a particularly important issue for further development of faster magnetic information storage/processing and spintronic nanodevices. The thermal effect limits the application of the technology of heatassisted magnetic recording due to relatively long cooling time (~1 ns) [6]. One of the solu‐

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

tionstothisproblemcanbeall-opticalnonthermalcontrolofthemagnetization.Forfundamental research, hybrid structures give the unique possibility to engineer high-quality two-dimen‐ sional interfaces and create phenomena which do not exist in a bulk material. On the contra‐ ry, new functionalities may emerge from the coexistence of two materials with complementary properties, such as magnetism and ferroelectricity, metallic and dielectric, antiferromagnetic and ferromagnetic, etc.

An interesting combination is formed by a metallic ferromagnetic ultrathin film on top of a dielectric ferrimagnet, based on yttrium iron garnet (YIG) with different substitutions. The functionality of YIG systems has been shown to be very broad, with examples such as the excitation of surface plasmons [7], the propagation of nonlinear spin-waves [8, 9], Bose-Einstein condensation of a magnon gas [10], high-temperature photomagnetism [11], the observation of the inverse Faraday effect induced by an ultrafast laser pulse [12–14], and many others. A combination of a metal layer on a garnet system may create the possibility to modify different properties. Recently, it was reported that ion beam sputtered Fe films on a 100 nmthick YIG layer possess a perpendicular magnetic anisotropy [15]. In the thickness range between 5 and 10 nm, the stripe domain structure of YIG was transferred into the Fe films due to the presence of strong interlayer exchange coupling [15]. Static and dynamic properties were also investigated for a 30-nm permalloy film on a 0.5 μm (YBiLu)3(FeAl)5O12 layer that is characterized by a perpendicular anisotropy [16]. A strong direct exchange coupling is revealed via the formation of enlarged closure domains with a preferred orientation at the interface between the permalloy film and the garnet layer. As a result, the domain pattern of such a heterostructure shows an increased zero-field stripe period in comparison to the parent garnet layer [16]. The magnetization reversal process and magnetic domain structure were the focus points of these studies. YIG films with iron partially substituted with Co2+ and Co3+ ions [17] show interesting magnetic properties, such as several spin-reorientation phase transitions in a temperature range of 20–300 K [18], and both quasistatic [19] and ultrafast [20] lightinduced changes in magnetic anisotropy. Light pulses excite large-angle magnetization precession in such garnets, the phase and the amplitude of the precession being determined by the polarization of the light. If coupled with a nanostructure ferromagnetic (metallic) overlayer, such photomagnetic effects in the garnet may also be transferred to the overlayer, thus creating new possibilities for ultrafast switching.

For instance, it is known for a metal/dielectric heterostructure that spin-orbital interaction may initiate a transfer of angular momentum between the layers and thus cause correlations in the magnetization dynamics [21]. Understanding optical control of the magnetism in magnetic heterostructures is a particularly important issue for further development of faster magnetic information storage/processing and spintronic nanodevices. Optical control of spins in Co/ SmFeO3 heterostructures by the X-ray pulse with duration 70 ps has been demonstrated using X-ray photoemission electron microscopy, revealing that the dynamics of the spins in the metallic Co and the dielectric SmFeO3 are strongly coupled [22]. In the general case, a novel ultrafast magnetization dynamics in ferromagnetic metal/garnet heterostructures can be expected due to the coupling between the ferromagnetic and garnet films and/or the influence of the effective magnetic field of the ferromagnetic metallic film. Using the YIG:Co film in the ferromagnetic/garnet heterostructures gives unique possibility to investigate light-induced magnetization dynamics at the sub-picosecond timescale.

This chapter describes experimental and theoretical studies of the magnetization behavior from statics to ultrafast light-induced magnetization dynamics in ultrathin 2 nm Co films deposited on Co-substituted yttrium iron garnet thin film. In particular, we demonstrate that ion beam sputtering can be used for the formation of Co/garnet heterostructures. The mag‐ netization reversal process and magnetic anisotropy of the Co/garnet heterostructures are measured by both magneto-optical magnetometry and ferromagnetic resonance (FMR). To investigate the ultrafast magnetization dynamics in both garnet and Co/garnet heterostructure induced by femtosecond laser pulses, we carried out time-resolved measurements at room temperature using a magneto-optical pump-probe method. We demonstrated that the frequency of the spin precession in a Co/garnet bilayer can be modulated by exciting linearly polarized femtosecond pulses. The experimental results presented here were obtained on 2 nm Co/garnet heterostructure, which has a strong magnetostatic interlayer coupling. In this heterostructure, two distinct precession frequencies were observed. One is attributed to the magnetization precession of the 2 nm cobalt and the other to that of the 1.8-μm-thick garnet. The spin oscillation frequencies of the two layers differ by about a factor of two and are strongly dependent on the out-of-plane external magnetic field. We compared magnetization dynamics in the Co and bare garnet films separately via selective probing and showed that magnetization precession in the garnet via the photomagnetic effect can be manipulated by the magnetostatic interlayer coupling. The experimental results are discussed within the phenomenological model.

## **2. Heterostructure preparation**

tionstothisproblemcanbeall-opticalnonthermalcontrolofthemagnetization.Forfundamental research, hybrid structures give the unique possibility to engineer high-quality two-dimen‐ sional interfaces and create phenomena which do not exist in a bulk material. On the contra‐ ry, new functionalities may emerge from the coexistence of two materials with complementary properties, such as magnetism and ferroelectricity, metallic and dielectric, antiferromagnetic

An interesting combination is formed by a metallic ferromagnetic ultrathin film on top of a dielectric ferrimagnet, based on yttrium iron garnet (YIG) with different substitutions. The functionality of YIG systems has been shown to be very broad, with examples such as the excitation of surface plasmons [7], the propagation of nonlinear spin-waves [8, 9], Bose-Einstein condensation of a magnon gas [10], high-temperature photomagnetism [11], the observation of the inverse Faraday effect induced by an ultrafast laser pulse [12–14], and many others. A combination of a metal layer on a garnet system may create the possibility to modify different properties. Recently, it was reported that ion beam sputtered Fe films on a 100 nmthick YIG layer possess a perpendicular magnetic anisotropy [15]. In the thickness range between 5 and 10 nm, the stripe domain structure of YIG was transferred into the Fe films due to the presence of strong interlayer exchange coupling [15]. Static and dynamic properties were also investigated for a 30-nm permalloy film on a 0.5 μm (YBiLu)3(FeAl)5O12 layer that is characterized by a perpendicular anisotropy [16]. A strong direct exchange coupling is revealed via the formation of enlarged closure domains with a preferred orientation at the interface between the permalloy film and the garnet layer. As a result, the domain pattern of such a heterostructure shows an increased zero-field stripe period in comparison to the parent garnet layer [16]. The magnetization reversal process and magnetic domain structure were the focus points of these studies. YIG films with iron partially substituted with Co2+ and Co3+ ions [17] show interesting magnetic properties, such as several spin-reorientation phase transitions in a temperature range of 20–300 K [18], and both quasistatic [19] and ultrafast [20] lightinduced changes in magnetic anisotropy. Light pulses excite large-angle magnetization precession in such garnets, the phase and the amplitude of the precession being determined by the polarization of the light. If coupled with a nanostructure ferromagnetic (metallic) overlayer, such photomagnetic effects in the garnet may also be transferred to the overlayer,

For instance, it is known for a metal/dielectric heterostructure that spin-orbital interaction may initiate a transfer of angular momentum between the layers and thus cause correlations in the magnetization dynamics [21]. Understanding optical control of the magnetism in magnetic heterostructures is a particularly important issue for further development of faster magnetic information storage/processing and spintronic nanodevices. Optical control of spins in Co/ SmFeO3 heterostructures by the X-ray pulse with duration 70 ps has been demonstrated using X-ray photoemission electron microscopy, revealing that the dynamics of the spins in the metallic Co and the dielectric SmFeO3 are strongly coupled [22]. In the general case, a novel ultrafast magnetization dynamics in ferromagnetic metal/garnet heterostructures can be expected due to the coupling between the ferromagnetic and garnet films and/or the influence of the effective magnetic field of the ferromagnetic metallic film. Using the YIG:Co film in the

and ferromagnetic, etc.

196 Magnetic Materials

thus creating new possibilities for ultrafast switching.

Initial garnet thin films composed of Y2Ca1Fe3.9Co0.1Ge1O12 (YIG:Co) were grown by liquidphase epitaxy on Gd3Ga5O12 (GGG) (001)-oriented substrate. The initial thickness of garnet films was 6.5 μm. The initial garnet surface was etching, and Co/YIG:Co heterostructures were formed using the dual ion beam sputtering technique [23] on the base of an A 700 Q Leybold vacuum system. The base pressure was below 8 × 10−6 mbar in the vacuum chamber. The damage-free etching of the garnet films and subsequent deposition of the Co layers were carried out *in situ* at a pressure of 2.5 × 10−4 mbar [24].

**Figure 1** illustrates the stage of the heterostructure preparation. The initial garnet film was smoothed to 5.8 μm thickness with a 0.6-keV oxygen ion beam with current density of 0.2 mA/ cm2 , corresponding to the ion flux of 3.2 × 1015 cm−2 × c−1 [24]. The oxygen ions improve garnet transmittance in the energy range between 0.5 and 1 keV. The garnet films are sputtered at a near-normal incidence angle. At this angle, optimal smoothing of the optical materials (quartz, glass, ceramic) is achieved for up to sub-nanometer roughness [25]. The garnet sputtering rate is about 0.22 μm/h. A final smoothing of the garnet surfaces was completed using a 0.3-keV oxygen ion beam for over 10 minutes. Au and Co targets were sputtered with a 1.5-keV argon ion beam at 0.25 mA/cm2 current density [24]. The incident angle of argon ions is 60° with respect to the target normal, so that the sputtered flux is deposited onto substrate at nearnormal incidence angle. The deposition rates of Au and Co are 8.4 and 5.4 nm/min, respec‐ tively. A 4-nm Au film was used to protect the 2-nm Co layer before oxidation. For this thickness, the Au film is continuous and exhibits surface roughness close to the substrate of about 0.2 nm [26]. The Co/YIG:Co heterostructures and reference YIG:Co films are prepared onto the same substrate and in the same experimental conditions.

**Figure 1.** Schematic configuration of the heterostructure during preparation: (a) the YIG:Co film after smoothing from 6.5 μm to 5.8 μm thickness, (b) after ion beam etching to 1.8 μm on the garnet part, (c) after deposition of 4-nm Au/2 nm Co bilayer on the garnet part, and (d) the 20 × 20 μm pattern area on the Co/garnet part.

A 20 × 20 μm Au/Co pattern, for comparison of coupling between Co and garnet films and domain structures modifications on garnets, was fabricated by a lift-off photolithography. The photolithographic process can be represented as follows. In the first step, the garnet film was coated with the light-sensitive chemical photoresist to form a homogeneous layer of about 1 μm thickness. In the second step, the photoresist on garnet surface was exposed through a lithographic mask with high-intensity ultraviolet (UV) radiation. This mask contains the copy of pattern. The 20 × 20 μm windows are opened to the exposing UV light passes through the mask. The dose of UV exposure and the development process were precisely controlled to result in a sharp edge profile of resist patterns. In the third step, the irradiated photoresist area was washed away, leaving the photoresist in the unexposed area. In the fourth step, after deposition of the Au/Co bilayers, a chemical etching was used to remove the previously unexposed photoresist. In such way, the pattern from mask was transferred to the garnet film. As a result, the Co(homogeneous) and Co(pattern)/garnet heterostructures as well as reference garnet films with discrete thicknesses were prepared onto the same GGG (001) substrate by combining the ion beam processing with photolithographic technique (see **Figure 1**).

respect to the target normal, so that the sputtered flux is deposited onto substrate at nearnormal incidence angle. The deposition rates of Au and Co are 8.4 and 5.4 nm/min, respec‐ tively. A 4-nm Au film was used to protect the 2-nm Co layer before oxidation. For this thickness, the Au film is continuous and exhibits surface roughness close to the substrate of about 0.2 nm [26]. The Co/YIG:Co heterostructures and reference YIG:Co films are prepared

**Figure 1.** Schematic configuration of the heterostructure during preparation: (a) the YIG:Co film after smoothing from 6.5 μm to 5.8 μm thickness, (b) after ion beam etching to 1.8 μm on the garnet part, (c) after deposition of 4-nm Au/2

A 20 × 20 μm Au/Co pattern, for comparison of coupling between Co and garnet films and domain structures modifications on garnets, was fabricated by a lift-off photolithography. The photolithographic process can be represented as follows. In the first step, the garnet film was coated with the light-sensitive chemical photoresist to form a homogeneous layer of about 1 μm thickness. In the second step, the photoresist on garnet surface was exposed through a lithographic mask with high-intensity ultraviolet (UV) radiation. This mask contains the copy of pattern. The 20 × 20 μm windows are opened to the exposing UV light passes through the mask. The dose of UV exposure and the development process were precisely controlled to result in a sharp edge profile of resist patterns. In the third step, the irradiated photoresist area was washed away, leaving the photoresist in the unexposed area. In the fourth step, after deposition of the Au/Co bilayers, a chemical etching was used to remove the previously unexposed photoresist. In such way, the pattern from mask was transferred to the garnet film. As a result, the Co(homogeneous) and Co(pattern)/garnet heterostructures as well as reference

nm Co bilayer on the garnet part, and (d) the 20 × 20 μm pattern area on the Co/garnet part.

onto the same substrate and in the same experimental conditions.

198 Magnetic Materials

**Figure 2.** (a) SEM images of the initial 6.5 μm YIG:Co film, (b) 5.8 μm YIG:Co film after etching, of YIG:Co films, and (c) the cross-sectional image of the Co(50nm)/YIG:Co interface .

The surface morphology of both the bare YIG:Co film and Co/YIG:Co heterostructure was measured by high-resolution scanning electron microscopy (SEM) using a FEI's Helios NanoLab DualBeam system. The root mean square (rms) surface roughness was examined by atomic force microscope in tapping mode. The initial garnet surface is rough with protrusions, while YIG:Co contains troughs of about 100–200 nm in diameter (see **Figure 2(a)**). The ion beam smoothing the garnet surface area showed significantly reduced rms parameters from 3.5 to 0.3 nm after etching the garnet film from 6.5 μm to 5.8 μm (see **Figure 2(b)**). The surface roughness remains approximately the same after ion beam etching down to 1 μm. Ion beam thinning of the garnet film also decreases the rms parameter to 0.25 nm. This is comparable to surfaces of roughness similar to high-quality Si substrate (0.18 nm).

The surfaces of the Co/garnet heterostructures are continuous and exhibit a slightly increased rms parameter from 0.3 to 0.37 nm after the deposition of Au(4nm)/Co(2 nm) bilayer structures on the ion beam-smoothed garnet surfaces. A cross section of the Co/garnet interface was observed using a 30-keV gallium-focused ion beam. The low contrast of the Co(≤5 nm)/garnet interfaces results from charge accumulation in the dielectric garnet film. Therefore, only for the SEM image observation, the thickness of the Co layer was increased up to 50 nm for the enhancement of the contrast at the Co/garnet interface. The Co/garnet interface is sharp, and the thickness of the transition layer is thinner than 1–2 nm (see inset of **Figure 2(c)**).

## **3. Optical and magnetic properties of Co/garnet heterostructures**

The optical transmittance, magneto-optical both Kerr (*θ*k) and Faraday (*θ*F) rotations were performed on Co/YIG:Co heterostructures and reference YIG:Co film using light from a modelocked Ti-sapphire laser (MaiTai HP, Spectra-Physics) operating within the 400–1040 nm range and a repetition rate of 80 MHz. For the detection of the angle of magneto-optical rotation, a lock-in amplifier was used in combination with a standard modulation technique with a photoelastic modulator.

#### **3.1. Optical and magneto-optical spectra**

The investigation of the optical absorption and the Faraday rotation spectra in YIG:Co garnet demonstrated that the contribution of Co ions in octahedral sites is substantially smaller than that of tetrahedral Co ions [27]. Furthermore, the latter can be observed in near-infrared range, where pure YIG is fully transparent. Both an optical transmittance and magneto-optical Faraday rotation spectra for YIG:Co film are shown in **Figure 3**. At wavelengths longer than about 800 nm, the absorption is small and is equal to about 102 cm−1 (see **Figure 3(b)**). Essentially in the wavelength range of 450–1300 nm, the absorption is caused by crystal field transitions of Fe3+, Co2+, and Co3+ ions in both tetrahedral and octahedral sites. The crystal field transitions in octahedral sites have weaker oscillator strength than that the tetrahedral ones. However, at wavelengths shorter than 450 nm, the strong optical absorption of the garnet film is related to charge transfer transitions from oxygen ligands O2− to octahedral Fe3+ and Co3+ ions. The scheme of crystal field and charge transfer transitions for Co ions (**Figure 3(a)**) was obtained from experimental and theoretical investigations [27, 28]. In a band model, the charge transfer transition is connected with electron excitation from a valence band to conduction ones, which are created by O *2p* and Fe (Co) *3d* orbitals, respectively. Although a determination of band gap *E*g is difficult owing to the garnets not exhibiting sharp absorption edge, the lowest charge transfer transitions of octahedral Co3+ (1 A1→<sup>1</sup> T2) ions give *E*g ≈ 2.85 eV. This value agrees well with the band gap of pure YIG (*E*g = 2.9 eV). In the general case, the optical absorption is correlated with the magneto-optical Faraday rotation (defined by rotation angle *θ*F) (see **Figure 3(c)**). The energy levels of the Co ions do not coincide with the *3d* levels of the Fe ions. Therefore, the optical excitation of YIG:Co film leads to additional transitions of Co ions as well as affect the Fe3+ ion transitions and consequently results in magneto-optical effects with spectral sensitivity.

while YIG:Co contains troughs of about 100–200 nm in diameter (see **Figure 2(a)**). The ion beam smoothing the garnet surface area showed significantly reduced rms parameters from 3.5 to 0.3 nm after etching the garnet film from 6.5 μm to 5.8 μm (see **Figure 2(b)**). The surface roughness remains approximately the same after ion beam etching down to 1 μm. Ion beam thinning of the garnet film also decreases the rms parameter to 0.25 nm. This is comparable to

The surfaces of the Co/garnet heterostructures are continuous and exhibit a slightly increased rms parameter from 0.3 to 0.37 nm after the deposition of Au(4nm)/Co(2 nm) bilayer structures on the ion beam-smoothed garnet surfaces. A cross section of the Co/garnet interface was observed using a 30-keV gallium-focused ion beam. The low contrast of the Co(≤5 nm)/garnet interfaces results from charge accumulation in the dielectric garnet film. Therefore, only for the SEM image observation, the thickness of the Co layer was increased up to 50 nm for the enhancement of the contrast at the Co/garnet interface. The Co/garnet interface is sharp, and

The optical transmittance, magneto-optical both Kerr (*θ*k) and Faraday (*θ*F) rotations were performed on Co/YIG:Co heterostructures and reference YIG:Co film using light from a modelocked Ti-sapphire laser (MaiTai HP, Spectra-Physics) operating within the 400–1040 nm range and a repetition rate of 80 MHz. For the detection of the angle of magneto-optical rotation, a lock-in amplifier was used in combination with a standard modulation technique with a

The investigation of the optical absorption and the Faraday rotation spectra in YIG:Co garnet demonstrated that the contribution of Co ions in octahedral sites is substantially smaller than that of tetrahedral Co ions [27]. Furthermore, the latter can be observed in near-infrared range, where pure YIG is fully transparent. Both an optical transmittance and magneto-optical Faraday rotation spectra for YIG:Co film are shown in **Figure 3**. At wavelengths longer than about 800 nm, the absorption is small and is equal to about 102 cm−1 (see **Figure 3(b)**). Essentially in the wavelength range of 450–1300 nm, the absorption is caused by crystal field transitions of Fe3+, Co2+, and Co3+ ions in both tetrahedral and octahedral sites. The crystal field transitions in octahedral sites have weaker oscillator strength than that the tetrahedral ones. However, at wavelengths shorter than 450 nm, the strong optical absorption of the garnet film is related to charge transfer transitions from oxygen ligands O2− to octahedral Fe3+ and Co3+ ions. The scheme of crystal field and charge transfer transitions for Co ions (**Figure 3(a)**) was obtained from experimental and theoretical investigations [27, 28]. In a band model, the charge transfer transition is connected with electron excitation from a valence band to conduction ones, which are created by O *2p* and Fe (Co) *3d* orbitals, respectively. Although a determination of band gap *E*g is difficult owing to the garnets not exhibiting sharp absorption edge, the lowest charge

A1→<sup>1</sup>

T2) ions give *E*g ≈ 2.85 eV. This value agrees well

the thickness of the transition layer is thinner than 1–2 nm (see inset of **Figure 2(c)**).

**3. Optical and magnetic properties of Co/garnet heterostructures**

surfaces of roughness similar to high-quality Si substrate (0.18 nm).

photoelastic modulator.

200 Magnetic Materials

**3.1. Optical and magneto-optical spectra**

transfer transitions of octahedral Co3+ (1

**Figure 3.** (a) Scheme of crystal field and charge transfer transitions according to Refs. [27, 28], (b) optical transmittance, and (c) magneto-optical Faraday rotation spectra of 1.8 μm YIG:Co film.

The contribution of Co ion transitions to magneto-optical Faraday rotation spectrum is clearly seen by comparison of previously reported spectra for both YIG [29] and YIG:Co films [27]. In our case, for the garnet film, we observed the reduction of *θ*<sup>F</sup> close to the optical transitions of tetrahedral Co2+ and Co3+ ions as well as octahedral Co3+ ones. It is important to note that for different garnet thicknesses and both YIG and YIG:Co films reported, *θ*<sup>F</sup> is practically the same in the wavelength range of 800–900 nm, where no optical transitions of Co ions are expected (see **Figure 3(b)**). This indicates that magnetic anisotropy (induced by the temperature, light, etc.) of the garnet can be modified due to inhomogeneous distribution of Co dopant in the garnet lattice. The contribution of low spin octahedral Co3+ ions to magnetic anisotropy is zero in single-ion approximation. Since tetrahedral Co2+ and Co3+ ions are responsible for growthinduced magnetic anisotropy [30], one can assume that the reduction in garnet thickness leads to a change in the uniaxial anisotropy and thus to a change in the magnetization reversal process. To confirm this, in the next sections we performed investigations of both the magnetic anisotropy and magnetization reversal processes in ultrathin Co layer and garnet thin films.

#### **3.2. Magnetization reversal in static regime**

The process of magnetization reversal has been studied at room temperature in reflection with the linear magneto-optic Kerr effect (MOKE) and in transmission with the Faraday effect. From the data, we separated different magneto-optical contributions from the Co layer and garnetonly films. The perpendicular magnetization component of the ultrathin Co layer was measured using the polar MOKE (P-MOKE) geometry, with the angle of incidence of the laser light close to the sample normal and the external magnetic field *H*<sup>Z</sup> perpendicular to the surface of the sample (see **Figure 4(a)**). The measurements of the in-plane magnetization components of the Co layer were performed in the longitudinal MOKE (L-MOKE) geometry, with a 49o angle of incidence of the light (see **Figure 5(a)**). The magnetic field *H*<sup>X</sup> was applied in the sample plane for various orientations with respect to the garnet [100] direction. The process of magnetization reversal to the determination of Faraday rotation angle *θ*<sup>F</sup> of the garnet-only films was studied in the magneto-optical Faraday geometry, with perpendicular and in-plane magnetic field orientation (**Figure 4**).

According to the optical absorption spectra in **Figure 3(b)**, Au/Co/garnet heterostructures are transparent enough to be investigated in transmission geometry, for example at 690 nm wavelength. From the experimental curves, we separated the different magneto-optical contributions of the Co layer and garnet films using vector magneto-optical magnetometry and measurements for reference garnet film [31]. The P-MOKE hysteresis loops observed for the 2-nm-thick Co film grown on garnet film indicate an in-plane magnetization of Co (see **Figure 4(c)**). **Figure 4(b)** and **5(b)** show Faraday rotation hysteresis loops measured for garnet film and a perpendicular applied field *H*Z and an in-plane field *H*X, respectively. From the hysteresis loop shown in **Figure 4(b)**, one deduces a Faraday rotation from the garnet layer of about *θ*<sup>F</sup> = 0.08 degrees and a paramagnetic linear contribution from the GGG substrate. For the in-plane applied magnetic field in the garnet [100] direction, the saturating field is about 0.6 kOe (**Figure 5(b)**).

Magnetization Statics and Ultrafast Photoinduced Dynamics in Co/garnet Heterostructures http://dx.doi.org/10.5772/62542 203

The contribution of Co ion transitions to magneto-optical Faraday rotation spectrum is clearly seen by comparison of previously reported spectra for both YIG [29] and YIG:Co films [27]. In our case, for the garnet film, we observed the reduction of *θ*<sup>F</sup> close to the optical transitions of tetrahedral Co2+ and Co3+ ions as well as octahedral Co3+ ones. It is important to note that for different garnet thicknesses and both YIG and YIG:Co films reported, *θ*<sup>F</sup> is practically the same in the wavelength range of 800–900 nm, where no optical transitions of Co ions are expected (see **Figure 3(b)**). This indicates that magnetic anisotropy (induced by the temperature, light, etc.) of the garnet can be modified due to inhomogeneous distribution of Co dopant in the garnet lattice. The contribution of low spin octahedral Co3+ ions to magnetic anisotropy is zero in single-ion approximation. Since tetrahedral Co2+ and Co3+ ions are responsible for growthinduced magnetic anisotropy [30], one can assume that the reduction in garnet thickness leads to a change in the uniaxial anisotropy and thus to a change in the magnetization reversal process. To confirm this, in the next sections we performed investigations of both the magnetic anisotropy and magnetization reversal processes in ultrathin Co layer and garnet thin films.

The process of magnetization reversal has been studied at room temperature in reflection with the linear magneto-optic Kerr effect (MOKE) and in transmission with the Faraday effect. From the data, we separated different magneto-optical contributions from the Co layer and garnetonly films. The perpendicular magnetization component of the ultrathin Co layer was measured using the polar MOKE (P-MOKE) geometry, with the angle of incidence of the laser light close to the sample normal and the external magnetic field *H*<sup>Z</sup> perpendicular to the surface of the sample (see **Figure 4(a)**). The measurements of the in-plane magnetization components of the Co layer were performed in the longitudinal MOKE (L-MOKE) geometry, with a 49o angle of incidence of the light (see **Figure 5(a)**). The magnetic field *H*<sup>X</sup> was applied in the sample plane for various orientations with respect to the garnet [100] direction. The process of magnetization reversal to the determination of Faraday rotation angle *θ*<sup>F</sup> of the garnet-only films was studied in the magneto-optical Faraday geometry, with perpendicular and in-plane

According to the optical absorption spectra in **Figure 3(b)**, Au/Co/garnet heterostructures are transparent enough to be investigated in transmission geometry, for example at 690 nm wavelength. From the experimental curves, we separated the different magneto-optical contributions of the Co layer and garnet films using vector magneto-optical magnetometry and measurements for reference garnet film [31]. The P-MOKE hysteresis loops observed for the 2-nm-thick Co film grown on garnet film indicate an in-plane magnetization of Co (see **Figure 4(c)**). **Figure 4(b)** and **5(b)** show Faraday rotation hysteresis loops measured for garnet film and a perpendicular applied field *H*Z and an in-plane field *H*X, respectively. From the hysteresis loop shown in **Figure 4(b)**, one deduces a Faraday rotation from the garnet layer of about *θ*<sup>F</sup> = 0.08 degrees and a paramagnetic linear contribution from the GGG substrate. For the in-plane applied magnetic field in the garnet [100] direction, the saturating field is about

**3.2. Magnetization reversal in static regime**

202 Magnetic Materials

magnetic field orientation (**Figure 4**).

0.6 kOe (**Figure 5(b)**).

**Figure 4.** (a) The experimental configuration with Kerr and Faraday effects for perpendicular magnetic field orienta‐ tion *H*Z to the sample plane. Hysteresis loops measured for YIG:Co and Co/YIG:Co at 690 nm wavelength in: (b) Fara‐ day and (c) P-MOKE geometries.

The L-MOKE magnetization curve for the Co layer measured with the in-plane external magnetic field *H*X are shown in **Figure 5(c)**. From L-MOKE hysteresis loops, the remanence parameter is plotted on inset of **Figure 5(c)** as a function of azimuthal angle *ϕ*H. The shape of these loops is practically independent on the azimuthal sample orientation and confirms the "easy plane" type of the magnetic anisotropy with a saturation in-plane field of about 0.3 kOe. To determine magnetic anisotropy of both garnet films and Co layer, we performed FMR measurements at room temperature.

**Figure 5.** (a) The experimental configuration with Kerr and Faraday effects for sample in-plane magnetic field orienta‐ tion *H*X. Hysteresis loops measured for YIG:Co and Co/YIG:Co at 690 nm wavelength in: (b) Faraday and (c) L-MOKE geometries.

#### **3.3. Magnetic anisotropy study**

The L-MOKE magnetization curve for the Co layer measured with the in-plane external magnetic field *H*X are shown in **Figure 5(c)**. From L-MOKE hysteresis loops, the remanence parameter is plotted on inset of **Figure 5(c)** as a function of azimuthal angle *ϕ*H. The shape of these loops is practically independent on the azimuthal sample orientation and confirms the "easy plane" type of the magnetic anisotropy with a saturation in-plane field of about 0.3 kOe. To determine magnetic anisotropy of both garnet films and Co layer, we performed FMR

**Figure 5.** (a) The experimental configuration with Kerr and Faraday effects for sample in-plane magnetic field orienta‐ tion *H*X. Hysteresis loops measured for YIG:Co and Co/YIG:Co at 690 nm wavelength in: (b) Faraday and (c) L-MOKE

measurements at room temperature.

204 Magnetic Materials

geometries.

The typical FMR line measured in the external magnetic field applied to the sample at polar angle *θ*H = 65° is presented in **Figure 6**. The Co layer and garnet film contributions to this FMR line can be clearly seen. The linewidth values of Co and garnet films are different. The peakto-peak FMR linewidth *ΔH* is related to the relaxation rate of magnetization motion, which is caused by intrinsic Gilbert damping α and magnetic inhomogeneities *ΔH*(0) in ferromagnet: *<sup>H</sup>* <sup>=</sup> <sup>2</sup> 3 *α <sup>γ</sup>* 2*π f* FMR + Δ*H* (0), where *γ* is the gyromagnetic ratio, and *f*FMR is the FMR frequency. The damping parameter estimated from above-mentioned *ΔH* values of Co and garnet films is equal to *α*Co = 0.04 and *α*garnet= 0.19. Nevertheless, the Gilbert damping of ultrathin Co layer grown on ultra-smoothed garnet film is comparable with the damping of high-quality single and polycrystalline Co layers obtained on metallic underlayers [32–34].

**Figure 6.** FMR lines for Co/YIG:Co heterostructure measured at *θ*H = 65° and *ϕ*H = 0° of the external magnetic field *H*.

The experimental dependencies of a resonance field *H*<sup>R</sup> on the angles *θ*H and *ϕ*<sup>H</sup> for the garnet film and the Co layer are plotted in **Figures 7** and **8**, respectively. The existence of easy magnetization axes along the <111> directions for the garnet contributions was deduced by analyzing *H*R(*θ*H,*ϕ*H) (see **Figure 7(a,b)**). This result correlates well with the Faraday experi‐ ments for garnet film, shown in **Figure 4(b)**. For the 2-nm Co layer, the easy magnetization axis lies in the sample plane (see **Figure 8(a)**) and is also connected with the "easy plane" type of the magnetic anisotropy (**Figure 8(b)**). As observed before, the magnetic anisotropy of the YIG:Co has two contributions [18]: magnetocrystalline cubic and growth-induced uniaxial ones. Hence, a qualitative analysis of the FMR and magnetization curves gives rise to the following description of the magnetic anisotropy energy *E*A, which contains cubic, growthinduced and uniaxial anisotropies:

$$E\_A \left( \vec{M}\_{gumr}, \vec{M}\_{Co} \right) = K\_1 \left[ \left( m\_x m\_y \right)^2 + \left( m\_x m\_z \right)^2 + \left( m\_z m\_y \right)^2 \right] + K\_{eff}^{gumr} \sin^2 \theta + K\_{gf}^{Co} \sin^2 \theta\_M \tag{1}$$

**Figure 7.** The polar (for *ϕ*H = 0° and 45°) and azimuthal (for *θ*<sup>H</sup> = 90°) dependences of the resonance field *H*R for YIG:Co film. The dots are experimental values, and solid lines were fitted using Eq. (1).

where *M* → garnet and *M* → Co are the magnetization vectors for garnet and Co films, respectively; *K*<sup>C</sup> is the cubic anisotropy constant of garnet film; *mx*, *my*, and *mz* are the direction cosines of garnet magnetization vector along the principle crystallographic axes defined as *mx* = sin*θ*cos*ϕ, my* = sin*θ*sin*ϕ, mz* = cos*θ* (*θ* and *ϕ*are the polar and azimuthal angles of magnetization, respectively); *K*eff garnet is the effective growth-induced (uniaxial) anisotropy constant for the garnet film, *K*eff Co is the effective uniaxial anisotropy constant of the 2-nm Co layer defined by the polar angle *θ*M. The bulk value of the saturation magnetization 1420 G was assumed for the 2-nm Co thickness. The saturation magnetization was 7 G [17]. For each resonance line of YIG:Co and ultrathin Co films, the magnetic anisotropy constants were fitted using Eq. (1) and standard FMR conditions [35, 36]:

analyzing *H*R(*θ*H,*ϕ*H) (see **Figure 7(a,b)**). This result correlates well with the Faraday experi‐ ments for garnet film, shown in **Figure 4(b)**. For the 2-nm Co layer, the easy magnetization axis lies in the sample plane (see **Figure 8(a)**) and is also connected with the "easy plane" type of the magnetic anisotropy (**Figure 8(b)**). As observed before, the magnetic anisotropy of the YIG:Co has two contributions [18]: magnetocrystalline cubic and growth-induced uniaxial ones. Hence, a qualitative analysis of the FMR and magnetization curves gives rise to the following description of the magnetic anisotropy energy *E*A, which contains cubic, growth-

( ) ( ) ( ) ( ) 2 2 <sup>2</sup> 2 2 <sup>1</sup> , sin sin *garnet Co E M M K mm mm mm K K A garnet Co x y x z z y eff*

é ù = ++ + + ê ú ë û

**Figure 7.** The polar (for *ϕ*H = 0° and 45°) and azimuthal (for *θ*<sup>H</sup> = 90°) dependences of the resonance field *H*R for YIG:Co

is the cubic anisotropy constant of garnet film; *mx*, *my*, and *mz* are the direction cosines of garnet magnetization vector along the principle crystallographic axes defined as *mx* = sin*θ*cos*ϕ, my* =

Co are the magnetization vectors for garnet and Co films, respectively; *K*<sup>C</sup>

film. The dots are experimental values, and solid lines were fitted using Eq. (1).

where *M* →

garnet and *M*

→

r r (1)

q

 q*eff M*

induced and uniaxial anisotropies:

206 Magnetic Materials

$$f\_{FMR} = \frac{1}{2\pi} \frac{\gamma}{M \sin \theta} \left[ \frac{\hat{\sigma}^2 E\_A}{\hat{\sigma} \theta^2} \frac{\hat{\sigma}^2 E\_A}{\hat{\sigma} \varphi^2} - \left( \frac{\hat{\sigma}^2 E\_A}{\hat{\sigma} \theta \hat{\sigma} \varphi} \right)^2 \right]^{\frac{1}{2}} \tag{2}$$

**Figure 8.** The polar (for *ϕ*H = 0° and 45°) and azimuthal (for *θ*H =90°) dependences of the resonance field *H*R for 2-nm Co layer on YIG:Co film. The dots are experimental values, and the solid line was fitted using Eq. (1).

where *f*FMR is the FMR frequency. The equilibrium angles *θ* and *ϕ* of the magnetization can be found by the minimization of *EA* : *∂EA ∂θ* =0 and *∂EA <sup>∂</sup>* <sup>ϕ</sup> =0. The FMR frequency was *f*FMR = 9.5 GHz (Xband spectrometer). The gyromagnetic ratio of Co layer and garnet films is suggested to be equal to γCo = 1.76 × 106 Hz/Oe and γgarnet = 1.65 × 106 Hz/Oe, respectively. The gyromagnetic ratio values of Co and garnet films correspond to the factors *gCo*= 2 and *g*garnet ≈ 1.9, which are comparable to the previously reported experimental data for Co [35] and the similar garnet compositions [37, 38]. The reduction of *g*garnet can be explained in terms of Wangsness model for the two-sublattice ferrimagnet [39]. The first sublattice is produced by tetrahedral and octahedral Fe3+ ions for which the *g*-factor is close to two, while second one is formed by highspin octahedral Co2+ ions with *g* ≈ 2.9 [38]. As a result, oppositely directed sublattices lead to the reduction of the effective *g*-factor. Solid lines in **Figures 7** and **8** show the results of the fitting procedure.

Thus, let us analyze, step by step, the magnetic anisotropy constants of the Co layer and garnet films from FMR field and magnetization loops. First, for the Co layer deposited on the garnet film, the effective anisotropy constant is *K*eff Co = −9.9×10<sup>6</sup> erg/cm<sup>3</sup> that corresponds to the case of in-plane magnetic anisotropy in the Co layer. Second, from the part of FMR spectrum which corresponds to garnet films, the cubic KC = –2 × 103 erg/cm3 anisotropy contribution for garnet film was deduced from the fitting procedure. In the case of negative KC, four easy magnetiza‐ tion-axis orientations along a <111>-type of crystallographic direction to the sample plane in garnet films exist [39]. Third, cubic constants KC determined by FMR technique were used for the fitting of Faraday loops measured for garnet parts of a sample. Since the direction of magnetization at equilibrium corresponds to the minimum of *E*A(*M*garnet), the effective growthinduced anisotropy constant *K*eff garnet= *<sup>K</sup>*<sup>U</sup> garnet−2*πM*garnet <sup>2</sup> can be determined from the minimiza‐ tion of *E*A(*M*garnet) with respect to the polar angle *θ* of magnetization: ∂ *E*A(*M*garnet) <sup>∂</sup> *<sup>θ</sup>* =0. After separation of the demagnetization contribution from the uniaxial anisotropy, the anisotropy constant *K*<sup>U</sup> garnet=103 erg/cm<sup>3</sup> for 1.8-μm-thick garnet film was obtained [40].

#### **3.4. Magnetostatic interlayer coupling**

Here, we report on an influence of the 2-nm Co layer on both the domain structure geometry and magnetization reversal processes in the YIG:Co film. The period and shape of domains in Co/YIG:Co heterostructure are explained by competition of different energies. Taking into account the domain period in garnet film of order of 10 μm, the 20 × 20 μm Au/Co pattern is required for the observation of domain structure of garnet films under ultrathin Co layer [40], i.e., the size of pattern square is larger than domain period of garnet films. **Figure 9** shows the images of domain structure for patterned Co/garnet area recorded at *H*Z = 0 and *H*Z = 40 Oe, respectively.

Magnetization Statics and Ultrafast Photoinduced Dynamics in Co/garnet Heterostructures http://dx.doi.org/10.5772/62542 209

where *f*FMR is the FMR frequency. The equilibrium angles *θ* and *ϕ* of the magnetization can be

*∂EA*

band spectrometer). The gyromagnetic ratio of Co layer and garnet films is suggested to be

ratio values of Co and garnet films correspond to the factors *gCo*= 2 and *g*garnet ≈ 1.9, which are comparable to the previously reported experimental data for Co [35] and the similar garnet compositions [37, 38]. The reduction of *g*garnet can be explained in terms of Wangsness model for the two-sublattice ferrimagnet [39]. The first sublattice is produced by tetrahedral and octahedral Fe3+ ions for which the *g*-factor is close to two, while second one is formed by highspin octahedral Co2+ ions with *g* ≈ 2.9 [38]. As a result, oppositely directed sublattices lead to the reduction of the effective *g*-factor. Solid lines in **Figures 7** and **8** show the results of the

Thus, let us analyze, step by step, the magnetic anisotropy constants of the Co layer and garnet films from FMR field and magnetization loops. First, for the Co layer deposited on the garnet

in-plane magnetic anisotropy in the Co layer. Second, from the part of FMR spectrum which

film was deduced from the fitting procedure. In the case of negative KC, four easy magnetiza‐ tion-axis orientations along a <111>-type of crystallographic direction to the sample plane in garnet films exist [39]. Third, cubic constants KC determined by FMR technique were used for the fitting of Faraday loops measured for garnet parts of a sample. Since the direction of magnetization at equilibrium corresponds to the minimum of *E*A(*M*garnet), the effective growth-

garnet−2*πM*garnet

separation of the demagnetization contribution from the uniaxial anisotropy, the anisotropy

Here, we report on an influence of the 2-nm Co layer on both the domain structure geometry and magnetization reversal processes in the YIG:Co film. The period and shape of domains in Co/YIG:Co heterostructure are explained by competition of different energies. Taking into account the domain period in garnet film of order of 10 μm, the 20 × 20 μm Au/Co pattern is required for the observation of domain structure of garnet films under ultrathin Co layer [40], i.e., the size of pattern square is larger than domain period of garnet films. **Figure 9** shows the images of domain structure for patterned Co/garnet area recorded at *H*Z = 0 and *H*Z = 40 Oe,

for 1.8-μm-thick garnet film was obtained [40].

garnet= *<sup>K</sup>*<sup>U</sup>

tion of *E*A(*M*garnet) with respect to the polar angle *θ* of magnetization:

Co = −9.9×10<sup>6</sup>

*<sup>∂</sup>* <sup>ϕ</sup> =0. The FMR frequency was *f*FMR = 9.5 GHz (X-

Hz/Oe, respectively. The gyromagnetic

erg/cm<sup>3</sup> that corresponds to the case of

erg/cm3 anisotropy contribution for garnet

<sup>2</sup> can be determined from the minimiza‐

∂ *E*A(*M*garnet)

<sup>∂</sup> *<sup>θ</sup>* =0. After

*∂EA ∂θ* =0 and

Hz/Oe and γgarnet = 1.65 × 106

found by the minimization of *EA* :

film, the effective anisotropy constant is *K*eff

induced anisotropy constant *K*eff

garnet=103

**3.4. Magnetostatic interlayer coupling**

constant *K*<sup>U</sup>

respectively.

corresponds to garnet films, the cubic KC = –2 × 103

erg/cm<sup>3</sup>

equal to γCo = 1.76 × 106

208 Magnetic Materials

fitting procedure.

**Figure 9.** Images of magnetic domain structure in 2-nm Co/YIG:Co pattern area recorded at: (a) *H*Z = 0 and (b) *H*Z = 40 Oe. The image size is 140 × 130 μm.

In **Figure 9(a)**, both in garnet and Co/garnet (square areas) structures, stripe domain structures are observed. In this case, the period and the domain size in the Co/garnet structure is less than in the garnet film.

**Figure 10.** The hysteresis loops recorded for both bare YIG:Co (full points) and Co/YIG:Co (open points) films.

At *H*Z = 40 Oe, the domain structure was observed only at Co/garnet pattern (see **Figure 9(b)**). Moreover, the clear difference in the magnetization reversal process with and without the 2nm cover Co layer on garnet film was observed in the field range near the coercivity (see **Figure 10**). First, for Co/garnet heterostructure, we observe the reduced *θ*F value compared to the bare garnet film, i.e., the contribution of the hard axis from the Co/garnet interface to hysteresis loop is found. Second, the value of the reversal magnetic collapse field is noticeably increasing from 40 to 55 Oe. In **Figure 9(b)**, the presence of Co/garnet domains on a monodomain background garnet area is well visible. In this case, the extra energy is required to switch the in-plane interfacial magnetic moment in the garnet film. For these reasons, the strong in-plane magnetic anisotropy of the ultrathin Co layer induces significant stray field on the garnet surface. Therefore, for the Co/garnet heterostructure, reduction of the domain period occurs as a consequence of decreasing the magnetostatic energy.

## **4. Ultrafast magnetization dynamics induced by femtosecond laser pulses in a Co/garnet heterostructure**

We present the results of a study of ultrafast photoinduced magnetization dynamics in Co/ YIG:Co heterostructures via the excitation of photomagnetic anisotropy [19, 20]. This aniso‐ tropy is related to an optically induced charge transfer between the anisotropic Co2+ and Co3+ ions on tetrahedral sites in the garnet lattice. The deposition of ultrathin Co layer on garnet film can result in a new type of magnetization dynamics due to the influence of the effective magnetic field of the Co layer and/or the magnetic coupling between the metallic layer and garnet film.

## **4.1. Time-resolved magneto-optical tools**

To investigate the ultrafast magnetization dynamics in both bare YIG:Co film and Co/YIG:Co heterostructure induced by femtosecond laser pulses, we carried out time-resolved measure‐ ments at room temperature using a conventional magneto-optical pump-probe method. Pump pulses with a duration of 35 fs from an amplifier (Spitfire Ace, Spectra-Physics) at a 500 Hz repetition rate were directed at an angle of incidence about 10° from the sample normal parallel to the [001] crystallographic axis of the sample, while the probe pulses at a 1 kHz repetition rate of the pump were incident along the sample normal, see **Figure 11**. A pump beam with a wavelength of 800 nm and energy of 2 μJ was focused onto a spot about 100 μm in diameter on the sample. The pump energy was relatively small in order to not heat significantly the metallic layers of Au and Co. The sample was excited by the pump through the Co side of the bilayer. A probe beam with a wavelength of 800 nm was about two times smaller in size and the energy than the pump. The parameter of delay time *Δt* (see **Figure 1**) between the pump and the probe pulses could be adjusted up to 1.3 ns. The linear polarization of the pump beam was defined by angle *φ* to the [100] axis. The amplitude of the magnetization precession was maximal when the polarization plane of the pump was along [100] or [010] axes. On the contrary, the polarization of the probe beam was along the [1–10] axis.

**Figure 11.** Sample configuration and the experimental geometry with the external magnetic field *H* applied with angle *θ*H = 65° .

In this experimental geometry, we measured the Faraday rotation angle *θ*F of the probe as a function of the delay time *Δt* between the pump and probe pulses. The rotation *θ*F(*Δt*) is proportional to the out-of-plane component of the magnetization *M*Z. An external magnetic field *H* up to 5 kOe was applied along the (1–10)plane at *θ*<sup>H</sup> = 65° with respect to the sample normal. At the same time, *H* was above domain collapse field, so that a coherent spin dynamics without domain structure was investigated.

#### **4.2. Spin precession modulation**

nm cover Co layer on garnet film was observed in the field range near the coercivity (see **Figure 10**). First, for Co/garnet heterostructure, we observe the reduced *θ*F value compared to the bare garnet film, i.e., the contribution of the hard axis from the Co/garnet interface to hysteresis loop is found. Second, the value of the reversal magnetic collapse field is noticeably increasing from 40 to 55 Oe. In **Figure 9(b)**, the presence of Co/garnet domains on a monodomain background garnet area is well visible. In this case, the extra energy is required to switch the in-plane interfacial magnetic moment in the garnet film. For these reasons, the strong in-plane magnetic anisotropy of the ultrathin Co layer induces significant stray field on the garnet surface. Therefore, for the Co/garnet heterostructure, reduction of the domain period occurs

**4. Ultrafast magnetization dynamics induced by femtosecond laser pulses**

We present the results of a study of ultrafast photoinduced magnetization dynamics in Co/ YIG:Co heterostructures via the excitation of photomagnetic anisotropy [19, 20]. This aniso‐ tropy is related to an optically induced charge transfer between the anisotropic Co2+ and Co3+ ions on tetrahedral sites in the garnet lattice. The deposition of ultrathin Co layer on garnet film can result in a new type of magnetization dynamics due to the influence of the effective magnetic field of the Co layer and/or the magnetic coupling between the metallic layer and

To investigate the ultrafast magnetization dynamics in both bare YIG:Co film and Co/YIG:Co heterostructure induced by femtosecond laser pulses, we carried out time-resolved measure‐ ments at room temperature using a conventional magneto-optical pump-probe method. Pump pulses with a duration of 35 fs from an amplifier (Spitfire Ace, Spectra-Physics) at a 500 Hz

to the [001] crystallographic axis of the sample, while the probe pulses at a 1 kHz repetition rate of the pump were incident along the sample normal, see **Figure 11**. A pump beam with a wavelength of 800 nm and energy of 2 μJ was focused onto a spot about 100 μm in diameter on the sample. The pump energy was relatively small in order to not heat significantly the metallic layers of Au and Co. The sample was excited by the pump through the Co side of the bilayer. A probe beam with a wavelength of 800 nm was about two times smaller in size and the energy than the pump. The parameter of delay time *Δt* (see **Figure 1**) between the pump and the probe pulses could be adjusted up to 1.3 ns. The linear polarization of the pump beam was defined by angle *φ* to the [100] axis. The amplitude of the magnetization precession was maximal when the polarization plane of the pump was along [100] or [010] axes. On the

from the sample normal parallel

as a consequence of decreasing the magnetostatic energy.

**in a Co/garnet heterostructure**

**4.1. Time-resolved magneto-optical tools**

repetition rate were directed at an angle of incidence about 10°

contrary, the polarization of the probe beam was along the [1–10] axis.

garnet film.

210 Magnetic Materials

The experimental results presented below were obtained on 2-nm Co/YIG:Co heterostructure, in which strong magnetostatic interlayer coupling has been found. **Figure 12** shows the magnetization precession (angle of Faraday rotation) as a function of the delay time *Δt* for different values of the amplitude of the external magnetic field with angle *θ*H = 65° . We expect that the magnetization dynamics corresponds to a precession of the Co and garnet moments around the effective field. For a relatively small external magnetic field, one can find a slow oscillation with a main single frequency of 4.2 GHz, see **Figure 12(a)**, corresponding to the garnet film [41]. We observe periodic oscillation modulated by a higher-frequency oscillation in **Figure 12(b)**. Fast Fourier transforms (FFTs) were taken for these dependences, and the resulting power spectra confirm the presence of two different oscillation frequencies *f1* and *f2* (see **Figure 12(b)**). Both of these frequencies increase with increasing amplitude of the external magnetic field. However, we observed a main single higher oscillation frequency for the external magnetic field above 4 kOe (see **Figure 12(c)**). The Faraday rotation transients for varying external magnetic field *H* were fitted (**Figure 12**) with two damped sine contributions:

$$\partial\_F \left( \Delta t \right) = A\_l \exp \left( \frac{-\Delta t}{\tau\_1} \right) \sin \left( 2\pi f\_l \Delta t + \phi\_l \right) + A\_2 \exp \left( \frac{-\Delta t}{\tau\_2} \right) \sin \left( 2\pi f\_2 \Delta t + \phi\_2 \right) \tag{3}$$

**Figure 12.** Time-resolved Faraday rotation as a function of the delay time *Δt* for (a) *H* = 1.47 kOe, (b) 2.31 kOe, and (c) 4.22 kOe. The red solid lines were fitted using FFT analysis and Eq. (3). The right panel—the FFT spectra.

where *τ*i is the time decay, *A*<sup>i</sup> the amplitude, and *φ*<sup>i</sup> the phase. The fitted curves using FFT analysis and Eq. (3) are in good agreement with the experimental data (see **Figure 12**).

**Figure 13.** Dependence of the magnetization component *M*<sup>Z</sup> on the amplitude of external field *H* for the garnet and Co layer.

From the experimental curves, we deduced amplitudes of the oscillations using fitting by Eq. (3). It is clearly seen that upon increasing *H*, the contribution from the garnet vanishes so that at the field above 4 kOe, the contribution from the Co layer dominates (see **Figure 13**). The dependence of perpendicular component of the magnetization *M*<sup>Z</sup> is proportional to the Faraday rotation *θ*F.

**Figure 12.** Time-resolved Faraday rotation as a function of the delay time *Δt* for (a) *H* = 1.47 kOe, (b) 2.31 kOe, and (c)

**Figure 13.** Dependence of the magnetization component *M*<sup>Z</sup> on the amplitude of external field *H* for the garnet and Co

the phase. The fitted curves using FFT

4.22 kOe. The red solid lines were fitted using FFT analysis and Eq. (3). The right panel—the FFT spectra.

the amplitude, and *φ*<sup>i</sup>

analysis and Eq. (3) are in good agreement with the experimental data (see **Figure 12**).

where *τ*i is the time decay, *A*<sup>i</sup>

212 Magnetic Materials

layer.

**Figure 14.** (a) Dependence of the frequency of magnetization precession on a function of magnetic field amplitude *H* for garnet (full points) and Co (open points) films of a heterostructure. The calculated FMR frequency dependences are shown using both Eqs. (1) and (2) with magnetic anisotropy constants (solid lines). The measured FMR data are shown as stars. (b) Calculation of magnetization orientation *θ*M as a function of the amplitude of *H* for YIG:Co film and 2-nm Co layer.

**Figure 14(a)** plots the frequencies *f*1 and *f*2 obtained from experimental data for different values of the *H*. The dashed line is determined by the FMR frequency where the resonance field values for Co and garnet films are located (stars). To compare obtained frequencies, we calculated the FMR frequency as a function of the external magnetic field with angle *θ*H = 65° in both the cobalt and garnet films using a typical FMR equation [35], considering constants of the magnetic anisotropy of the 2-nm Co and 1.8 μm garnet film. The frequencies *f*1 and *f*<sup>2</sup> differing by about a factor of two correspond to the precession of the magnetization excited in garnet and Co films, respectively. We see from **Figure 14(a)** that the experimental magneto-optical response data (points) agree well with the measured FMR results with single 9.5 GHz frequency (stars) and calculated FMR frequency (solid lines) for both contributions in the bilayer using Eq. (2).

Such a layer selective probing of the magnetization dynamics can be understood by a simple phenomenological model. The equilibrium state of magnetization vector at the Co/YIG:Co heterostructure could be found using the phenomenological model of magnetic anisotropy (Eq. (1)) after minimizing the total energy including energies of the magnetic anisotropies, the Zeeman at external magnetic field, and the demagnetization. **Figure 14(b)** shows the depend‐ ence of magnetization angle *θ*M, on an external magnetic field *H* for both Co and garnet films. According the Faraday configuration, the polarization rotation of the probe beam was proportional to the perpendicular magnetization component along [001] axis at the garnet (see **Figure 11**). Thus, *θ*<sup>F</sup> is proportional to the amplitude of the magnetization precession. During increasing *θ*M, we observed increasing the amplitude of the magnetization precession. A quantitative analysis of dependences of the angle on the external magnetic field shows the possibility of the excitation of magnetization precession at two regimes: first, at low magnetic field below 1 kOe, the amplitude of magnetization precession dominates at the garnet film due to the large angle between magnetic field *H* and magnetization of garnet *M*garnet and small perpendicular magnetization component of cobalt *M*Co; second, at high magnetic field above 4 kOe, the amplitude of magnetization precession is dominated at the Co film with the significant perpendicular component *M*Co when the magnetization vector *M*garnet is close to *H*.

**Figure 15.** Graphical illustration of the precessional dynamics for: (a) *H* < 1.5 kOe, (b) 1.5 < *H* < 4.3 kOe, and (c) *H* > 4.3 kOe.

We can conclude that we observe three types of magnetization precession in the bilayer: (i) mainly single-frequency precession (1–5 GHz) from the garnet for *H* < 1.5 kOe, (ii) a double frequency to modulated signal for 1.5 < *H* < 4.3 kOe, and (iii) mainly single-frequency preces‐ sion (>20 GHz) from the cobalt film for *H* > 4.3 kOe (see the graphical illustration of the precessional dynamics in **Figure 15**).

#### **4.3. Laser-induced phase-sensitive magnetization precession**

**Figure 14(a)** plots the frequencies *f*1 and *f*2 obtained from experimental data for different values of the *H*. The dashed line is determined by the FMR frequency where the resonance field values for Co and garnet films are located (stars). To compare obtained frequencies, we calculated the FMR frequency as a function of the external magnetic field with angle *θ*H = 65° in both the cobalt and garnet films using a typical FMR equation [35], considering constants of the magnetic anisotropy of the 2-nm Co and 1.8 μm garnet film. The frequencies *f*1 and *f*<sup>2</sup> differing by about a factor of two correspond to the precession of the magnetization excited in garnet and Co films, respectively. We see from **Figure 14(a)** that the experimental magneto-optical response data (points) agree well with the measured FMR results with single 9.5 GHz frequency (stars) and calculated FMR frequency (solid lines) for both contributions in the bilayer using Eq. (2).

Such a layer selective probing of the magnetization dynamics can be understood by a simple phenomenological model. The equilibrium state of magnetization vector at the Co/YIG:Co heterostructure could be found using the phenomenological model of magnetic anisotropy (Eq. (1)) after minimizing the total energy including energies of the magnetic anisotropies, the Zeeman at external magnetic field, and the demagnetization. **Figure 14(b)** shows the depend‐ ence of magnetization angle *θ*M, on an external magnetic field *H* for both Co and garnet films. According the Faraday configuration, the polarization rotation of the probe beam was proportional to the perpendicular magnetization component along [001] axis at the garnet (see **Figure 11**). Thus, *θ*<sup>F</sup> is proportional to the amplitude of the magnetization precession. During increasing *θ*M, we observed increasing the amplitude of the magnetization precession. A quantitative analysis of dependences of the angle on the external magnetic field shows the possibility of the excitation of magnetization precession at two regimes: first, at low magnetic field below 1 kOe, the amplitude of magnetization precession dominates at the garnet film due to the large angle between magnetic field *H* and magnetization of garnet *M*garnet and small perpendicular magnetization component of cobalt *M*Co; second, at high magnetic field above 4 kOe, the amplitude of magnetization precession is dominated at the Co film with the significant perpendicular component *M*Co when the magnetization vector *M*garnet is close to *H*.

**Figure 15.** Graphical illustration of the precessional dynamics for: (a) *H* < 1.5 kOe, (b) 1.5 < *H* < 4.3 kOe, and (c) *H* > 4.3

kOe.

214 Magnetic Materials

In this part, we compare magnetization dynamics in the Co and bare garnet films separately via selective probing and show that magnetization precession in the garnet can be manipulated by magnetostatic interlayer coupling.

**Figure 16.** Time-resolved Faraday rotation of the Co/garnet heterostructure as a function of the delay time ∆*t* for differ‐ ent (a) magnetic field amplitude and (b) pump polarization. Solid line was fitted using the classical oscillation function including damping for a 2-nm Co layer on a garnet film.

A rather unique combination of magnetic properties of the layers allows us to realize different regimes of the laser-induced dynamics. Changing the strength of the out-of-plane *H*, we were able to obtain conditions when the magnetization dynamics was dominated either by the Co or the garnet layer. As discussed in the previous part, for *H* < 1 kOe photoinduced dynamics of Co/garnet, the heterostructure is dominated by the magnetization precession of the garnet film, while at *H* > 4 kOe, the magnetization precession results from the Co layer. Time dependence of the *z*-component of the magnetization precession was on the function of the external magnetic field *H* and the angle of polarization plane of the pump beam. **Figure 16(a)** shows the magnetization precession curves measured at *H* = 1.5 kOe, 2.3 kOe, and 4.6 kOe for *φ* = 0o . The laser-excited precessions of the magnetizations at two different frequencies are deduced from **Figure 14** as FMR frequencies in both the Co and the garnet films.

**Figure 17.** Graphical illustration of an ultrafast demagnetization dynamics in a 2-nm Co layer for (a) *Δt* < 0, (b) 0 <*Δt* <*tw* (pulse duration), and (c) *Δt* > *tw*.

The photoinduced magnetization precession for different pump beam polarizations at an external magnetic field with 4.6 kOe is shown in **Figure 16(b)**. These curves demonstrate no polarization dependence of the magnetization precession [42]. For such metallic ferromagnets, the ultrafast light-induced demagnetization is typical [43, 44]. The thermal demagnetization is seen as a sub-picosecond change of the magneto-optical signal measured at *H* = 4.6 kOe. The observed light-induced magnetization dynamics is a result of temperature increase of electron system on femtosecond timescale and a subsequent ultrafast reduction of *M*Co [45], which effectively change the equilibrium orientation of the magnetization in this layer and thus triggers spin oscillations (see the graphical illustration in **Figure 17**).

To study the influence of the Co film on the ultrafast magnetization dynamics at the garnet film, the time-resolved Faraday measurements at low-field regime below 1 kOe were per‐ formed [42]. In this case, the amplitude of magnetization precession at YIG:Co film always dominates that of the Co film (see **Figure 13**). First, we measured the laser-induced magneti‐ zation dynamics in a bare garnet film. **Figure 18(a)** shows that changing the polarization of the pump induces a shift of the phase of the precession *Δψ* = 120o in the bare garnet film. In this case, the decay coefficient of photoinduced anisotropy is *τ*g ~ 20 ps. In case of the deposition of the 2-nm Co film on this garnet film, the polarization sensitivity of the magnetization precession disappears. The polarization angles of pump beam with *φ* = 0 and 90o trigger magnetization precession in YIG:Co with the same phase (*Δψ* ≈ 0), see **Figure 18(b)**. The time of relaxation of magnetization precession after pump pulse is *τ*c ~ 60 ps. This value is enlarged due to the influence of light-induced demagnetization at Co layer. The magnetization dynam‐ ics triggered in YIG:Co film and the Co/YIG:Co heterostructure with the same polarization of the pump light are clearly different. However, the frequencies of these precessions are similar.

A rather unique combination of magnetic properties of the layers allows us to realize different regimes of the laser-induced dynamics. Changing the strength of the out-of-plane *H*, we were able to obtain conditions when the magnetization dynamics was dominated either by the Co or the garnet layer. As discussed in the previous part, for *H* < 1 kOe photoinduced dynamics of Co/garnet, the heterostructure is dominated by the magnetization precession of the garnet film, while at *H* > 4 kOe, the magnetization precession results from the Co layer. Time dependence of the *z*-component of the magnetization precession was on the function of the external magnetic field *H* and the angle of polarization plane of the pump beam. **Figure 16(a)** shows the magnetization precession curves measured at *H* = 1.5 kOe, 2.3 kOe, and 4.6

are deduced from **Figure 14** as FMR frequencies in both the Co and the garnet films.

**Figure 17.** Graphical illustration of an ultrafast demagnetization dynamics in a 2-nm Co layer for (a) *Δt* < 0, (b) 0 <*Δt*

The photoinduced magnetization precession for different pump beam polarizations at an external magnetic field with 4.6 kOe is shown in **Figure 16(b)**. These curves demonstrate no polarization dependence of the magnetization precession [42]. For such metallic ferromagnets, the ultrafast light-induced demagnetization is typical [43, 44]. The thermal demagnetization is seen as a sub-picosecond change of the magneto-optical signal measured at *H* = 4.6 kOe. The observed light-induced magnetization dynamics is a result of temperature increase of electron system on femtosecond timescale and a subsequent ultrafast reduction of *M*Co [45], which effectively change the equilibrium orientation of the magnetization in this layer and thus

To study the influence of the Co film on the ultrafast magnetization dynamics at the garnet film, the time-resolved Faraday measurements at low-field regime below 1 kOe were per‐ formed [42]. In this case, the amplitude of magnetization precession at YIG:Co film always dominates that of the Co film (see **Figure 13**). First, we measured the laser-induced magneti‐ zation dynamics in a bare garnet film. **Figure 18(a)** shows that changing the polarization of the pump induces a shift of the phase of the precession *Δψ* = 120o in the bare garnet film. In this case, the decay coefficient of photoinduced anisotropy is *τ*g ~ 20 ps. In case of the deposition

triggers spin oscillations (see the graphical illustration in **Figure 17**).

. The laser-excited precessions of the magnetizations at two different frequencies

kOe for *φ* = 0o

216 Magnetic Materials

<*tw* (pulse duration), and (c) *Δt* > *tw*.

**Figure 18.** Time-resolved Faraday rotation of (a) bare garnet and (b) Co/garnet films as a function of the delay time *Δt* for *H*(*θ*H = 65°) = 0.75 kOe and different pump polarization *φ*. Dashed lines were fitted using the exponential function with decay coefficients *τ*L.

The laser excitation of Co/YIG:Co heterostructure leads to both an thermal demagnetization at Co film and a photomagnetic effect at the garnet [20]. These effects induced changing the magnetization orientation given by the effective field *H*eff in the heterostructure (see **Figure 17**). In this case, ultrafast change triggers the precession of the magnetization vector around the new orientation *H*\* eff (see **Figure 17(c)**). In YIG:Co, the polarization-dependent excitation with different initial phase of magnetization precession leads to a photoinduced magnetic anisotropy [19]. However, in our heterostructure, the phase of magnetization precession is defined by both the effective anisotropy (magnetocrystalline, uniaxial, and photoinduced) field and the stray field from 2-nm Co film (the magnetization of cobalt is significant larger than the magnetization of garnet). The magnetostatic coupling between Co and YIG:Co films leads to a change in the phase of magnetization precession in YIG:Co film. Thus in hetero‐ structure, the magnetization is precessed around the effective magnetic field with the isotropic in-plane component due to the "easy plane" of magnetic anisotropy of Co film.

## **5. Conclusion**

In this chapter, we have presented the experimental investigation of ultrathin Co/garnet heterostructure by using time-resolved pump-probe magneto-optical spectroscopy in combi‐ nation with linear magneto-optical Faraday and Kerr effects and ferromagnetic resonance. Ion beam processing procedure for preparation of Au/Co/garnet heterostructure with a subnanometer roughness parameter at the interface has been proposed. It was found that Gilbert damping of the ultrathin Co layers on the garnet surfaces is comparable to the damping of high-quality single and polycrystalline Co layers grown on metallic underlayers. We showed that the magnetic and magneto-optical properties of Co/garnet heterostructures can be engineered by covering the ultrathin Co layer. In particular, a strong magnetostatic interlayer coupling between the 2-nm Co layer and YIG:Co film has been found. In addition, the modification of the domain structure due to the magnetostatic coupling has been demonstrat‐ ed. In principle, depositing ultrathin ferromagnetic layers on a garnet film can also lead to new effects in magnetization dynamics, due to the influence of the effective magnetic field of the ferromagnetic layer and/or the coupling between ferromagnetic layer and garnet.

The growth of a 2-nm Co layer on top of the garnet significantly changes the mechanism of the laser-induced precession in the heterostructure. We observed the modulation of spin precession in a Co/garnet heterostructure with distinct frequencies. The excitation efficiency of these precessions strongly depends on the amplitude and orientation of external magnetic field. In addition, we demonstrate that the laser pulse triggers polarization-independent precession in both the Co and garnet layers via the magnetostatic coupling between these layers.

These results demonstrate that magnetic metal/dielectric heterostructures are interesting and promising objects for further investigations of all-optical ultrafast light-induced phenomena and their potential applications.

## **Acknowledgements**

This work was supported by the National Science Centre Poland for OPUS project DEC-2013/09/B/ST3/02669. The author would like to acknowledge the contributions of M. Pashkevich for measurements and A. Stognij for heterostructures preparation. The author is grateful to M. Tekielak, R. Gieniusz, A. Maziewski, A. Kirilyuk, A. Kimel, and T. Rasing for fruitful discussions and research support.

## **Author details**

anisotropy [19]. However, in our heterostructure, the phase of magnetization precession is defined by both the effective anisotropy (magnetocrystalline, uniaxial, and photoinduced) field and the stray field from 2-nm Co film (the magnetization of cobalt is significant larger than the magnetization of garnet). The magnetostatic coupling between Co and YIG:Co films leads to a change in the phase of magnetization precession in YIG:Co film. Thus in hetero‐ structure, the magnetization is precessed around the effective magnetic field with the isotropic

In this chapter, we have presented the experimental investigation of ultrathin Co/garnet heterostructure by using time-resolved pump-probe magneto-optical spectroscopy in combi‐ nation with linear magneto-optical Faraday and Kerr effects and ferromagnetic resonance. Ion beam processing procedure for preparation of Au/Co/garnet heterostructure with a subnanometer roughness parameter at the interface has been proposed. It was found that Gilbert damping of the ultrathin Co layers on the garnet surfaces is comparable to the damping of high-quality single and polycrystalline Co layers grown on metallic underlayers. We showed that the magnetic and magneto-optical properties of Co/garnet heterostructures can be engineered by covering the ultrathin Co layer. In particular, a strong magnetostatic interlayer coupling between the 2-nm Co layer and YIG:Co film has been found. In addition, the modification of the domain structure due to the magnetostatic coupling has been demonstrat‐ ed. In principle, depositing ultrathin ferromagnetic layers on a garnet film can also lead to new effects in magnetization dynamics, due to the influence of the effective magnetic field of the

in-plane component due to the "easy plane" of magnetic anisotropy of Co film.

ferromagnetic layer and/or the coupling between ferromagnetic layer and garnet.

The growth of a 2-nm Co layer on top of the garnet significantly changes the mechanism of the laser-induced precession in the heterostructure. We observed the modulation of spin precession in a Co/garnet heterostructure with distinct frequencies. The excitation efficiency of these precessions strongly depends on the amplitude and orientation of external magnetic field. In addition, we demonstrate that the laser pulse triggers polarization-independent precession in both the Co and garnet layers via the magnetostatic coupling between these

These results demonstrate that magnetic metal/dielectric heterostructures are interesting and promising objects for further investigations of all-optical ultrafast light-induced phenomena

This work was supported by the National Science Centre Poland for OPUS project DEC-2013/09/B/ST3/02669. The author would like to acknowledge the contributions of M. Pashkevich for measurements and A. Stognij for heterostructures preparation. The author is

**5. Conclusion**

218 Magnetic Materials

layers.

and their potential applications.

**Acknowledgements**

Andrzej Stupakiewicz

Address all correspondence to: and@uwb.edu.pl

Laboratory of Magnetism, Faculty of Physics, University of Bialystok, Bialystok, Poland

## **References**


[23] I. G. Brown. The Physics and Technology of Ion Sources. NewYork: Wiley; 2004.

[9] S. Parchenko, A. Stupakiewicz, I. Yoshimine, T. Satoh, and A. Maziewski. Wide frequencies range of spin excitations in a rare-earth Bi-doped iron garnet with a giant

[10] S.O. Demokritov, V.E. Demidov, O. Dzyapko, G.A. Melkov, A.A. Serga, B. Hillebrands, A.N. Slavin. Bose–Einstein condensation of quasi-equilibrium magnons at room

[11] A.B. Chizhik, I.I. Davidenko, A. Maziewski, A. Stupakiewicz. High-temperature photomagnetism in Co-doped yttrium iron garnet films. Phys. Rev. B. 1998;57:14366.

[12] F. Hansteen, A. V. Kimel, A. Kirilyuk, and Th. Rasing. Femtosecond Photomagnetic Switching of Spins in Ferrimagnetic Garnet Films. Phys. Rev. Lett.. 2005;95:047402.

[13] A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Balbashov and Th. Rasing. Ultrafast non-thermal control of magnetization by instantaneous photomagnetic

[14] S. Parchenko, T. Satoh, I. Yoshimine, F. Stobiecki, A. Maziewski, and A. Stupakiewicz. Non-thermal optical excitation of terahertz-spin precession in a magneto-optical

[15] Y. S. Chun and Kannan M. Krishnan. Interlayer perpendicular domain coupling between thin Fe films and garnet single-crystal underlayers. J. Appl. Phys..

[16] N. Vukadinovic, J. Ben Youssef, V. Castel, M. Labrune. Magnetization dynamics in interlayer exchange-coupled in-plane/out-of-plane anisotropy bilayers. Phys. Rev. B.

[17] A. Maziewski. Unexpected magnetization processes in YIG+Co films. J. Magn. Magn.

[18] M. Tekielak, A. Stupakiewicz, A. Maziewski and J. M. Desvignes. Temperature induced phase transitions in Co-doped YIG films. J. Magn. Magn. Mater. 2003;254–255:562.

[19] A. Stupakiewicz, A. Maziewski, I. Davidenko, and V. Zablotskii. Light-induced magnetic anisotropy in Co-doped garnet films. Phys. Rev. B.. 2001;64:064405.

[20] F. Atoneche, A.M. Kalashnikova, A.V. Kimel, A. Stupakiewicz, A. Maziewski, A. Kirilyuk, and Th. Rasing. Large ultrafast photoinduced magnetic anisotropy in a cobalt-

[21] G. Woltersdorf, O. Mosendz, B. Heinrich and C.H. Back. Magnetization Dynamics due to Pure Spin Currents in Magnetic Double Layers. Phys. Rev. Lett.. 2007;99:246603.

[22] L. Le Guyader, A. Kleibert, F. Nolting, L. Joly, P. M. Derlet, R. V. Pisarev, A. Kirilyuk, Th. Rasing and A. V. Kimel. Dynamics of laser-induced spin reorientation in Co/

substituted yttrium iron garnet. Phys. Rev. B. 2010;81:214440.

SmFeO3 heterostructure. Phys. Rev. B. 2013;87:054437.

Faraday rotation. Appl. Phys. Lett.. 2013;103:172402.

temperature under pumping. Nature. 2006;443:430.

pulses. Nature. 2005;435:655.

2004;95:6858.

220 Magnetic Materials

2009;79:184405.

Mater.. 1990;88:325.

insulator. Appl. Phys. Lett.. 2016;108:032404.


## **Chapter 10**

## **Magnetic Micro-Origami**

Leszek Malkinski and Rahmatollah Eskandari

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64293

#### **Abstract**

[38] M. Maryško, P. Grnert and J. Pačes. Magnetic Properties of Cobalt-Doped YIG Films

[40] M. Pashkevich, A. Stupakiewicz, A. Kirilyuk, A. Maziewski, A. Stognij, N. Novitskii, A. Kimel, Th. Rasing. Tunable magnetic properties in ultrathin Co/garnet heterostruc‐

[41] A. Stupakiewicz, M. Pashkevich, A. Maziewski, A. Stognij, N. Novitskii. Spin preces‐ sion modulation in a magnetic bilayer. Appl. Phys. Lett.. 2012;101:262406.

[42] M. Pashkevich, A. Stupakiewicz, A. Kimel, A. Kirilyuk, A. Stognij, N. Novitskii, A. Maziewski and Th. Rasing. Laser-induced magnetization dynamics in a cobalt/garnet

[43] J.-Y. Bigot, M. Vomir, L. H. F. Andrade, E. Beaurepaire. Ultrafast magnetization dynamics in ferromagnetic cobalt: The role of the anisotropy. Chem. Phys..

[44] M. Vomir, L. H. F. Andrade, L. Guidoni, E. Beaurepaire, and J.-Y. Bigot. Real Space Trajectory of the Ultrafast Magnetization Dynamics in Ferromagnetic Metals. Phys.

[45] J. Kisielewski, A. Kirilyuk, A. Stupakiewicz, A. Maziewski, A. Kimel, Th. Rasing, L.T. Baczewski, and A. Wawro. Laser-induced manipulation of magnetic anisotropy and magnetization precession in an ultrathin cobalt wedge. Phys. Rev. B. 2012;85:184429.

Compensated by Ge4+ and Ti4+. Phys. Stat. Sol. A. 1991;123:303.

tures. J. Appl. Phys.. 2012;111:023913.

2005;318:137.

222 Magnetic Materials

Rev. Lett.. 2005;94:237601.

heterostructure. Europhys. Lett.. 2014;105:27006.

[39] G. Winkler. Magnetic Garnets. Braunschweig: Friedr. Vieweg & Sohn; 1981.

Microscopic origami figures can be created from thin film patterns using surface tension of liquids or residual stresses in thin films. The curvature of the structures, direction of bending, twisting, and folding of the patterns can be controlled by their shape, thickness, and elastic properties and by the strength of the residual stresses. Magnetic materials used for micro- and nano-origami structures play an essential role in many applica‐ tions. Magnetic force due to applied magnetic field can be used for remote actuation of microrobots. It can also be used in targeted drug delivery to direct cages loaded with drugs or microswimmers to transport drugs to specific organs. Magnetoelastic properties of free-standing micro-origami patterns can serve for stress or magnetic field sensing. Also, the stress-induced anisotropy and magnetic shape anisotropy provide a convenient method of tuning magnetic properties by designing a shape of the microorigami figures instead of varying the composition of the films. Micro-origami figures can also serve as building blocks for two- and three-dimensional meta-materials with unique properties such as negative index of refraction. Micro-origami techniques provide a powerful method of self-assembly of magnetic circuits and integrating them with microelectro-mechanical systems or other functional devices.

**Keywords:** micro-origami, nano-origami, self-assembly, self-rolling, magnetic micro‐ tubes, thin film patterns, magnetic thin films, magnetic anisotropy, residual stresses, magnetoelastic effects, magnetoelectric effects, multiferroic composites

## **1. Introduction to origami and micro-origami**

The meaning of the Japanese name "origami" is paper folding. Although the techniques of paper folding were developed in Europe and China in seventeenth and eighteenth centuries, they became the most popular in Japan. There is a vast literature on the history and practical instructions for assembly of three-dimensional objects from pieces of paper by folding [1, 2].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Origamiisprimarilyanartbutithas alsoanimpactontechnology.Theorigamitechniqueswere implemented in satellite solar cells, airbag design, and stent implants [3]. Currently, mathe‐ matical [4] and computer models such as TreeMaker [5] allow designing complex threedimensional structures fordecorativearts,aswellas technologicalapplications.Some examples of origami figures are presented in **Figure 1** [6].

**Figure 1.** Various origami figures (reproduced from Ref. [6]).

The traditional origami methods rely on folding a single rectangular piece of paper by hand. More advanced techniques take advantage of using tools, such as bone folder, clips, or tweezers. More complex designs require cutting the paper into various patterns (different from rectangle), coloring them, combining with other materials (e.g., aluminum foil), and using multiple pieces of paper, which is called a modular origami. In contrast to static designs, some origami patterns can possess movable parts, which can be activated by kinetic energy of human's hand or inflation [7]. Another interesting trend in origami is tessellation of the figures, which is in fact a method of assembly of larger figures from building origami blocks [8].

The smallest origami figures were made from the paper pieces as small as 1 mm2 , using a needle and optical microscope. At this point a question arises whether we can do even smaller microorigami figures and use them to advance technology? The answer is "yes." It is possible to fabricate origami figures with features as small as 2 nm, actuate them, and assemble them into meta-materials. The submillimeter or submicrometer figures made from different materials using origami techniques are called micro- or nano-origami, respectively. A list of examples of applications of origami and micro-origami include bendable microelectronics, cell origami, origami nanorobot, pollen origami, origami lens, origami DNA, self-deployable origami stent, etc.

The materials used for micro- and nano-origami must be much thinner and tougher than conventional paper. Good candidates are thin foils and thin films. Although, in principle, it is possible to use nanomanipulators and nanotweezers to bend and fold these materials, to make individual figures in microscale, this does not seem to be a practical approach for a mass production of various devices. Instead, other forces can be used which emerge at micro- and nanoscale. Adhesion forces, surface tension, or interfacial stresses start playing important roles when the size of the figures decreases below several micrometers [9].

Different materials and phenomena can be used for self-assembly and animation or actuation of origami figures. For example, shape memory alloys or polymers undergo significant deformations when heated by contact or radiation [10–13], capillary forces can deform paper structures [14], photosensitive polymers deform when exposed to laser light [15], and internal stresses produce deformations when the structure is released from the substrate.

Some of these forces can be used to create the micro-origami figures, while others can be used to produce motion of already formed structures. The microrobots made from stimuli-respon‐ sive materials can move, walk, or swim. These functions are especially useful in biomedical applications [16–22]. Magnetostrictive and multiferroic materials take a special place among the stimuli-responsive materials, because they couple magnetic, elastic, and electronic properties of the materials.

Currently demonstrated functional robots [21] have size of the order of centimeters, but biomedical applications require devices with dimensions smaller by at least two orders of magnitude. They should be made from thin films with submicrometer or nanometer thickness. Even the thinnest magnetic thin films preserve their magnetic and magnetostrictive properties in contrast to some shape memory alloys, which require certain thickness to undergo phase transition to produce their conformation. Therefore, magnetic films are good candidates for the micro- and nano-origami devices. In this chapter, we will discuss methods of fabrication of magnetic micro-origami structures, present experimental results on their physical proper‐ ties, and indicate potential applications of magnetic micro-origami techniques.

## **2. Fabrication of micro-origami structures**

## **2.1. Forces responsible for conformations**

A large variety of forces is available to form or actuate thin film patterns into micro-origami figures. The magnitude of the force, elastic moduli, and the thickness of the film ultimately determine the curvature of the three-dimensional shapes. In addition, anisotropic stresses, shape of the pattern, and direction of etching decide about the direction of rolling or folding of the patterns.

#### *2.1.1. Surface tension*

Origamiisprimarilyanartbutithas alsoanimpactontechnology.Theorigamitechniqueswere implemented in satellite solar cells, airbag design, and stent implants [3]. Currently, mathe‐ matical [4] and computer models such as TreeMaker [5] allow designing complex threedimensional structures fordecorativearts,aswellas technologicalapplications.Some examples

The traditional origami methods rely on folding a single rectangular piece of paper by hand. More advanced techniques take advantage of using tools, such as bone folder, clips, or tweezers. More complex designs require cutting the paper into various patterns (different from rectangle), coloring them, combining with other materials (e.g., aluminum foil), and using multiple pieces of paper, which is called a modular origami. In contrast to static designs, some origami patterns can possess movable parts, which can be activated by kinetic energy of human's hand or inflation [7]. Another interesting trend in origami is tessellation of the figures, which is in fact a method of assembly of larger figures from building origami blocks [8].

and optical microscope. At this point a question arises whether we can do even smaller microorigami figures and use them to advance technology? The answer is "yes." It is possible to fabricate origami figures with features as small as 2 nm, actuate them, and assemble them into meta-materials. The submillimeter or submicrometer figures made from different materials using origami techniques are called micro- or nano-origami, respectively. A list of examples of applications of origami and micro-origami include bendable microelectronics, cell origami, origami nanorobot, pollen origami, origami lens, origami DNA, self-deployable origami stent,

The materials used for micro- and nano-origami must be much thinner and tougher than conventional paper. Good candidates are thin foils and thin films. Although, in principle, it is

, using a needle

The smallest origami figures were made from the paper pieces as small as 1 mm2

of origami figures are presented in **Figure 1** [6].

224 Magnetic Materials

**Figure 1.** Various origami figures (reproduced from Ref. [6]).

etc.

Capillary forces or surface tension are negligible in macroscale; however, they are of primary importance in micro- and nanoscales. Gagler [21] and Gracias et al. [23–31] showed that the surface tension of evaporating drop of liquid is sufficient to pull the walls of the photolitho‐ graphically defined thin film patterns together and form various figures, such as boxes or pyramids with the size of several micrometers. These patterns typically consist of more rigid areas connected by thinner areas, which serve as hinges, when the thicker walls fold. This approach is versatile and can be applied to magnetic films or magnetic/nonmagnetic compo‐ sites. Self-assembled structures can serve as building blocks for designing mesoscopic metamaterials with interesting responses to electromagnetic radiation in microwave, millimeter wave, and optical ranges [27, 28]. In some cases, the capillary forces can produce reversible conformations due to swelling and dehydrating of porous structures. Examples of microorigami figures are presented in **Figure 2**.

**Figure 2.** Examples of self-folding micro-origami structures (left and middle picture reproduced with permission from Ref. [21] and the right picture from [23]).

At this point, it is worth noting that in some cases the surface tension may cause undesirable effects. For instance, it may oppose or prevent deformation of patterns which would otherwise deform due to internal stresses or thermal stresses.

#### *2.1.2. Residual and interfacial stresses*

Different types of growth of the polycrystalline materials may result in significant residual stresses in thin film materials [32, 33]. Island growth (Volmer-Weber) or Stanski-Krastanow growth of polycrystalline films may lead to significant residual stresses due to coalescence of grains. Also, growth of bilayered or multilayered films of different materials can produce interfacial stresses due to lattice mismatch between constituent phases. When the films with residual stresses are released from the substrate on which they were grown they undergo deformation.

The curvature of the films depends on the internal stress level and the thickness of the film. For the simple bilayered beam, the continuum elasticity theory predicts that the curvature *κ* (inverse of radius *r*) is [32].

$$\kappa = \frac{6E\_1E\_2(h\_1+h\_2)h\_1h\_2\varepsilon}{E\_1^2h\_1^4 + E\_2^2h\_2^4 + 4E\_1E\_2h\_1^3h\_2 + 4E\_1E\_2h\_2^3h\_1 + 6E\_1E\_2h\_1^2h\_2^2} \tag{1}$$

where *E*1 and *E*<sup>2</sup> are Young's moduli, *h*1 and *h*<sup>2</sup> are thicknesses of the layers, and *ε* denotes the interfacial strain between the two layers. Based on this equation, it is easy to demonstrate the general rule, which states that for the layers with similar thicknesses and Young's moduli the radius of the structures is proportional to the film thickness. Thus, the smaller origami figures we wish to design the thinner films we must use. Multilayered patterns or complex shapes require numerical solutions by the means of computer simulations to predict their conforma‐ tions at certain level of residual stresses. The microstructure of thin films can vary with their thickness, which results in variation of residual stresses across the film thickness. Thus, even the single polycrystalline magnetic films can form magnetic microtubes [34] or other microorigami figures.

areas connected by thinner areas, which serve as hinges, when the thicker walls fold. This approach is versatile and can be applied to magnetic films or magnetic/nonmagnetic compo‐ sites. Self-assembled structures can serve as building blocks for designing mesoscopic metamaterials with interesting responses to electromagnetic radiation in microwave, millimeter wave, and optical ranges [27, 28]. In some cases, the capillary forces can produce reversible conformations due to swelling and dehydrating of porous structures. Examples of micro-

**Figure 2.** Examples of self-folding micro-origami structures (left and middle picture reproduced with permission from

At this point, it is worth noting that in some cases the surface tension may cause undesirable effects. For instance, it may oppose or prevent deformation of patterns which would otherwise

Different types of growth of the polycrystalline materials may result in significant residual stresses in thin film materials [32, 33]. Island growth (Volmer-Weber) or Stanski-Krastanow growth of polycrystalline films may lead to significant residual stresses due to coalescence of grains. Also, growth of bilayered or multilayered films of different materials can produce interfacial stresses due to lattice mismatch between constituent phases. When the films with residual stresses are released from the substrate on which they were grown they undergo

The curvature of the films depends on the internal stress level and the thickness of the film. For the simple bilayered beam, the continuum elasticity theory predicts that the curvature *κ*

> 1 2 1 2 12 24 24 3 3 2 2 1 1 2 2 1 21 2 1 221 1 21 2

446 *EE h h hh E h E h EEhh EEhh EEh h*

where *E*1 and *E*<sup>2</sup> are Young's moduli, *h*1 and *h*<sup>2</sup> are thicknesses of the layers, and *ε* denotes the interfacial strain between the two layers. Based on this equation, it is easy to demonstrate the

e

<sup>+</sup> <sup>=</sup> ++ + + (1)

6( )

origami figures are presented in **Figure 2**.

226 Magnetic Materials

Ref. [21] and the right picture from [23]).

*2.1.2. Residual and interfacial stresses*

deformation.

(inverse of radius *r*) is [32].

k

deform due to internal stresses or thermal stresses.

If the tensile stresses in the bilayers are smaller near the substrate than on the film surface, the film released from the substrate tends to bend under and may form wrinkles rather than regular micro-origami patterns. An example of wrinkled squares of magnetic films is presented in **Figure 3**. This indicates that the sequence of the deposition of the films matters. For instance, depositing metal A on top of B will not result in the same structure as depositing B on A.

**Figure 3.** (a) Wrinkling of permalloy-Ti films and (b) correct rolling of the edges of Ti-permalloy squares.

The residual stresses due to grain coalescence depend on the deposition conditions, such as deposition method (sputtering, evaporation, or laser ablation), base pressure in the chamber, pressure of Ar during sputtering, and deposition rate or temperature of the substrate [33]. For this reason, it is difficult to control them and reproduce in different deposition systems.

Much better control of stresses can be achieved in heteroepitaxial structures. An excellent example of use of interfacial stresses is the technology developed by Prinz et al. [35–39].

They used misfit between single crystalline semiconductor films grown epitaxially on top of each other, as shown in **Figure 4**. Indium arsenide atoms arriving on the AlAs surface must reduce their interatomic distances to match the lattice of AlAs. Therefore, the InAs film on AlAs is in compressed state. On the other hand, GaAs atoms experience tensile stresses when they form single crystal film on the top of InAs with larger lattice constant. When AlAs sacrificial layer is selectively etched (with selectivity better than 1:1000), the initially com‐ pressed InAs expands and the strained GaAs shrinks resulting in bending and rolling of the pattern of the bilayered film of InAs/GaAs which eventually forms a multiwall tube. For very thin films (a few atomic layers), the 7.5% mismatch strain between InAs and GaAs lattices results in a very small diameter of the tubes (down to 2 nm). Depending on the size of the rectangular pattern the number of turns can change between 1 and 40. The diameter of the tubes can be designed using formula (**1**). Here, it is important to note that ferromagnetic films such as single crystalline Fe or antiferromagnetic films such as Cr, KCoF3, or KFeF3 can be grown epitaxially on top of GaAs [40]. In fact, a similar semiconductor template was used by the group of Mendach to prepare three-layered scrolls of InGaAs/GaAs/Au films with tunable plasma frequency in the optical range [41] and magnonic InGaAs/GaAs/NiFe films [42].

**Figure 4.** Heteroepitaxial semiconductor structures which result in formation of nanotubes of GaAs/InAs when sacrifi‐ cial layer of AlAs on InP substrate is selectively etched releasing the film pattern from the substrate (reproduced with permission from Ref. [38]).

Thermal stresses in thin films provide another way to deform flat patterns after release from the substrate. Deposition of bilayers consisting of materials with markedly different expansion coefficients can be used to introduce internal strains when the bilayers are deposited at low or high temperatures and the films are released from the substrate at room temperature. This technique was used by Moiseeva et al. [43] to fabricate sophisticated cages from the patterns of magnetic films on top of thermal oxide with large compressive stresses. Some magnetic alloys called INVARs (Fe64Ni36) take advantage of magnetostrictive properties to reduce their linear coefficient of thermal expansion by more than one order of magnitude as compared to other metals. On the other hand, some metals such as Zn or polymers have exceptionally large thermal expansion coefficients. Combination of these dissimilar materials can result in large strains associated with relatively small temperature range during deposition or in applications.

#### *2.1.3. Other useful forces*

There are more forces which have potential for interesting applications in micro-origami. External forces were used by Jackman et al. [44] to assemble millimeter-sized cubes. Deposition of magnetic films on strained substrates has advantage over other methods: uniaxial or biaxial stresses can be applied along different directions with respect to a pattern and the direction can be varied during deposition of subsequent layers. Application of external stresses can be realized by deposition of the films on bent or strained substrates. The stress level and distri‐ bution in the films can be predicted and highly reproducible (like in the heteroepitaxial structures) and can be easily controlled in a broad range by adjusting the curvature of the substrate or external forces. A combination of polymers with relatively small Young's modu‐ lus, which can be easily stretched, and rigid inorganic magnetic films deposited on them seems to be suitable for this kind of micro-origami applications.

pattern of the bilayered film of InAs/GaAs which eventually forms a multiwall tube. For very thin films (a few atomic layers), the 7.5% mismatch strain between InAs and GaAs lattices results in a very small diameter of the tubes (down to 2 nm). Depending on the size of the rectangular pattern the number of turns can change between 1 and 40. The diameter of the tubes can be designed using formula (**1**). Here, it is important to note that ferromagnetic films such as single crystalline Fe or antiferromagnetic films such as Cr, KCoF3, or KFeF3 can be grown epitaxially on top of GaAs [40]. In fact, a similar semiconductor template was used by the group of Mendach to prepare three-layered scrolls of InGaAs/GaAs/Au films with tunable plasma frequency in the optical range [41] and magnonic InGaAs/GaAs/NiFe films [42].

**Figure 4.** Heteroepitaxial semiconductor structures which result in formation of nanotubes of GaAs/InAs when sacrifi‐ cial layer of AlAs on InP substrate is selectively etched releasing the film pattern from the substrate (reproduced with

Thermal stresses in thin films provide another way to deform flat patterns after release from the substrate. Deposition of bilayers consisting of materials with markedly different expansion coefficients can be used to introduce internal strains when the bilayers are deposited at low or high temperatures and the films are released from the substrate at room temperature. This technique was used by Moiseeva et al. [43] to fabricate sophisticated cages from the patterns of magnetic films on top of thermal oxide with large compressive stresses. Some magnetic alloys called INVARs (Fe64Ni36) take advantage of magnetostrictive properties to reduce their linear coefficient of thermal expansion by more than one order of magnitude as compared to other metals. On the other hand, some metals such as Zn or polymers have exceptionally large thermal expansion coefficients. Combination of these dissimilar materials can result in large strains associated with relatively small temperature range during deposition or in applications.

There are more forces which have potential for interesting applications in micro-origami. External forces were used by Jackman et al. [44] to assemble millimeter-sized cubes. Deposition of magnetic films on strained substrates has advantage over other methods: uniaxial or biaxial stresses can be applied along different directions with respect to a pattern and the direction can be varied during deposition of subsequent layers. Application of external stresses can be realized by deposition of the films on bent or strained substrates. The stress level and distri‐ bution in the films can be predicted and highly reproducible (like in the heteroepitaxial

permission from Ref. [38]).

228 Magnetic Materials

*2.1.3. Other useful forces*

Finally, significant stresses in thin films can occur when the films undergo change of crystal structure or are chemically altered. Shape memory alloys, which deform due to reversible transition from the austenitic to the martensitic phase, fall into this category. A special place among memory alloys take magnetic memory alloys such as Ni-Mn-Ga [45], which can produce strain as large as 9% when subjected to the action of a magnetic field. Strains in giant magnetostrictive alloys are almost two orders of magnitude smaller (a small fraction of %) and are considered to be insufficient to efficiently form the micro-origami figures. However, magnetostrictive materials with even smaller magnetostriction coefficients, but large magne‐ tomechanical coupling, are expected to be effective in stimulating already formed structures to perform certain functions, such as vibrations.

Large changes of volume of the order of 30% occur in some materials during their oxidation [46]. This effect is analogous to swelling of polymers or other porous materials. The change of the volume is associated with the increase of the linear dimensions. To exemplify this method we demonstrate the effect of the Ti oxide formation on the diameter of self-rolled microtubes of Ti/FeGa/Au and Ti/FeNi/Au. It has been suggested by Nastaushev et al. [47] that oxidation of titanium in the process of removal of the sacrificial layer may produce stresses, which affect formation of the micro-origami patterns.

**Figure 5.** Effect of anodization of the Ti layer on the radius of the Ti/FeGa/Au film. (a) Original microtube, (b) anodized microtube. [48].

In our experiments, we used anodizing to completely oxidize Ti layer in already formed microtubes. A thin layer of Au was used to protect magnetic films from oxidation. The results of the experiment, displayed in **Figure 5**, show that the stresses from Ti layer, converted into TiO, reduced the diameter of the tubes to about a half of its original value. It was estimated that the strain associated with the oxidation was about 1% [48]. An interesting approach would be to design processes in which magnetic metals such as Ni or Fe are chemically altered into magnetic compounds such as antiferromagnetic NiO or magnetite (Fe3O4). This would allow engineering stresses in the structures simultaneously with their magnetic properties.

## **2.2. Controlling direction of self-assembly**

As demonstrated by the origami, the same flat shape, such as rectangle, can be used to create hundreds of the origami figures. What differentiates these shapes is the sequence and direction in which the original shapes were folded. The fundamental question arises how we can control direction of bending or twisting of the flat patterns in micro- and nanoscale?

First of all, the shape itself may define the direction in which deformation occurs. In our early experiments with rectangular patterns of magnetic films grown on top of PMMA photoresist, we observed that only the longer edges of the AuCo film patterns rolled and formed long double tubes as shown in **Figure 6(a)**. This tendency can be interpreted in terms of the bending moment which for the films with uniform in-plane stresses is proportional to the length of the edge. Thus, when the etching progresses uniformly from all sides, the bending of longer edges prevails. The self-rolling of the same pattern will progress differently if a part of the pattern is attached to the substrate at the short edge, which prohibits rolling of the shorter edge. However, the constraint may not be effective for the rectangles with very large aspect ratio of the sides. Also, rigid parts of the patterns, such as thicker walls of origami figures from **Figure 2**, can act as constraints on bending the patterns. A theory of deformations of thin bilayered films has been developed by Cendula et al. [49]. They predicted that for certain stress gradient level a regular wrinkling is expected rather than bending. Computer modeling can be used for predicting formation of origami figures from more complex film patterns.

**Figure 6.** (a) Free-standing double tube of Cu/Co bilayer and (b) self-rolling of Ti/Ni bilayer which is attached at one end to the substrate and forms a single microtube.

Control of rolling direction is easier to achieve in heteroepitaxial structures. Prinz et al. [37] took advantage of different etching rates of Si in different crystallographic directions to fabricate microtubes or helical springs from GeSi/Si film patterns, which were deposited at different angles with respect to the crystallographic directions. Elegant experimental results by Li [50] illustrate different stages of the process of formation of an In0.3Ga0.7As/GaA microtube as the etching of the sacrificial layer progresses. They also demonstrate that anisotropic elastic properties in combination with selective anisotropic etching can be used to fabricate variety of three-dimensional structures by depositing film patterns at different angles with respect to (001) direction of the GaAs substrate.

It is also possible to achieve anisotropic lateral elastic properties of polycrystalline films by engineering their microstructure. This goal can be achieved by depositing films on tilted substrates. The angular deposition results in anisotropic magnetic properties [51]. Another option is to take advantage of nanocomposites. For instance, aligned carbon nanotubes embedded in polymer or magnetic film can control the pitch of the helical structures depending on the angle between the pattern and the direction of the enforcing elements (see **Figure 7**).

**Figure 7.** A concept of using anisotropic properties of composite materials to control rolling direction.

Finally, the external stresses applied to the substrates during the deposition are capable of providing a control over anisotropic film strains. The only inconvenience of this approach is the necessity of varying the stress level or direction inside a vacuum chamber, or preventing film contamination if the stresses are varied outside the chamber.

## **2.3. A sacrificial layer**

be to design processes in which magnetic metals such as Ni or Fe are chemically altered into magnetic compounds such as antiferromagnetic NiO or magnetite (Fe3O4). This would allow

As demonstrated by the origami, the same flat shape, such as rectangle, can be used to create hundreds of the origami figures. What differentiates these shapes is the sequence and direction in which the original shapes were folded. The fundamental question arises how we can control

First of all, the shape itself may define the direction in which deformation occurs. In our early experiments with rectangular patterns of magnetic films grown on top of PMMA photoresist, we observed that only the longer edges of the AuCo film patterns rolled and formed long double tubes as shown in **Figure 6(a)**. This tendency can be interpreted in terms of the bending moment which for the films with uniform in-plane stresses is proportional to the length of the edge. Thus, when the etching progresses uniformly from all sides, the bending of longer edges prevails. The self-rolling of the same pattern will progress differently if a part of the pattern is attached to the substrate at the short edge, which prohibits rolling of the shorter edge. However, the constraint may not be effective for the rectangles with very large aspect ratio of the sides. Also, rigid parts of the patterns, such as thicker walls of origami figures from **Figure 2**, can act as constraints on bending the patterns. A theory of deformations of thin bilayered films has been developed by Cendula et al. [49]. They predicted that for certain stress gradient level a regular wrinkling is expected rather than bending. Computer modeling can be used for

**Figure 6.** (a) Free-standing double tube of Cu/Co bilayer and (b) self-rolling of Ti/Ni bilayer which is attached at one

Control of rolling direction is easier to achieve in heteroepitaxial structures. Prinz et al. [37] took advantage of different etching rates of Si in different crystallographic directions to fabricate microtubes or helical springs from GeSi/Si film patterns, which were deposited at different angles with respect to the crystallographic directions. Elegant experimental results by Li [50] illustrate different stages of the process of formation of an In0.3Ga0.7As/GaA microtube

engineering stresses in the structures simultaneously with their magnetic properties.

direction of bending or twisting of the flat patterns in micro- and nanoscale?

predicting formation of origami figures from more complex film patterns.

**2.2. Controlling direction of self-assembly**

230 Magnetic Materials

end to the substrate and forms a single microtube.

Although it has been demonstrated that it is possible to assemble micro-origami structures on the air/water interface [52], vast majority of techniques uses solid sacrificial underlayers to build patterns on top of them.

In the case of the amorphous and polycrystalline sacrificial micro-origami structures, there are two fundamental requirements:

(a) The sacrificial layer must form a smooth surface, promote proper growth of the film, and enable patterning. It is worth mentioning that the microstructure of the polycrystalline films may strongly depend on the type of a substrate. Metals usually form smooth films when grown on top of a metal or semiconductor surface; however, when deposited on some dielectrics or organic materials they may exhibit enhanced roughness or columnar growth. An example is shown in **Figure 8**. The growth of the films can usually be improved by increasing the temperature of the substrate with the sacrificial layer, but it can create a problem with some organic sacrificial layers which melt at relatively low temperatures.

**Figure 8.** (a) Al/Pt film pattern deposited on top of photoresist and (b) the same bilayered film deposited on top of glucose film (images obtained by optical profiler).

The sacrificial layer should also be insensitive to the agents used in the patterning process, so that the film can be released only after the pattern is defined. Depending on the patterning technique, the agents used for dry etching (reactive or corrosive gasses) or wet etching (water, acetone, and acids) should not attack the sacrificial layer.

(b) The sacrificial layer must be from the material which has markedly different etching properties than the film pattern. An excellent example is the ratio of HF solution etching rate of GaAs to AlAs exceeding 10,000. This sacrificial layer was used by Prinz et al. [35] and Li [50] to fabricate free standing semiconductor nanostructures. Even much smaller selectivity of 1:80 for Si/SiGe system etched by the 3.7 wt% of NH4OH allowed fabrication of high-quality microorigami patterns. Reactive gases, such as xenon difluoride (XeF2) vapor and CHF3/O2, were used to etch Si substrate [43] and to remove Ge layer [36], respectively. Polycrystalline magnetic films can be grown on a photoresist layer which can be dissolved by acetone [52]. Aluminum sacrificial surface layer was used to grow Au/Ti bilayers and was etched with KOH-based solution [47]. Our group used 50 nm thick Cu film on Si as a sacrificial layer to deposit magnetic films [53, 54].

A disadvantage of wet etching method is that the surface tension or capillary forces of liquids used for the etching can interfere with the residual stresses and can prevent deformations of the pattern or even crack the pattern. The test for the strength of the surface tension forces in microscale is the fact that the capillary forces inside the tubes are able to collapse already formed tubes when water trapped inside the tube dries [36]. Potential solution to this problem can be the usage of supercritical conditions by elevating the temperature of water to a boiling point. Another option is to use organic solvents with much lower surface tension. Using gases instead of liquids removes this problem. However, the gasses used for etching are highly corrosive and toxic.

temperature of the substrate with the sacrificial layer, but it can create a problem with some

**Figure 8.** (a) Al/Pt film pattern deposited on top of photoresist and (b) the same bilayered film deposited on top of

The sacrificial layer should also be insensitive to the agents used in the patterning process, so that the film can be released only after the pattern is defined. Depending on the patterning technique, the agents used for dry etching (reactive or corrosive gasses) or wet etching (water,

(b) The sacrificial layer must be from the material which has markedly different etching properties than the film pattern. An excellent example is the ratio of HF solution etching rate of GaAs to AlAs exceeding 10,000. This sacrificial layer was used by Prinz et al. [35] and Li [50] to fabricate free standing semiconductor nanostructures. Even much smaller selectivity of 1:80 for Si/SiGe system etched by the 3.7 wt% of NH4OH allowed fabrication of high-quality microorigami patterns. Reactive gases, such as xenon difluoride (XeF2) vapor and CHF3/O2, were used to etch Si substrate [43] and to remove Ge layer [36], respectively. Polycrystalline magnetic films can be grown on a photoresist layer which can be dissolved by acetone [52]. Aluminum sacrificial surface layer was used to grow Au/Ti bilayers and was etched with KOH-based solution [47]. Our group used 50 nm thick Cu film on Si as a sacrificial layer to deposit magnetic

A disadvantage of wet etching method is that the surface tension or capillary forces of liquids used for the etching can interfere with the residual stresses and can prevent deformations of the pattern or even crack the pattern. The test for the strength of the surface tension forces in microscale is the fact that the capillary forces inside the tubes are able to collapse already formed tubes when water trapped inside the tube dries [36]. Potential solution to this problem can be the usage of supercritical conditions by elevating the temperature of water to a boiling point. Another option is to use organic solvents with much lower surface tension. Using gases

organic sacrificial layers which melt at relatively low temperatures.

glucose film (images obtained by optical profiler).

films [53, 54].

232 Magnetic Materials

acetone, and acids) should not attack the sacrificial layer.

Finding a proper sacrificial layer for the heteroepitaxial systems is even a greater challenge. In addition to the requirement of high selectivity, the sacrificial layer must also be a part of the heteroepitaxial system. This means that it must match both the structure of the substrate and the films which are grown on top of it. Satisfying all these three requirements simultaneously is a tough task.

This indicates a need for a search for new sacrificial layers for heteroepitaxial structures which promote single crystal growth and yet can be selectively etched. Ideally, such layers would be eco- and biofriendly.

Here, we would like to point at two prospective sacrificial layers. Single crystal NaCl (salt) sacrificial layer is a good candidate to grow magnetic films with cubic crystal structure. NaCl was a popular substrate for deposition of transition metal films in the 1960s [55], but it was not implemented in industrial processes because of its hygroscopic properties. Ironically, the same property predisposes NaCl films for the micro-origami applications. Reflection highenergy electron diffraction (RHEED) images of the MgO substrate, NaCl layer, and Cr film are presented in **Figure 9**.

**Figure 9.** RHEED images of (a) the MgO substrate with 5 nm MgO film, (b) 170 nm NaCl film, and (c) 15 nm Cr film on top of NaCl sacrificial layer.

The following procedure for the electron beam evaporation was used to grow heteroepitaxial structures with NaCl sacrificial layer:

– A thin layer of MgO (typically 5 nm) was deposited on MgO substrate to improve the quality of the surface.

– NaCl was evaporated at the rate of 0.05 nm/s at 350°C.

– Various magnetic and nonmagnetic transition metal films, such as Fe, Cr, V, and Ag, were grown epitaxially on top of NaCl.

Other substrates, such as GaAs and deposition methods can also be used to grow heteroepi‐ taxial structures with NaCl layer. This layer is biofriendly and dissolves in water; therefore, it has a great potential for biomedical applications of micro-origami structures. Glucose films which can be made by spin coating of water solutions on different substrates are also an interesting option for biomedical applications. However, the growth of some films may lead to unexpected results, as shown in **Figure 8**.

Zn and Mg are interesting materials for the sacrificial layers because they sublimate in vacuum at relatively low temperatures. Therefore, they can be removed in vacuum chamber by increasing the substrate temperature. This approach does not require corrosive gasses or liquids which affect the release of the micro-origami structures because of the surface tension. We carried out initial studies on growth and sublimation of Zn films. Zn films have hexagonal structure and a reasonably good match to lattice constants of Ru, Ti, graphene, and, most importantly, magnetic films of Co. Although literature data [56] indicate that the temperature of sublimation of Zn is 250°C, the actual sublimation temperature was found to be substantially lower (below 200°C) in ultra-high vacuum conditions. Our RHEED studies revealed that single crystal or highly textured Zn films can be grown on Ru and Ti films deposited on sapphire substrates. It was also found that the thin film growth is strongly affected by the deposition conditions. Different morphologies of the Zn film due to different growth conditions, such as deposition rate and the temperature of the substrate are shown in **Figure 10**. The best results were achieved for the deposition of Zn on Ti film at deposition rate of 0.02 nm/s and at temperatures above 100°C.

**Figure 10.** Zn film on Ru deposited (a) at room temperature and rate of 0.02 nm/s, (b) room temperature and 0.1 nm/s, and (c) at 100°C at 0.05 nm/s.

## **3. Link between the shape and magnetic properties**

A discussion on static magnetic properties of magnetic scrolls has been initiated in the articles by Müller et al. [51, 57]. Angular deposition of Au/Co/Au films resulted in the in-plane magnetic anisotropy of rectangular thin film patterns. They ascribed it to stress-induced anisotropy in the as-deposited films. They also observed changes in the shape of the hysteresis loop and evolution of magnetic domain structure when the film patterns rolled and formed microtubes.

The films fabricated in our group [48, 53, 54] were isotropic in the film plane. Therefore, the effect of the self-rolling on the static magnetic properties was easier to interpret than for the anisotropic films. Two kinds of magnetic microtubes were fabricated using the same technol‐ ogy described below.

interesting option for biomedical applications. However, the growth of some films may lead

Zn and Mg are interesting materials for the sacrificial layers because they sublimate in vacuum at relatively low temperatures. Therefore, they can be removed in vacuum chamber by increasing the substrate temperature. This approach does not require corrosive gasses or liquids which affect the release of the micro-origami structures because of the surface tension. We carried out initial studies on growth and sublimation of Zn films. Zn films have hexagonal structure and a reasonably good match to lattice constants of Ru, Ti, graphene, and, most importantly, magnetic films of Co. Although literature data [56] indicate that the temperature of sublimation of Zn is 250°C, the actual sublimation temperature was found to be substantially lower (below 200°C) in ultra-high vacuum conditions. Our RHEED studies revealed that single crystal or highly textured Zn films can be grown on Ru and Ti films deposited on sapphire substrates. It was also found that the thin film growth is strongly affected by the deposition conditions. Different morphologies of the Zn film due to different growth conditions, such as deposition rate and the temperature of the substrate are shown in **Figure 10**. The best results were achieved for the deposition of Zn on Ti film at deposition rate of 0.02 nm/s and at

**Figure 10.** Zn film on Ru deposited (a) at room temperature and rate of 0.02 nm/s, (b) room temperature and 0.1 nm/s,

A discussion on static magnetic properties of magnetic scrolls has been initiated in the articles by Müller et al. [51, 57]. Angular deposition of Au/Co/Au films resulted in the in-plane magnetic anisotropy of rectangular thin film patterns. They ascribed it to stress-induced anisotropy in the as-deposited films. They also observed changes in the shape of the hysteresis loop and evolution of magnetic domain structure when the film patterns rolled and formed

The films fabricated in our group [48, 53, 54] were isotropic in the film plane. Therefore, the effect of the self-rolling on the static magnetic properties was easier to interpret than for the

**3. Link between the shape and magnetic properties**

to unexpected results, as shown in **Figure 8**.

234 Magnetic Materials

temperatures above 100°C.

and (c) at 100°C at 0.05 nm/s.

microtubes.

First, the 50 μm × 50 μm holes were defined in a PMMA photoresist using exposure of the photoresist to deep UV light through as mask. Thin film of Cu was deposited by sputtering on the Si wafer with (001) orientation. During a lift-off process the Cu film pieces on top of photoresist were removed by ultrasonication of the wafer immersed in acetone. The remaining 50 nm thick Cu squares served as sacrificial layer. Another mask with 20 μm × 50 μm rectangles was used to deposit the trilayered Ti/GaFe/Au and Ti/Ni/Au films. This mask was aligned in such a way that the majority of the area of the rectangular holes in photoresist was on top of the Cu squares and a smaller part on exposed Si. After deposition of the trilayer and the second lift-off process the rectangles remained on top of Cu patches, which were partially attached to Si, as presented in **Figure 11(a)**. During selective etching of the sacrificial Cu underlayer, the films with residual stresses, caused by the grain coalescence, self-rolled, and formed magnetic microtubes with 3–4 turns, diameter of 5–10 μm, and the length of 20 μm (**Figure 11b**).

**Figure 11.** (a) Optical microscope image of an array of flat rectangular film patches of Ti (20 nm)/Ni (30 nm)/Au (2 nm) on top of Si wafer and partially overlapping with sacrificial Cu films squares. (b) Scanning microscope image of the array of magnetic scrolls and a magnified image of a single scroll (in the inset) formed after selective etching of Cu.

The same masks were used to deposit Ti/FeGa/Au films. A thin layer of gold was used to protect magnetic layer against oxidation. The static magnetic properties were characterized by means of vibrating sample magnetometry. The hysteresis loops of the microtubes with Ni are presented in **Figure 12**. The magnetic field was applied in two transverse directions in the substrate plane. The direction marked as 0° is the direction of the axis of the tubes formed from the patterns and the 90° is transverse to the tubes. Hysteresis loops (black lines) representing magnetization of flat patterns in these two directions are almost identical. Slight differences between the curves can be attributed to the shape anisotropy of the rectangular shapes of the patterns. Similar statement refers to the hysteresis loops of the flat patterns of the Ti (20 nm)/ (GaFe 40 nm)/(Au 15 nm) film. The coercive field of the patterns with Ni was 13.4 Oe, whereas it was 60 Oe for the GaFe films.

**Figure 12.** Magnetization hysteresis loops of rectangular film patterns 20 μm × 50 μm with Ni layer (black line), micro‐ tubes (red line), and anodized microtubes (blue line). Top part refers to the 0° angle and the bottom to 90° angle of the applied magnetic field. (Reproduced with permission from Ref. [48].)

**Figure 13.** Magnetization hysteresis loops of rectangular film patterns 20 μm × 50 μm with GaFe layer (black line), mi‐ crotubes (red line), and anodized microtubes (blue line). Top part refers to the 0° angle and the bottom to 90° angle of the applied magnetic field. (Reproduced with permission from Ref. [48].)

Marked differences between the magnetization loops for the two directions of magnetizing field were observed for both types of magnetic materials (red symbols curves in **Figures 12** and **13**). This is the result of the change of the shape and evolution of strains of the patterns undergoing deformation after release from the substrate.

As discussed in Ref. [48], the behavior of the GaFe films could be interpreted in terms of the shape anisotropy of the microtubes for which the technical magnetization saturation is achieved at lower fields for the field applied along the easy magnetization axis (along the tubes), whereas the loops for the hard direction (perpendicular to the tubes) are tilted and approach saturation magnetization at higher fields. However, the behavior of Ni tubes opposes that of GaFe, in spite of similar contribution from the shape anisotropy. In addition, both types of materials exhibit opposite trends in the change of the coercive field. The coercivity of Ni tubes almost triples for the field applied at 90° while it decreases by about 30% for GaFe films as compared to the rectangular patterns measured in the same direction. These facts prove that the change of shape and associated shape anisotropy alone is unable to explain the changes of magnetic properties.

An important distinction between these two magnetic materials is their magnetostriction. Ni has negative linear magnetostriction coefficient of −38 × 10−6, whereas GaFe has positive coefficient of magnetostriction of about +70 × 10−6. For this reason, the magnetization responds in different ways when strains in the applied magnetic field vary by about 1% during selfrolling process.

**Figure 12.** Magnetization hysteresis loops of rectangular film patterns 20 μm × 50 μm with Ni layer (black line), micro‐ tubes (red line), and anodized microtubes (blue line). Top part refers to the 0° angle and the bottom to 90° angle of the

**Figure 13.** Magnetization hysteresis loops of rectangular film patterns 20 μm × 50 μm with GaFe layer (black line), mi‐ crotubes (red line), and anodized microtubes (blue line). Top part refers to the 0° angle and the bottom to 90° angle of

applied magnetic field. (Reproduced with permission from Ref. [48].)

236 Magnetic Materials

the applied magnetic field. (Reproduced with permission from Ref. [48].)

Additional evidence of the importance of the magnetoelastic contribution to the magnetization change is that the differences between the materials continue to diversify when Ti layer undergoes anodization. Expanding TiO, formed from Ti layer, exerts additional stress on the magnetic layers and reduces the diameter of the tubes by about 50%, which is also reflected in magnetic properties. The time of the anodizing was adjusted in the range from 10 to 25 s so that the entire layer of Ti could be converted into Ti oxide. The reduced saturation magneti‐ zation for the anodized samples (see **Figures 12** and **13**) indicates that the oxidation partially affected GaFe and Ni. The saturation magnetization was unaffected by the fabrication processes (coating with PMMA, using a water solution of a developer, and washing with acetone) because of the presence of a protective layer of gold.

Another magnetic method, which gives even more insight into residual stresses, is based on high-frequency measurements of spin dynamics. Spin precession at Ferromagnetic resonance (FMR) is affected by local magnetic field *Heff*, where demagnetizing field *HD* and stress-induced anisotropy field *Hσ*, associated with stress *σ*, contribute. The relation derived from Landau-Lifshitz-Gilbert equation for magnetically isotropic material with magnetostriction *λS*, gives the relation between the stress-induced anisotropy field *Hσ* = 2*σλS*/*MS* due to stress *σ*, saturation magnetization *MS* of the material, applied bias field *HA* and a frequency *fr* of microwave absorption at resonant conditions:

$$f\_r = \frac{\gamma}{2\pi} \sqrt{(H\_A + H\_D + H\_\sigma)(M\_S + H\_A + H\_D + H\_\sigma)}\tag{2}$$

where *γ* is a gyromagnetic ratio of the magnetic material. The distribution of internal stresses in magnetostrictive materials determines the linewidth of the resonant curve. Examples of FMR spectra for rectangular patterns of Ni films with thickness of 30 nm and for corresponding microtubes are presented in **Figure 14**. The resonant fields are approximately the same for the two orientations of the in-plane applied field. Larger resonant field for the out-of-plane direction of the applied field results from large demagnetization factor for this orientation. The FMR absorption spectra become more complex for rolled-up patterns. The resonance peak along the tube axis remains unaffected, except of some broadening. However, the curves measured with the field applied transverse to the microtubes are markedly different. In particular, the intensity of the absorption measured normal to the substrate decreases and additional peak forms at lower fields. This peak can be attributed to the microtubes. The high field peak may result from the part of the flat patterns which did not roll—they attach the tubes to the substrate. In the Ni tubes, the "unrolled" area was about 40% of the rectangles, but we were able to reduce it to 10% for GaFe films by adjusting technological parameters.

**Figure 14.** Ferromagnetic resonance spectra of the rectangular patterns of Ni films (a) as compared to the spectra of the microtubes (b) measured with the field out of the substrate plane (blue curves) and two directions in the film plane (field at 0° along the tubes and at 90°. (Reproduced with permission from Ref. [54].)

More detailed studies of spin dynamics in magnetic microtubes made by Balhorn et al. [42] involve spin wave properties in multiwall magnetic microtubes prepared by micro-origami techniques. They observed a series of four resonant peaks which corresponded to the con‐ structive interference of Damon-Eshbach-type spin waves traveling along the circumference of the multiwall tubes of 20 nm permalloy film. The resonances could be tuned by the diameter and the number of turns of the tubes.

Magnetic layers can also be a part of multiferroic or magnetoelectric composites. These materials exhibit coupling between polarization and magnetization through the interfacial stresses between piezoelectric and magnetostrictive layer. Changes of external magnetic field produce magnetostrictive strains in the magnetic material which are transferred to the mechanically coupled piezoelectric and result in changes of polarization. On the other hand, electric field applied to the piezoelectric layer produces piezoelectric strains which are transferred to the magnetic material and change its magnetization [58]. A common problem in the multilayered films is that the magnetoelectric functions are greatly reduced because either piezoelectric or magnetostrictive layer is attached to a massive substrate which prevents straining of the materials adhering to Origami technology. This is called a clamping effect. An advantage of free-standing micro-origami structures is that they do not restrict the exchange of stresses between the piezoelectric and magnetic phases and make the stress-mediated mechanism of electric and magnetic energies highly effective. In addition, magnetic scrolls occupy much smaller area than the cantilevers with the same mass. Piezoelectric/ferromagnetic composite Au (5 nm)/AlN (20 nm)/CoFe (40 nm)/Au (5 nm) form microtubes when released from the substrate [54].

## **4. Functions and applications**

where *γ* is a gyromagnetic ratio of the magnetic material. The distribution of internal stresses in magnetostrictive materials determines the linewidth of the resonant curve. Examples of FMR spectra for rectangular patterns of Ni films with thickness of 30 nm and for corresponding microtubes are presented in **Figure 14**. The resonant fields are approximately the same for the two orientations of the in-plane applied field. Larger resonant field for the out-of-plane direction of the applied field results from large demagnetization factor for this orientation. The FMR absorption spectra become more complex for rolled-up patterns. The resonance peak along the tube axis remains unaffected, except of some broadening. However, the curves measured with the field applied transverse to the microtubes are markedly different. In particular, the intensity of the absorption measured normal to the substrate decreases and additional peak forms at lower fields. This peak can be attributed to the microtubes. The high field peak may result from the part of the flat patterns which did not roll—they attach the tubes to the substrate. In the Ni tubes, the "unrolled" area was about 40% of the rectangles, but we

were able to reduce it to 10% for GaFe films by adjusting technological parameters.

**Figure 14.** Ferromagnetic resonance spectra of the rectangular patterns of Ni films (a) as compared to the spectra of the microtubes (b) measured with the field out of the substrate plane (blue curves) and two directions in the film plane

More detailed studies of spin dynamics in magnetic microtubes made by Balhorn et al. [42] involve spin wave properties in multiwall magnetic microtubes prepared by micro-origami techniques. They observed a series of four resonant peaks which corresponded to the con‐ structive interference of Damon-Eshbach-type spin waves traveling along the circumference of the multiwall tubes of 20 nm permalloy film. The resonances could be tuned by the diameter

Magnetic layers can also be a part of multiferroic or magnetoelectric composites. These materials exhibit coupling between polarization and magnetization through the interfacial stresses between piezoelectric and magnetostrictive layer. Changes of external magnetic field produce magnetostrictive strains in the magnetic material which are transferred to the mechanically coupled piezoelectric and result in changes of polarization. On the other hand,

(field at 0° along the tubes and at 90°. (Reproduced with permission from Ref. [54].)

and the number of turns of the tubes.

238 Magnetic Materials

#### **4.1. Functionality of the micro-origami structures**

Converting flat pattern into micro-origami figures increases their functionality and potential for applications. For example, when magnetostrictive films are attached to the rigid substrate, the only response of the magnetic material to the applied field is a change of its magnetization. For a free-standing micro-origami structure, in addition to the change of magnetization, magnetic force can actuate the structure; it can give rise to a change of shape due to magne‐ tostrictive strains and external strains can vary magnetization, as well.

As already mentioned in the previous section, there is a mutual link between the magnetism and shape of the micro-origami figures. This feature can be used for tuning magnetic properties or resonant microwave absorption of the micro-origami patterns. The shape of the hysteresis loops, magnetic anisotropy, and coercivity can be controlled by fabricating materials with different shapes rather than changing the composition of the magnetic material. Magnetic shape anisotropy can control anisotropic behavior of nonmagnetostrictive materials, whereas residual stresses in the magnetic layers play primary role in magnetostrictive structures. Frequency of ferromagnetic resonance and frequency of spin wave modes can be controlled by the number of turns and the diameter of the microtubes. Because the micro-origami shapes can be fabricated in the form of arrays of identical complex objects, they may exhibit interesting responses to the electromagnetic radiation.

Helicity of magnetic scrolls has been utilized to make meta-materials with negative index of refraction [59]. Similar arrays of free-standing helical structures were envisioned as the way of enhancing magnetic field for magnetic resonance imaging [60].

Micro-origami techniques provide an efficient method of self-assembly of micro- and nano‐ structures. Just to exemplify this statement, we propose in **Figure 15** the sequence of processes of assembly of a microscopic electromagnet consisting of a coil with a hollow magnetic core.

**Figure 15.** Three stages of fabrication of three-dimensional inductor: (a) Deposition of a wire on top of a sacrificial lay‐ er, (b) deposition of insulating and magnetic layers, and (c) self-assembly.

Multiple turns can be fabricated by adding more wires or using diagonal direction of selfrolling to produce helical springs like in Refs. [50] and [61].

It greatly simplifies fabrication of three-dimensional patterns, which usually would require many more masking and deposition processes, angular deposition, and deep etching. In addition to self-assembly of structures attached to the substrate, micro-origami figures disconnected from the substrate can serve as building blocks for meta-materials, where magnetic elements of the figures or surface tension at hydrophilic parts can be used to put these blocks together in two- or three-dimensional networks [26]. Here, tessellation methods of origami patterns can be used.

#### **4.2. Prospective applications**

Micro-origami techniques have a great potential for numerous applications, although they have not been implemented in large-scale production, yet.

Magnetic and magnetoelastic properties of the micro-origami patterns can be used in various magneto-electro-mechanical systems (MEMS) such as stress or strain sensors, microscopic actuators, magnetic field sensors, and optical shutters [62]. As described in the previous section, enhanced performance of magnetoelectric functions is expected in the free-standing micro-origami patterns as compared to the planar structures on thick substrates. This gives a promise for increased sensitivity of the mutiferroic composites for magnetic field sensors [63], which have potential to reach the sensitivity of SQUID magnetometer. Another potential microelectronic application is in microwave devices based on laminated multiferroic compo‐ sites such as filters where the frequency of microwave absorption peak at ferromagnetic resonance can be tuned by the means of voltage applied to the piezoelectric layer [64]. Microorigami design can reduce size and increase tunability of laminated mutiferroic composites in such devices.

Because of excellent mechanical performance of microtubes [57], the self-assembly of microorigami structures can be used to build parts of microfluidic systems. They can serve as ducts and microchambers for chemical reactions. Magnetic and magnetostrictive properties of the tubes can be advantageous for the liquid pressure sensing or measuring flow of liquids or gases [65]. Micro-origami techniques can also be used to assemble parts of micropumps and valves in microfluidic systems, where either magnetoelastic or magnetostatic energies can be used to actuate micromotor or control shutters.

The most recent publications on micro-origami structures emphasize prospective applications in the biomedical field and biotechnology. First of all, the micro-origami methods are capable of fabricating biomimetic materials. Magnetic materials are envisioned as candidates for targeted drug delivery [23]. Different magnetic cages [21, 23] can be loaded with drugs, dragged with the help of magnetic force to the infected organs, and released in the location where they are the most effective. The targeted delivery of drugs can be achieved with the assistance of microswimmers [16, 66], which are able to move against blood stream. Helical magnetic structures made by micro-origami techniques can function as microdrillers to remove blood clogs in the veins when remotely activated by a rotating magnetic field [67]. Microgrippers and magnetic tweezers take advantage of self-folding of micro-origami patterns, as mentioned in the introduction [29].

More advanced devices which combine microtubes with giant magnetoresistive sensors or semiconducting chemical sensors are available [68, 69]. Magnetoresistive sensors prepared by micro-origami method were capable of detecting single magnetic nanoparticle passing thought a microtube. This will allow a precise control of functionalized magnetic nanoparticles for drug delivery or hyperthermia.

## **5. Conclusions**

**Figure 15.** Three stages of fabrication of three-dimensional inductor: (a) Deposition of a wire on top of a sacrificial lay‐

Multiple turns can be fabricated by adding more wires or using diagonal direction of self-

It greatly simplifies fabrication of three-dimensional patterns, which usually would require many more masking and deposition processes, angular deposition, and deep etching. In addition to self-assembly of structures attached to the substrate, micro-origami figures disconnected from the substrate can serve as building blocks for meta-materials, where magnetic elements of the figures or surface tension at hydrophilic parts can be used to put these blocks together in two- or three-dimensional networks [26]. Here, tessellation methods

Micro-origami techniques have a great potential for numerous applications, although they

Magnetic and magnetoelastic properties of the micro-origami patterns can be used in various magneto-electro-mechanical systems (MEMS) such as stress or strain sensors, microscopic actuators, magnetic field sensors, and optical shutters [62]. As described in the previous section, enhanced performance of magnetoelectric functions is expected in the free-standing micro-origami patterns as compared to the planar structures on thick substrates. This gives a promise for increased sensitivity of the mutiferroic composites for magnetic field sensors [63], which have potential to reach the sensitivity of SQUID magnetometer. Another potential microelectronic application is in microwave devices based on laminated multiferroic compo‐ sites such as filters where the frequency of microwave absorption peak at ferromagnetic resonance can be tuned by the means of voltage applied to the piezoelectric layer [64]. Microorigami design can reduce size and increase tunability of laminated mutiferroic composites in

Because of excellent mechanical performance of microtubes [57], the self-assembly of microorigami structures can be used to build parts of microfluidic systems. They can serve as ducts and microchambers for chemical reactions. Magnetic and magnetostrictive properties of the tubes can be advantageous for the liquid pressure sensing or measuring flow of liquids or

er, (b) deposition of insulating and magnetic layers, and (c) self-assembly.

rolling to produce helical springs like in Refs. [50] and [61].

have not been implemented in large-scale production, yet.

of origami patterns can be used.

**4.2. Prospective applications**

240 Magnetic Materials

such devices.

Micro-origami techniques are very versatile and can be applied to various materials including magnetic materials. They are envisioned as a very powerful self-assembly method. Unlike traditional origami, where folding of a paper is done by hands, micro- and nano-origami methods take advantage of forces in the microscale, such as surface tension or residual stresses, to shape materials by bending, twisting, and folding thin film patterns. The curvature of the structures and direction of deformation can be controlled in wide range by the magnitude of the residual or interfacial stress, elastic properties of the patterns, the shape, and thickness of the film patterns. This makes possible fabrication of complex three-dimensional architectures from flat patterns, which are released from the substrate by selective wet etching, reactive gas etching, dissolving, or sublimation of the sacrificial layer.

Magnetic micro-origami has a special place among various micro-origami designs. Magneto‐ static interactions between magnetic parts of the structures and/or external magnetic field can be used to assemble building blocks into meta-materials or actuate parts of microrobots. The external field gradient can be used to direct various micromagnetic cages loaded with drugs to infected organs, where the drugs will be released. Microswimmers take advantage of alternating fields to move in liquids in controlled way and rotating magnetic field can be used to rotate microdrills to open blood clogs in veins.

The magnetic properties of the micro-origami structures can be affected by their shape in three ways:

– Shape magnetic anisotropy varies when the flat patterns form three-dimensional structures. An example was provided where flat patterns possessed isotropic magnetic properties when measured with the field along different directions in the film plane, but magnetic hysteresis loops and ferromagnetic resonance curves showed marked differences for the transverse configuration of the applied fields when magnetic patterns scrolled and formed microtubes.

– Magnetoelastic properties affect magnetization of magnetostrictive films when the stress level and/or direction in the films change. This refers to the relaxation of residual stresses in the magnetic material, as well as external stresses from the adhering nonmagnetic layers exerted on magnetic layer when the multilayered film patterns bend after release from substrate. The stress-induced anisotropy affects domain structure and magnetization proc‐ esses. For example, self-rolling of magnetic films with positive (FeGa) and negative magneto‐ striction (Ni) lead to different trends in magnetization changes as evidenced by **Figures 12** and **13**.

– The change of chemical composition of magnetic films can alter magnetic properties. For example, the ferromagnetic Ni subjected to oxidation changes into antiferromagnetic NiO, and soft magnetic Fe may evolve into magnetite (Fe3O4) with larger magnetocrystalline anisotropy, coercivity, and saturation field, but reduced saturation magnetization. The changes of magnetic properties of chemically altered films can be associated with enhancement of residual stresses which are responsible for the formation of the micro-origami patterns. Thus, in certain cases the changes of magnetic properties can promote change of the shape if the chemical changes are followed by the phase or composition change which produces deformation.

The changes of magnetic shape anisotropy and stress-induced anisotropy, associated with the deformation of the film patterns, provide a convenient method of tuning magnetic properties by shape design.

The coupling between elastic and magnetic properties is mutual, i.e., the magnetization changes produce magnetostrictive strains but external stresses can change magnetization. Free-standing micro-origami patterns have increased functionality. Bending of magnetostric‐ tive layers can be used for stress, strain, or pressure sensing. Straining magnetostrictive layers in magnetoelectric composites is useful for tuning ferromagnetic resonance frequency in microwave filters by voltage applied to the piezoelectric layer. On the other hand, magneto‐ strictive strains generated in multiferroic composites by external fields can be converted into voltage and serve for the magnetic field sensing. Magnetoelectric performance of microorigami structures is expected to be superior to that of flat patterns on substrates because of lack of the clamping effect. Giant magnetoresistive structures integrated with the microfluidic ducts in a single micro-origami assembly process are capable of detecting a single nanoparticle flowing through a duct.

The micro- and especially nano-origami architectures have great potential for biomedical applications. Majority of publications on magnetic origami concern objects with the radius of a few micrometers. Future applications of the micro-origami in biotechnology may require reduction of the size of magnetic structures to sub-micrometers or nanometers and combining them with organic materials. Also, the preference for these applications is for biocompatible magnetic materials such as magnetite and biofriendly sacrificial layers. Initial results presented here look promising. More information about nano-origami techniques is available in the recent publication by Cavallo and Lagally [70].

## **Acknowledgements**

– Shape magnetic anisotropy varies when the flat patterns form three-dimensional structures. An example was provided where flat patterns possessed isotropic magnetic properties when measured with the field along different directions in the film plane, but magnetic hysteresis loops and ferromagnetic resonance curves showed marked differences for the transverse configuration of the applied fields when magnetic patterns scrolled and formed microtubes.

– Magnetoelastic properties affect magnetization of magnetostrictive films when the stress level and/or direction in the films change. This refers to the relaxation of residual stresses in the magnetic material, as well as external stresses from the adhering nonmagnetic layers exerted on magnetic layer when the multilayered film patterns bend after release from substrate. The stress-induced anisotropy affects domain structure and magnetization proc‐ esses. For example, self-rolling of magnetic films with positive (FeGa) and negative magneto‐ striction (Ni) lead to different trends in magnetization changes as evidenced by **Figures 12** and

– The change of chemical composition of magnetic films can alter magnetic properties. For example, the ferromagnetic Ni subjected to oxidation changes into antiferromagnetic NiO, and soft magnetic Fe may evolve into magnetite (Fe3O4) with larger magnetocrystalline anisotropy, coercivity, and saturation field, but reduced saturation magnetization. The changes of magnetic properties of chemically altered films can be associated with enhancement of residual stresses which are responsible for the formation of the micro-origami patterns. Thus, in certain cases the changes of magnetic properties can promote change of the shape if the chemical changes are followed by the phase or composition change which produces deformation.

The changes of magnetic shape anisotropy and stress-induced anisotropy, associated with the deformation of the film patterns, provide a convenient method of tuning magnetic properties

The coupling between elastic and magnetic properties is mutual, i.e., the magnetization changes produce magnetostrictive strains but external stresses can change magnetization. Free-standing micro-origami patterns have increased functionality. Bending of magnetostric‐ tive layers can be used for stress, strain, or pressure sensing. Straining magnetostrictive layers in magnetoelectric composites is useful for tuning ferromagnetic resonance frequency in microwave filters by voltage applied to the piezoelectric layer. On the other hand, magneto‐ strictive strains generated in multiferroic composites by external fields can be converted into voltage and serve for the magnetic field sensing. Magnetoelectric performance of microorigami structures is expected to be superior to that of flat patterns on substrates because of lack of the clamping effect. Giant magnetoresistive structures integrated with the microfluidic ducts in a single micro-origami assembly process are capable of detecting a single nanoparticle

The micro- and especially nano-origami architectures have great potential for biomedical applications. Majority of publications on magnetic origami concern objects with the radius of a few micrometers. Future applications of the micro-origami in biotechnology may require reduction of the size of magnetic structures to sub-micrometers or nanometers and combining them with organic materials. Also, the preference for these applications is for biocompatible

**13**.

242 Magnetic Materials

by shape design.

flowing through a duct.

The authors acknowledge contributions from Dr. Seonggi Min and summer interns Adam Wang and Brandon Buchanan who carried out research on NaCl and Zn sacrificial layers. We also acknowledge support though grants LEQSF-EPS(2012)-Pfund-302, NSF EPSCoR LA-SiGMA project under award #EPS-1003897 with additional support from the Louisiana Board of Regents through contract NSF (2010-15)-RII-UNO.

## **Author details**

Leszek Malkinski\* and Rahmatollah Eskandari

\*Address all correspondence to: lmalkins@uno.edu

Department of Physics and Advanced Materials Research Institute, University of New Orleans, New Orleans, Louisiana, USA

## **References**


[20] Diller E, Giltinan J, Lum GZ, Ye Z, Sitti M. Six-degrees-of-freedom remote actuation of magnetic microrobots. In: Proceedings of Robotics Science and Systems Conference X. Berkeley, USA, July 12–16, 2014, DOI: 10.15607/RSS.2014.X.013.

[6] Origami History [Internet]. Available from: http://japanese-old-customs.weebly.com/

[7] Lang RJ. Origami in Action: Paper Toys That Fly, Flap, Gobble, and Inflate. 1st ed. St.

[8] Origami Resource Center, Origami Science [Internet]. 2016. Available from: http://

[9] Paul KB, Malkinski L. Friction on the microscale. Review of Scientific Instruments, 2009:

[10] Tolley MT, Felton SM, Miyashita S, Aukes D, Rus D, Wood RJ. Self-folding origami: Shape memory composites activated by uniform heating. Smart Materials and Struc‐

[11] Felton S, Tolley M, Demaine E, Rus D, Wood R. A method for building self-folding

[12] Hubert A, Calchand N, Le Gorrec Y, Gauthier JY. Magnetic shape memory alloys as smart materials for micro-positioning devices. Advanced Electromagnetics. 2012;1(2):

[13] Yasu K, Inami M. POPAPY: Instant paper craft made up in a microwave oven. Advan‐ ces in Computer Entertainment. Berlin Heidelberg: Springer; 2012: pp. 406–420. DOI:

[14] Guberan C., Hydro-Fold by ECAL [Internet]. 2012. Available from: http://www.chris‐

[15] Fusco S, Sakar MS, Kennedy S, Peters C, Bottani R, Starsich F, Mao A, Sotiriou GA, Pané S, Pratsinis SE, Mooney D. An integrated microrobotic platform for on‐demand, targeted therapeutic interventions. Advanced Materials. 2014;26(6):952–957. DOI:

[16] Honda T, Arai KI, Ishiyama K. Micro swimming mechanisms propelled by external magnetic fields. IEEE Transactions on Magnetics. 1996;32(5):5085–5087. DOI:

[17] Ishiyama K, Sendoh M, Arai KI. Magnetic micromachines for medical applications. Journal of Magnetism and Magnetic Materials. 2002;242:41–46. DOI:10.1016/

[18] Pawashe C, Floyd S, Sitti M. Modeling and experimental characterization of an untethered magnetic micro-robot. The International Journal of Robotics Research.

[19] Vollmers K, Frutiger DR, Kratochvil BE, Nelson BJ. Wireless resonant magnetic microactuator for untethered mobile microrobots. Applied Physics Letters. 2008;92(14):

2009;28(8):1077–1094. DOI: 10.1177/0278364909341413

machines. Science. 2014;345(6197):644–646. DOI: 10.1126/science.1252610

origami.html

244 Magnetic Materials

Martin's Griffin Press, New York: 1997.

80:085110–1. DOI: 10.1063/1.3212672.

75–84. DOI:10.7716/aem.v1i2.10

10.1007/978-3-642-34292-9\_29

topheguberan.ch/Hydro-Fold.

10.1002/adma.201304098

10.1109/20.539498

S0304-8853(01)01181-7

144103. DOI: 10.1063/1.2907697

www.origami-resource-center.com/origami-science.html.

tures. 2014; 23(9):094006. DOI:10.1088/0964-1726/23/9/094006


[45] Heczko O, Scheerbaum N, Gutfleisch O. Magnetic shape memory phenomena. In: Nanoscale Magnetic Materials and Applications. Springer, USA. 2009; pp. 399–439. DOI: 10.1007/978-0-387-85600-1

[33] Koch R. The intrinsic stress of polycrystalline and epitaxial thin metal films. Journal of Physics: Condensed Matter. 1994;6(45):9519. DOI: 10.1088/0953-8984/6/45/005

[34] Songmuang R, Deneke C, Schmidt OG. Rolled-up micro-and nanotubes from singlematerial thin films. Applied Physics Letters. 2006;89(22):223109. DOI:

[35] Prinz VY, Vorob'ev AB, Seleznev VA. Three-dimensional structuring using self-rolling of strained InGaAs/GaAs films. 28th International Symposium of Compound Semi‐ conductors, Tokyo, Japan, 1–4 October 2001, Institute of Physics Conference Series,

[36] Prinz VY. Precise semiconductor, metal and hybrid nanotubes and nanofibers. Nano‐ engineered Nanofibrous Materials. 2004;169:47. DOI: 10.1007/978-1-4020-2550-1\_1

[37] Golod SV, Prinz VY, Mashanov VI, Gutakovsky AK. Fabrication of conducting GeSi/Si micro-and nanotubes and helical microcoils. Semiconductor Science and

[38] Prinz VY. A new concept in fabricating building blocks for nanoelectronic and nano‐ mechanic devices. Microelectronic Engineering. 2003;69(2):466–475. DOI: 10.1016/

[39] Seleznev VA, Prinz VY, Aniskin VM, Maslov AA. Generation and registration of disturbances in a gas flow. 1. Formation of arrays of tubular microheaters and micro‐ sensors. Journal of Applied Mechanics and Technical Physics. 2009;50(2):291–296. DOI:

[40] Malkinski L, O'Keevan T, Camley RE, Celinski Z, Wee L, Stamps RL, Skrzypek D. Exchange bias in the Fe/KCoF3 system: A comprehensive magnetometry study. Journal

[41] Schwaiger S, Bröll M, Krohn A, Stemmann A, Heyn C, Stark Y, Stickler D, Heitmann D, Mendach S. Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime. Physical Review Letters. 2009;102(16):163903. DOI:

[42] Balhorn F, Mansfeld S, Krohn A, Topp J, Hansen W, Heitmann D, Mendach S. Spinwave interference in three-dimensional rolled-up ferromagnetic microtubes. Physical

[43] Moiseeva E, Senousy YM, McNamara S, Harnett CK. Single-mask microfabrication of three-dimensional objects from strained bimorphs. Journal of Micromechanics and

[44] Jackman RJ, Brittain ST, Adams A, Prentiss MG, Whitesides GM. Design and fabrication of topologically complex, three-dimensional microstructures. Science. 1998;280(5372):

Review Letters. 2010;104(3):037205. DOI: 10.1103/PhysRevLett.104.037205

Microengineering. 2007;17(9):N63. DOI: 10.1088/0960-1317/17/9/N01

2089–2091. DOI: 10.1126/science.280.5372.2089

Technology. 2001;16(3):181–185. DOI: 10.1088/0268-1242/16/3/311

of Applied Physics. 2003;93(10):6835–6837. DOI: 10.1063/1.1558653

10.1063/1.2390647

246 Magnetic Materials

2002; 170:319–323.

S0167-9317(03)00336-8

10.1007/s10808-009-0039-5

10.1103/PhysRevLett.102.163903

