**3.2 Generation of pure spin currents through SSE using NM/BaM structures and photo-spin-voltaic effect in Pt/BaM structure**

the bilayer heterostructure becomes very important. Heavy metals, such as Pt and Au, have strong spin-orbit coupling [43, 44], offering an effective mechanism to convert a transverse spin current into a longitudinal charge current through inverse spin Hall effect (ISHE) [43, 45–47]. The ISHE charge current across the heavy metal surface creates an electric field *E*ISHE that can be measured with a voltmeter. The magnitude and sign of *E*ISHE depend on internal and external factors. In **Figure 5b**, an external magnetic field *H* is applied in the *x* direction. The magnetization *M* of the MI layer is aligned to the *x* direction as well. The temperature gradient is applied across the *z* direction, generating a spin voltage in the MI layer, injecting spin current across the interface and into the normal metal layer parallel to the temperature gradient. The polarity of electron spins in the normal metal layer is influenced by *M* from the MI layer. The ISHE field, *E*ISHE, is measured across the *y* direction. *E*ISHE is proportional to the cross product of the spatial direction of the generated spin current *Js* and the polarity vector of electron spins in the normal metal layer. The following equation explains the relationship between *E*ISHE, *Js*, and *σ* [19]:

In summary, the voltage measured across the normal metal surface is strongest when *M* is perpendicular to both the heat gradient and *E*ISHE; the voltage will flip its sign if *M* is flipped by flipping the external magnetic field *H*; the voltage measured

This discussion sheds light on the importance of the existence of an external magnetic field *H* to enable *E*ISHE when using soft magnetic insulators such as spinels and garnets. A strong enough *H* is necessary to saturate the magnetization of such insulators, as well as to control the direction of the magnetization. Indeed, SSE cannot be observed in samples incorporating spinels or garnets with a temperature gradient alone. Due to their low remnant magnetization, an appropriate external

An exception to the external magnetic field requirement is made when using BaM thin films due to their strong uniaxial anisotropy [18]. In the absence of an external magnetic field, the magnetization of BaM films, caused by the spins of unpaired electrons, tend to favor one axis, called the easy axis, over any other axis. Thus, most electron spins within the BaM film tend to align themselves with the easy axis, randomly up or down, in the absence of an external magnetic field. Therefore, BaM films have uniaxial anisotropy. The uniaxial field of BaM was found to be around 16.5 kOe [9, 18]. Applying a magnetic field of this value or higher along the easy axis of the film causes all the electron spins to align themselves in the direction of the magnetic field, removing the magnetic field then will leave a large remnant magnetization within the BaM film owing to its uniaxial anisotropy. Namely, the film becomes self-biased and does not require an external field to magnetize it.

An LSSE experiment and its results using a Pt/BaM heterostructure [18] will be discussed next. In this experiment the sample consisted of a micron-thick BaM layer, topped with a 2.5-nm-thick Pt layer. The BaM layer was grown on a 0.5 mm sapphire substrate. The easy axis of the BaM film was in the plane of the film.

**Figure 6** shows the experiment setup and results. **Figure 6a** shows a schematic diagram of the experimental setup that was used to test LSSE within the sample. The sample was put on an aluminum plate to act as a heat sink. An incandescent light bulb was placed directly on top of the sample, acting as the heat source. The easy axis of the BaM layer was along the *y*-axis, and the voltage was measured along the *x*-axis. All measurements were performed without an external magnetic field. However, a magnetic field of 10 kOe was used prior to the experiment to set the magnetization *M* of the BaM film in the positive (or negative) *y* direction.

will be zero when *M* is parallel to *E*ISHE.

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

magnetic field is required to saturate them.

**45**

*E*ISHE ∝*Js σ* (4)

### *3.2.1 The spin Seebeck effect*

The traditional Seebeck effect, first discovered by Thomas Seebeck in 1821 [34], refers to the generation of electric potential in a conductor when a temperature gradient is applied to it. The electric potential is caused by charge carriers within the conductor moving from the hot region to the cold region. A thermocouple consists of two dissimilar conductors that are joined to form a junction; when a heat gradient is applied across the thermocouple (see **Figure 5a**), a voltage difference can be observed across them. The sign of the voltage flips when the direction of the temperature gradient is flipped. The traditional Seebeck effect is the basic principle behind most thermoelectric generators.

The spintronic equivalent of the traditional Seebeck effect, called the spin Seebeck effect, was first discovered in 2008 [19, 28]. SSE is a phenomenon that can be observed in ferromagnetic and ferrimagnetic materials when a heat gradient is applied to them [19, 28, 35]. The heat gradient induces a spin voltage in the ferromagnet that can be used to inject pure spin currents into a conductor attached to the ferromagnet. Here, spin voltage is a potential for the spin of electrons, rather than their charge, to drive spin current [19, 36–38]. Previously mentioned bilayer heterostructures of normal metal/magnetic material have been used to study the SSE in two different configurations: transverse and longitudinal [19, 39]. In the transverse configuration, the generated spin current is perpendicular to the temperature gradient [28]. The generated spin current in the longitudinal configuration is parallel to the temperature gradient [19] (see **Figure 5b**). The longitudinal configuration has been the dominant choice for SSE research, owing to its simplicity [19]. Magnetic insulators (such as YIG, BaM, etc.) offer an ideal platform for observing the longitudinal spin Seebeck effect (LSSE) [19, 40]. In a conductive ferromagnet, the longitudinal configuration can give rise to a large anomalous Nernst effect (ANE)-induced voltage, which makes it difficult to distinguish between ANE and SSE [19, 33, 41, 42].

If SSE generates pure spin currents, then an important question would be how do we measure them? The absence of charge flow makes it impossible to use conventional methods to measure the spin currents. One way to measure LSSEgenerated spin current is to first convert it into a charge current that can then be measured by conventional means. In this context, the choice of the normal metal in

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

**3.2 Generation of pure spin currents through SSE using NM/BaM structures**

The spintronic equivalent of the traditional Seebeck effect, called the spin Seebeck effect, was first discovered in 2008 [19, 28]. SSE is a phenomenon that can be observed in ferromagnetic and ferrimagnetic materials when a heat gradient is applied to them [19, 28, 35]. The heat gradient induces a spin voltage in the ferromagnet that can be used to inject pure spin currents into a conductor attached to the ferromagnet. Here, spin voltage is a potential for the spin of electrons, rather than their charge, to drive spin current [19, 36–38]. Previously mentioned bilayer heterostructures of normal metal/magnetic material have been used to study the SSE in two different configurations: transverse and longitudinal [19, 39]. In the transverse configuration, the generated spin current is perpendicular to the temperature gradient [28]. The generated spin current in the longitudinal configuration is parallel to the temperature gradient [19] (see **Figure 5b**). The longitudinal configuration has been the dominant choice for SSE research, owing to its simplicity [19]. Magnetic insulators (such as YIG, BaM, etc.) offer an ideal platform for observing the longitudinal spin Seebeck effect (LSSE) [19, 40]. In a conductive ferromagnet, the longitudinal configuration can give rise to a large anomalous Nernst effect (ANE)-induced voltage, which makes it difficult to distinguish

If SSE generates pure spin currents, then an important question would be how

do we measure them? The absence of charge flow makes it impossible to use conventional methods to measure the spin currents. One way to measure LSSEgenerated spin current is to first convert it into a charge current that can then be measured by conventional means. In this context, the choice of the normal metal in

*Schematic illustrations of (a) the conventional Seebeck effect and (b) longitudinal spin Seebeck effect.*

The traditional Seebeck effect, first discovered by Thomas Seebeck in 1821 [34], refers to the generation of electric potential in a conductor when a temperature gradient is applied to it. The electric potential is caused by charge carriers within the conductor moving from the hot region to the cold region. A thermocouple consists of two dissimilar conductors that are joined to form a junction; when a heat gradient is applied across the thermocouple (see **Figure 5a**), a voltage difference can be observed across them. The sign of the voltage flips when the direction of the temperature gradient is flipped. The traditional Seebeck effect is the basic principle

**and photo-spin-voltaic effect in Pt/BaM structure**

*3.2.1 The spin Seebeck effect*

*Magnetic Materials and Magnetic Levitation*

behind most thermoelectric generators.

between ANE and SSE [19, 33, 41, 42].

**Figure 5.**

**44**

the bilayer heterostructure becomes very important. Heavy metals, such as Pt and Au, have strong spin-orbit coupling [43, 44], offering an effective mechanism to convert a transverse spin current into a longitudinal charge current through inverse spin Hall effect (ISHE) [43, 45–47]. The ISHE charge current across the heavy metal surface creates an electric field *E*ISHE that can be measured with a voltmeter. The magnitude and sign of *E*ISHE depend on internal and external factors. In **Figure 5b**, an external magnetic field *H* is applied in the *x* direction. The magnetization *M* of the MI layer is aligned to the *x* direction as well. The temperature gradient is applied across the *z* direction, generating a spin voltage in the MI layer, injecting spin current across the interface and into the normal metal layer parallel to the temperature gradient. The polarity of electron spins in the normal metal layer is influenced by *M* from the MI layer. The ISHE field, *E*ISHE, is measured across the *y* direction. *E*ISHE is proportional to the cross product of the spatial direction of the generated spin current *Js* and the polarity vector of electron spins in the normal metal layer. The following equation explains the relationship between *E*ISHE, *Js*, and *σ* [19]:

$$E\_{\rm ISEE} \propto J\_s \times \sigma \tag{4}$$

In summary, the voltage measured across the normal metal surface is strongest when *M* is perpendicular to both the heat gradient and *E*ISHE; the voltage will flip its sign if *M* is flipped by flipping the external magnetic field *H*; the voltage measured will be zero when *M* is parallel to *E*ISHE.

This discussion sheds light on the importance of the existence of an external magnetic field *H* to enable *E*ISHE when using soft magnetic insulators such as spinels and garnets. A strong enough *H* is necessary to saturate the magnetization of such insulators, as well as to control the direction of the magnetization. Indeed, SSE cannot be observed in samples incorporating spinels or garnets with a temperature gradient alone. Due to their low remnant magnetization, an appropriate external magnetic field is required to saturate them.

An exception to the external magnetic field requirement is made when using BaM thin films due to their strong uniaxial anisotropy [18]. In the absence of an external magnetic field, the magnetization of BaM films, caused by the spins of unpaired electrons, tend to favor one axis, called the easy axis, over any other axis. Thus, most electron spins within the BaM film tend to align themselves with the easy axis, randomly up or down, in the absence of an external magnetic field. Therefore, BaM films have uniaxial anisotropy. The uniaxial field of BaM was found to be around 16.5 kOe [9, 18]. Applying a magnetic field of this value or higher along the easy axis of the film causes all the electron spins to align themselves in the direction of the magnetic field, removing the magnetic field then will leave a large remnant magnetization within the BaM film owing to its uniaxial anisotropy. Namely, the film becomes self-biased and does not require an external field to magnetize it.

An LSSE experiment and its results using a Pt/BaM heterostructure [18] will be discussed next. In this experiment the sample consisted of a micron-thick BaM layer, topped with a 2.5-nm-thick Pt layer. The BaM layer was grown on a 0.5 mm sapphire substrate. The easy axis of the BaM film was in the plane of the film.

**Figure 6** shows the experiment setup and results. **Figure 6a** shows a schematic diagram of the experimental setup that was used to test LSSE within the sample. The sample was put on an aluminum plate to act as a heat sink. An incandescent light bulb was placed directly on top of the sample, acting as the heat source. The easy axis of the BaM layer was along the *y*-axis, and the voltage was measured along the *x*-axis. All measurements were performed without an external magnetic field. However, a magnetic field of 10 kOe was used prior to the experiment to set the magnetization *M* of the BaM film in the positive (or negative) *y* direction.

#### **Figure 6.**

*Light-induced generation of spin currents. (a) The experimental setup. (b) and (c) Respective voltage signals measured for M*∥*y and M*∥*(y), in response to the light that was turned on at 100s then turned off at 200s. The graphs also show the responses of the temperature difference (*Δ*T) between the top and bottom of the Pt/BaM/ Saphire structure. (d) Voltage amplitude as a function of* Δ*T. Source: [18], p. 3.*

The heat from the light bulb, along with the aluminum plate acting as a heat sink, created the temperature gradient across the BaM film thickness; the difference in temperature between the bottom surface and top surface of BaM, Δ*T*, was measured using two thermocouples connected to them. When the light is turned on, SSE occurs, the heat gradient induces a spin voltage in the BaM film that injects spin currents across the interface and into the Pt layer. Due to ISHE, the spin current is converted to a charge current across the Pt surface creating a voltage. The voltage was measured by connecting a nanovoltmeter to the opposite ends of the Pt surface across the *x*-axis.

Using a Peltier cooler as an added source for the temperature gradient in addi-

*Control measurements. (a) Voltage changes caused by moving the bulb along the x-axis. (b) Voltage and* Δ*T signals obtained when both a bulb and a Peltier cooler were used to control the temperature. The data in (a) and (b) were obtained with the same sample as Figure 6. (c) SSE in a Pt(2.5 nm)/BaM(0.4 μm)/sapphire (0.5 mm) sample. (d) Voltage and* Δ*T signals obtained with a Cu(9 nm)/BaM(1.2 μm)/sapphire (0.5 mm)*

The importance of using a metal with strong spin-orbit coupling is demonstrated through **Figure 7d**, where Cu, which has very weak spin-orbit coupling, and therefore very weak ISHE, was used in a Cu (9 nm)/BaM (1.2 μm)/sapphire (0.5 mm) sample. The figure shows a behavior that is different from the Pt/BaM samples, indicating the absence of SSE in this sample. A likely source for the signal shown in **Figure 7d** is the conventional Seebeck effect, caused by a temperature gradient across the sample's length. (All figures, experimentation setup and results were

A closely related but fundamentally different effect to SSE is the photo-spinvoltaic effect (PSVE). PSVE happens in NM/MI heterostructures; it generates pure spin currents across the NM thickness that can be measured through ISHE. Light can generate spin voltage and drive spin currents through PSVE. While the spin voltage is generated in the MI layer in the SSE case, the spin voltage in PSVE is

tion to the light bulb also did not have a noticeable change in the relationship between the measured voltage and Δ*T*. This is shown in **Figure 7b**, where a light source was used to create Δ*T*, and a Peltier cooler was turned on under the sample midway through. **Figure 7c** shows the voltage change with time for a similar sample with a BaM layer thickness of 0.4 μm, and only a Peltier cooler was used to create the temperature gradient. Both **Figure 7b** and **c** show the same result: the measured voltage is directly related to Δ*T*, regardless of the method used to achieve Δ*T*.

taken from [18] with appropriate permissions).

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

*3.2.2 Photo-spin-voltaic effect*

**47**

**Figure 7.**

*sample. Source: [18], p. 3.*

**Figures 6b** and **c** demonstrate the relationship between the difference in temperatures Δ*T* and the generated voltage, with time, for *M*∥*y* and *M*∥*y*, respectively. Δ*T* was changed by changing the height of the light bulb. These results show that the SSE-generated spin current, and therefore the observed voltage, changes in exactly the same manner that Δ*T* changes with. This result is expected as the difference in temperature is what causes the spin voltage in the BaM film, which ultimately gives us the voltage reading across the Pt layer.

**Figure 6d** shows an important property of SSE, namely, the sign of the generated voltage flips when the direction of the BaM magnetization is flipped. The graph shows the relationship between Δ*T* and measured voltage for *M*∥*y* (red) and *M*∥*y* (blue). The result again proves that the voltage change with respect to Δ*T* is identical (mirrored when *M*∥*y* due to the sign flip), in both cases.

Control measurements were performed and are shown in **Figure 7**. Changing the lateral position of the light bulb did not have any noticeable effect on the measured voltage. This is to be expected, as the temperature gradient depends on the height of the light bulb, rather than its lateral position. This is demonstrated in **Figure 7a**, where the light position was changed to six different lateral positions. The figure shows that, other than jumps from electrical disturbance caused by the position change, the measured voltage remained largely unchanged.

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

**Figure 7.**

The heat from the light bulb, along with the aluminum plate acting as a heat sink, created the temperature gradient across the BaM film thickness; the difference in temperature between the bottom surface and top surface of BaM, Δ*T*, was measured using two thermocouples connected to them. When the light is turned on, SSE occurs, the heat gradient induces a spin voltage in the BaM film that injects spin currents across the interface and into the Pt layer. Due to ISHE, the spin current is converted to a charge current across the Pt surface creating a voltage. The voltage was measured by connecting a nanovoltmeter to the opposite ends of the Pt surface

*Light-induced generation of spin currents. (a) The experimental setup. (b) and (c) Respective voltage signals measured for M*∥*y and M*∥*(y), in response to the light that was turned on at 100s then turned off at 200s. The graphs also show the responses of the temperature difference (*Δ*T) between the top and bottom of the Pt/BaM/*

**Figures 6b** and **c** demonstrate the relationship between the difference in temperatures Δ*T* and the generated voltage, with time, for *M*∥*y* and *M*∥*y*, respectively. Δ*T* was changed by changing the height of the light bulb. These results show that the SSE-generated spin current, and therefore the observed voltage, changes in exactly the same manner that Δ*T* changes with. This result is expected as the difference in temperature is what causes the spin voltage in the BaM film, which

**Figure 6d** shows an important property of SSE, namely, the sign of the generated voltage flips when the direction of the BaM magnetization is flipped. The graph shows the relationship between Δ*T* and measured voltage for *M*∥*y* (red) and *M*∥*y* (blue). The result again proves that the voltage change with respect to Δ*T* is

Control measurements were performed and are shown in **Figure 7**. Changing the lateral position of the light bulb did not have any noticeable effect on the measured voltage. This is to be expected, as the temperature gradient depends on the height of the light bulb, rather than its lateral position. This is demonstrated in **Figure 7a**, where the light position was changed to six different lateral positions. The figure shows that, other than jumps from electrical disturbance caused by the position

ultimately gives us the voltage reading across the Pt layer.

*Saphire structure. (d) Voltage amplitude as a function of* Δ*T. Source: [18], p. 3.*

*Magnetic Materials and Magnetic Levitation*

change, the measured voltage remained largely unchanged.

identical (mirrored when *M*∥*y* due to the sign flip), in both cases.

across the *x*-axis.

**46**

**Figure 6.**

*Control measurements. (a) Voltage changes caused by moving the bulb along the x-axis. (b) Voltage and* Δ*T signals obtained when both a bulb and a Peltier cooler were used to control the temperature. The data in (a) and (b) were obtained with the same sample as Figure 6. (c) SSE in a Pt(2.5 nm)/BaM(0.4 μm)/sapphire (0.5 mm) sample. (d) Voltage and* Δ*T signals obtained with a Cu(9 nm)/BaM(1.2 μm)/sapphire (0.5 mm) sample. Source: [18], p. 3.*

Using a Peltier cooler as an added source for the temperature gradient in addition to the light bulb also did not have a noticeable change in the relationship between the measured voltage and Δ*T*. This is shown in **Figure 7b**, where a light source was used to create Δ*T*, and a Peltier cooler was turned on under the sample midway through. **Figure 7c** shows the voltage change with time for a similar sample with a BaM layer thickness of 0.4 μm, and only a Peltier cooler was used to create the temperature gradient. Both **Figure 7b** and **c** show the same result: the measured voltage is directly related to Δ*T*, regardless of the method used to achieve Δ*T*.

The importance of using a metal with strong spin-orbit coupling is demonstrated through **Figure 7d**, where Cu, which has very weak spin-orbit coupling, and therefore very weak ISHE, was used in a Cu (9 nm)/BaM (1.2 μm)/sapphire (0.5 mm) sample. The figure shows a behavior that is different from the Pt/BaM samples, indicating the absence of SSE in this sample. A likely source for the signal shown in **Figure 7d** is the conventional Seebeck effect, caused by a temperature gradient across the sample's length. (All figures, experimentation setup and results were taken from [18] with appropriate permissions).

#### *3.2.2 Photo-spin-voltaic effect*

A closely related but fundamentally different effect to SSE is the photo-spinvoltaic effect (PSVE). PSVE happens in NM/MI heterostructures; it generates pure spin currents across the NM thickness that can be measured through ISHE. Light can generate spin voltage and drive spin currents through PSVE. While the spin voltage is generated in the MI layer in the SSE case, the spin voltage in PSVE is

generated in the atomic layers of the NM that are close to the interface due to magnetic proximity effect [48]. When light of a certain wavelength hits the sample, photons excite electrons in the Pt layer, causing them to move to higher energy bands. The efficiency of this photon-driven excitation varies because of the spin orientation. The difference in efficiency, along with different diffusion rates of excited electrons and holes, generates the spin voltage through PSVE [48].

**Figure 8** shows PSVE in a Pt/MI structure. An important question arises due to the extremely similar setup of both LSSE and PSVE: how can we determine the source of the ISHE generated voltage? It could be due to LSSE, or PSVE, or both. Fortunately, research in this area determined several distinguishable factors that make it possible to disentangle LSSE from PSVE. The most important factor is the wavelength of the light used to excite the sample. Experimental results determined that PSVE can only be observed when the wavelength of the light used falls in the range 1600–2000 nm [48]. Using a light source with a wavelength outside that range or a heat source other than light, such as a Peltier cooler, will only give us LSSE in our sample and no PSVE [49]. Other factors include the type of materials and device geometries used in the studies. For example, different MI types and thicknesses give widely different signals in LSSE. A recent work showed that the main contribution in the voltage comes from LSSE rather than PSVE [50]. However, experiments have shown that using a light source with the appropriate wavelength gives extremely similar results in Pt that is coupled with MI of varying types and thicknesses [48].

**Figure 9** shows the results of PSVE in three different samples: Pt (2.5 nm)/YIG (78 μm), Pt (2.5 nm)/YIG (21 nm), and Pt (2.5 nm)/BaM (1.2 μm). For each sample, three different experimental setup configurations were tested: illuminating from the sample's top, illuminating from the sample's bottom, and illuminating from both the top and bottom of the sample. The phenomena of PSVE in all cases were similar, with a difference that is no bigger than an order of magnitude. This confirms that the voltage is induced by PSVE instead of SEE. Only the sign of the voltage, but not its magnitude, flipped with the flipping of the magnetization of the MI film; this confirms the spin origin of the measured voltage. (All the PSVE information and experimental setup and discussion were taken from [48] with appropriate permissions).

**3.3 Spin-orbit torque-assisted switching in magnetic insulators**

magnetic memory systems commercially [51].

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

considerably [51].

**49**

**Figure 9.**

The uniaxial anisotropy and the nonvolatile nature of easy axis-aligned magnetization within the BaM film can be used to design memory and logic-based systems. If the magnetization is up, it will keep its direction until a magnetic field flips it toward the opposite direction. If an efficient way can be found to switch the magnetization states of the magnetic insulator thin films, then they can be used in

*Measurements for different illumination/magnetization configurations for three different samples Pt (2.5 nm)/*

*YIG (78 μm), Pt (2.5 nm)/YIG (21 nm), and Pt (2.5 nm)/BaM (1.2 μm). Source: [48], p. 863.*

In a NM/MI structure, such as Pt/BaM, SHE can be used to convert a charge current across the Pt surface into a spin current that flows across the thickness of Pt through spin-orbit coupling; this process will accumulate spins at the Pt/BaM interface. The spin accumulation generates spin-orbit torques (SOTs) that can be used to switch the BaM magnetization. Each electron provided by the charge current can undergo several spin-flip scatterings at the interface, breaking the conventional spin-torque switching limit and increasing the switching efficiency

We discuss the SOT experimental details of a Pt(5 nm)/BaM(3 nm) sample. The easy axis of the BaM film was perpendicular to the surface of the film. **Figure 10b** shows the hysteresis loop of the film, measured by a vibrating sample magnetometer, when an out-of-plane external magnetic field was applied (red curve). The olive curve shows the hysteresis loop along the hard axis when the external magnetic field is applied in the plane of the film. This figure confirms the perpendicular uniaxial anisotropy of the film, with a perpendicular anisotropy field of 17.6 kOe. A

Hall bar structure was fabricated out of the Pt/BaM bilayer and is shown in

for the gauging of *M*<sup>⊥</sup> in the BaM film by simply measuring *R*AHE.

**Figure 10a**. **Figure 10c** shows a hysteresis loop on the Hall resistance, revealing an anomalous Hall effect (AHE)-like behavior. It is unclear whether the AHE-like behavior is from magnetic proximity effect or spin Hall magnetoresistance. However, *R*AHE behaves in a very similar manner to the perpendicular magnetization component of the BaM film *M*<sup>⊥</sup> (compare **Figure 10b** to **Figure 10c**). This allows

The first experiment demonstrated was the out-of-plane switching; the external magnetic field is fixed out of the film's plane and 20° off the easy axis. The purpose of this tilt was to break the magnetization symmetry due to the external field,

#### **Figure 8.**

*(a) Photo-spin-voltaic effect in Pt/MI bilayer heterostructure. (b) Sketch of the physical mechanism underlying PSVE. When light illuminates the sample, photons excite electrons and generate nonequilibrium hot electrons and holes in the Pt atomic layers that are in proximity to the MI (the gridded region). The excited electrons and holes diffuse from Pt/MI interface to the Pt interface (along the +z direction), giving rise to spin currents (J*<sup>e</sup> *and J*h*). Source: [48], pp. 861, 865.*

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

#### **Figure 9.**

generated in the atomic layers of the NM that are close to the interface due to magnetic proximity effect [48]. When light of a certain wavelength hits the sample, photons excite electrons in the Pt layer, causing them to move to higher energy bands. The efficiency of this photon-driven excitation varies because of the spin orientation. The difference in efficiency, along with different diffusion rates of excited electrons and holes, generates the spin voltage through PSVE [48].

*Magnetic Materials and Magnetic Levitation*

and thicknesses [48].

permissions).

**Figure 8.**

**48**

*J*h*). Source: [48], pp. 861, 865.*

**Figure 8** shows PSVE in a Pt/MI structure. An important question arises due to the extremely similar setup of both LSSE and PSVE: how can we determine the source of the ISHE generated voltage? It could be due to LSSE, or PSVE, or both. Fortunately, research in this area determined several distinguishable factors that make it possible to disentangle LSSE from PSVE. The most important factor is the wavelength of the light used to excite the sample. Experimental results determined that PSVE can only be observed when the wavelength of the light used falls in the range 1600–2000 nm [48]. Using a light source with a wavelength outside that range or a heat source other than light, such as a Peltier cooler, will only give us LSSE in our sample and no PSVE [49]. Other factors include the type of materials and device geometries used in the studies. For example, different MI types and thicknesses give widely different signals in LSSE. A recent work showed that the main contribution in the voltage comes from LSSE rather than PSVE [50]. However, experiments have shown that using a light source with the appropriate wavelength gives extremely similar results in Pt that is coupled with MI of varying types

**Figure 9** shows the results of PSVE in three different samples: Pt (2.5 nm)/YIG (78 μm), Pt (2.5 nm)/YIG (21 nm), and Pt (2.5 nm)/BaM (1.2 μm). For each sample, three different experimental setup configurations were tested: illuminating from the sample's top, illuminating from the sample's bottom, and illuminating from both the top and bottom of the sample. The phenomena of PSVE in all cases were similar, with a difference that is no bigger than an order of magnitude. This confirms that the voltage is induced by PSVE instead of SEE. Only the sign of the voltage, but not its magnitude, flipped with the flipping of the magnetization of the MI film; this confirms the spin origin of the measured voltage. (All the PSVE information and experimental setup and discussion were taken from [48] with appropriate

*(a) Photo-spin-voltaic effect in Pt/MI bilayer heterostructure. (b) Sketch of the physical mechanism underlying PSVE. When light illuminates the sample, photons excite electrons and generate nonequilibrium hot electrons and holes in the Pt atomic layers that are in proximity to the MI (the gridded region). The excited electrons and holes diffuse from Pt/MI interface to the Pt interface (along the +z direction), giving rise to spin currents (J*<sup>e</sup> *and*

*Measurements for different illumination/magnetization configurations for three different samples Pt (2.5 nm)/ YIG (78 μm), Pt (2.5 nm)/YIG (21 nm), and Pt (2.5 nm)/BaM (1.2 μm). Source: [48], p. 863.*

#### **3.3 Spin-orbit torque-assisted switching in magnetic insulators**

The uniaxial anisotropy and the nonvolatile nature of easy axis-aligned magnetization within the BaM film can be used to design memory and logic-based systems. If the magnetization is up, it will keep its direction until a magnetic field flips it toward the opposite direction. If an efficient way can be found to switch the magnetization states of the magnetic insulator thin films, then they can be used in magnetic memory systems commercially [51].

In a NM/MI structure, such as Pt/BaM, SHE can be used to convert a charge current across the Pt surface into a spin current that flows across the thickness of Pt through spin-orbit coupling; this process will accumulate spins at the Pt/BaM interface. The spin accumulation generates spin-orbit torques (SOTs) that can be used to switch the BaM magnetization. Each electron provided by the charge current can undergo several spin-flip scatterings at the interface, breaking the conventional spin-torque switching limit and increasing the switching efficiency considerably [51].

We discuss the SOT experimental details of a Pt(5 nm)/BaM(3 nm) sample. The easy axis of the BaM film was perpendicular to the surface of the film. **Figure 10b** shows the hysteresis loop of the film, measured by a vibrating sample magnetometer, when an out-of-plane external magnetic field was applied (red curve). The olive curve shows the hysteresis loop along the hard axis when the external magnetic field is applied in the plane of the film. This figure confirms the perpendicular uniaxial anisotropy of the film, with a perpendicular anisotropy field of 17.6 kOe. A Hall bar structure was fabricated out of the Pt/BaM bilayer and is shown in **Figure 10a**. **Figure 10c** shows a hysteresis loop on the Hall resistance, revealing an anomalous Hall effect (AHE)-like behavior. It is unclear whether the AHE-like behavior is from magnetic proximity effect or spin Hall magnetoresistance. However, *R*AHE behaves in a very similar manner to the perpendicular magnetization component of the BaM film *M*<sup>⊥</sup> (compare **Figure 10b** to **Figure 10c**). This allows for the gauging of *M*<sup>⊥</sup> in the BaM film by simply measuring *R*AHE.

The first experiment demonstrated was the out-of-plane switching; the external magnetic field is fixed out of the film's plane and 20° off the easy axis. The purpose of this tilt was to break the magnetization symmetry due to the external field,

the direction of pure spin current-generated SOTs near the interface, the magnitude of which is proportional to the intensity of the supplied current. Flipping the direction of the supplied charge currents flips the direction of the SOT as shown in **Figure 11b**. The resultant hysteresis loops, shown in **Figure 11d**, become narrower as the supplied charge current increases, indicating that SOT, in the direction of *H*, assisted in the magnetization flipping, reducing the overall total external field

Further experiments were performed to confirm the existence of spin currentgenerated SOT near the Pt/BaM interface. This time, the external field *H* was within the film plane. This means that applying a saturation field in the film plane will align the electron spins along the hard axis of the BaM film. When *H* is removed, the spins will return to their easy axis, randomly up or down, resulting in a net *M*<sup>⊥</sup> of zero. However, when a charge current is supplied to the Pt surface, SOT near the interface will influence the direction of the spins of electrons when *H* is reduced and they start to align to their easy axis. This results in remnant magnetization that is represented by a hysteresis loop. If the direction of the supplied charge current is flipped, the resultant hysteresis loop will be the opposite of the first hysteresis loop. This is shown in **Figure 12**. This confirms that the direction of the SOT can be

These results confirm that SOT due to pure spin currents, generated by SHE in Pt/BaM structures, can be used to assist the magnetization switching in BaM films. It should be noted however, that SHE generates two different torques: a dampinglike torque (DLT) and a field-like torque (FLT). The effective fields for DLT and FLT are *H*DLT and *H*FLT, respectively. Thus, the total field affecting *M*<sup>⊥</sup> of the BaM

where *H* is the external field as indicated in **Figure 11**, *H*<sup>a</sup> is the anisotropy field

Carrying out both simulations involved three main steps: first, *H*<sup>c</sup> was calculated when *J*<sup>c</sup> is set to zero. *H*DLT and *H*FLT were both set to zero as well. *H*<sup>a</sup> was set such that when *H* is equal to the experimentally measured *H*<sup>c</sup> and pointing in the direction opposite to its initial direction, *m* flips. The second step considers the case when

*Anomalous Hall resistance R*AHE *measured as a function of a magnetic field along the* y *axis for* I*= +6 mA and*

of the BaM film, and *x* is the unit vector along the +*x* direction. Two different simulation models were carried out to determine the SOT field strength: macrospin

*H*total ¼ *H* þ *H*<sup>a</sup> þ *H*FLT*x* þ *H*DLTð Þ *m* � *x* (5)

controlled by changing the sign of the supplied charge current.

needed to flip *M*<sup>⊥</sup> in the BaM film.

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

film can be written as follows [51]:

**Figure 12.**

**51**

I*=* �*6 mA, respectively. Source: [51], p. 5.*

model simulation and microspin model simulation.

**Figure 10.**

*(a) Optical image of the Pt (5 nm)/BaM (3 nm) Hall bar structure. (b) Magnetic hysteresis loops of the BaM film. (c) Anomalous Hall resistance R*AHE *of the Hall bar measured as a function of a magnetic field. The inset is a schematic showing the magnetic field H direction which is in the yz plane and 20 degrees away from the +z axis. Source: [51], p. 3.*

allowing for the observation of the SOT effect. One would expect that if the SOT field is along the -*z* direction, it would act against the external field, thereby increasing the total field required to saturate the magnetization within the BaM film, while a SOT field along the *z* direction will aid the external field, resulting in a smaller field required to saturate the magnetization of the BaM film.

Indeed, experimental results, shown in **Figure 11**, confirm exactly that. Namely, when charge currents of varying intensities are applied to the Pt film along the *y* direction, the SOT direction is opposite to that of *H* (as shown in **Figure 11a**), and the resultant hysteresis loops, gauged by *R*AHE, become wider as the current intensity increases. This is shown in **Figure 11c**, where the gray loop is for *I* = 0; blue, *I* = 2 mA; olive, *I* = 4 mA; and red, *I* = 6 mA. This confirms the existence and

#### **Figure 11.**

*Switching responses in Pt/BaM for out-of-plane magnetic fields. (a) and (b) Effects of charge currents* I *in the Pt film on switching of the magnetization* M *in the BaM film under an out-of-plane field H. The red spheres with arrows represent spin-polarized electrons deflecting toward the BaM layer.* M *represents the magnetization of BaM. τ represents the spin torque due to SHE. The direction of* H *is indicated in the insert. (c) and (d) Anomalous Hall resistance* R*AHE of the Hall bar measured as a function of a magnetic field for different charge currents. The field was applied 20 degrees away from the z axis, as shown in the insets of (a) and (b). In (c) gray,* I *= 0; blue,* I *= 2 mA; olive,* I *= 4 mA; and red,* I *= 6 mA. In (d) gray,* I *= 0; blue,* I *= 2 mA; olive,* I *= 4mA; and red,* I *= 6 mA. Source: [51], p. 4.*

#### *Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

the direction of pure spin current-generated SOTs near the interface, the magnitude of which is proportional to the intensity of the supplied current. Flipping the direction of the supplied charge currents flips the direction of the SOT as shown in **Figure 11b**. The resultant hysteresis loops, shown in **Figure 11d**, become narrower as the supplied charge current increases, indicating that SOT, in the direction of *H*, assisted in the magnetization flipping, reducing the overall total external field needed to flip *M*<sup>⊥</sup> in the BaM film.

Further experiments were performed to confirm the existence of spin currentgenerated SOT near the Pt/BaM interface. This time, the external field *H* was within the film plane. This means that applying a saturation field in the film plane will align the electron spins along the hard axis of the BaM film. When *H* is removed, the spins will return to their easy axis, randomly up or down, resulting in a net *M*<sup>⊥</sup> of zero. However, when a charge current is supplied to the Pt surface, SOT near the interface will influence the direction of the spins of electrons when *H* is reduced and they start to align to their easy axis. This results in remnant magnetization that is represented by a hysteresis loop. If the direction of the supplied charge current is flipped, the resultant hysteresis loop will be the opposite of the first hysteresis loop. This is shown in **Figure 12**. This confirms that the direction of the SOT can be controlled by changing the sign of the supplied charge current.

These results confirm that SOT due to pure spin currents, generated by SHE in Pt/BaM structures, can be used to assist the magnetization switching in BaM films. It should be noted however, that SHE generates two different torques: a dampinglike torque (DLT) and a field-like torque (FLT). The effective fields for DLT and FLT are *H*DLT and *H*FLT, respectively. Thus, the total field affecting *M*<sup>⊥</sup> of the BaM film can be written as follows [51]:

$$H\_{\text{total}} = H + H\_{\text{a}} + H\_{\text{FLT}}\infty + H\_{\text{DLT}}(m \times \infty) \tag{5}$$

where *H* is the external field as indicated in **Figure 11**, *H*<sup>a</sup> is the anisotropy field of the BaM film, and *x* is the unit vector along the +*x* direction. Two different simulation models were carried out to determine the SOT field strength: macrospin model simulation and microspin model simulation.

Carrying out both simulations involved three main steps: first, *H*<sup>c</sup> was calculated when *J*<sup>c</sup> is set to zero. *H*DLT and *H*FLT were both set to zero as well. *H*<sup>a</sup> was set such that when *H* is equal to the experimentally measured *H*<sup>c</sup> and pointing in the direction opposite to its initial direction, *m* flips. The second step considers the case when

#### **Figure 12.**

*Anomalous Hall resistance R*AHE *measured as a function of a magnetic field along the* y *axis for* I*= +6 mA and* I*=* �*6 mA, respectively. Source: [51], p. 5.*

allowing for the observation of the SOT effect. One would expect that if the SOT field is along the -*z* direction, it would act against the external field, thereby increasing the total field required to saturate the magnetization within the BaM film, while a SOT field along the *z* direction will aid the external field, resulting in a

*(a) Optical image of the Pt (5 nm)/BaM (3 nm) Hall bar structure. (b) Magnetic hysteresis loops of the BaM film. (c) Anomalous Hall resistance R*AHE *of the Hall bar measured as a function of a magnetic field. The inset is a schematic showing the magnetic field H direction which is in the yz plane and 20 degrees away from the +z*

Indeed, experimental results, shown in **Figure 11**, confirm exactly that. Namely, when charge currents of varying intensities are applied to the Pt film along the *y* direction, the SOT direction is opposite to that of *H* (as shown in **Figure 11a**), and the resultant hysteresis loops, gauged by *R*AHE, become wider as the current intensity increases. This is shown in **Figure 11c**, where the gray loop is for *I* = 0; blue, *I* = 2 mA; olive, *I* = 4 mA; and red, *I* = 6 mA. This confirms the existence and

*Switching responses in Pt/BaM for out-of-plane magnetic fields. (a) and (b) Effects of charge currents* I *in the Pt film on switching of the magnetization* M *in the BaM film under an out-of-plane field H. The red spheres with arrows represent spin-polarized electrons deflecting toward the BaM layer.* M *represents the magnetization of BaM. τ represents the spin torque due to SHE. The direction of* H *is indicated in the insert. (c) and (d) Anomalous Hall resistance* R*AHE of the Hall bar measured as a function of a magnetic field for different charge currents. The field was applied 20 degrees away from the z axis, as shown in the insets of (a) and (b). In (c) gray,* I *= 0; blue,* I *= 2 mA; olive,* I *= 4 mA; and red,* I *= 6 mA. In (d) gray,* I *= 0; blue,* I *= 2 mA;*

smaller field required to saturate the magnetization of the BaM film.

**Figure 10.**

**Figure 11.**

**50**

*olive,* I *= 4mA; and red,* I *= 6 mA. Source: [51], p. 4.*

*axis. Source: [51], p. 3.*

*Magnetic Materials and Magnetic Levitation*

*J*<sup>c</sup> 6¼ 0 and *H*FLT = 0. Simulations are then performed at given *H*DLT values to find the corresponding *H*<sup>c</sup> values. This is because a flip in the direction of *H*DLT breaks the symmetry, thereby affecting *H*c. A flip in the direction of *H*FLT on the other hand does not affect *H*<sup>c</sup> as *H*FLT is orthogonal to *H*a, *H*, and *m*. The third step considers non-zero values of *H*DLT and repeats the simulations to find *H*<sup>c</sup> for given combinations of *H*DLT and *H*FLT values.

states are time-reversal symmetry-protected. Due to the very strong spin-orbit coupling of TIs [10, 52], if a charge current is supplied to their surface, the surface states induce spin polarity and therefore generate a spin current, owing to the SHE. The SHE in TIs is several times stronger than in heavy metals such as Pt, and it can

Theoretically, the very strong SHE in a TI can generate SOT that is much stronger than its counterpart in heavy metals. This strong SOT can then be exploited for magnetization switching by pairing it with a ferromagnet, similar to what was discussed in the previous section. Using a conductive ferromagnet, however, can completely suppress the surface states of a TI [49–56], preventing the generation of spin currents, therefore making it impossible for SOT magnetization

Here, the usefulness and importance of magnetic insulators are again empha-

In another experiment, the authors used a Bi2Se3/BaM heterostructure to explore the effect of topological surface state in switching the magnetization of a magnetic insulator [10]. The BaM layer used had similar characteristics to the BaM layer used in the Pt/BaM experiment. The BaM film was 5-nm-thick and had a uniaxial anisotropy axis perpendicular to the surface, as shown by the two hysteresis loops in **Figure 15a**. The blue hysteresis loop was measured when the external field was applied perpendicular to the BaM film's surface. The red loop was measured when an external field was applied along the BaM film plane. The two loops together confirm the perpendicular orientation of the anisotropy axis of the BaM film.

A Hall bar was fabricated on the Bi2Se3/BaM bilayer film. **Figure 15c** shows that, similar to the Hall bar setup of the Pt/BaM experiment discussed in the previous section, the AHE contribution to the Hall bar resistance, *R*AHE, scales with the

*(a) and (b) Hall traces of TIG/(BixSb1x)2 Te3 for* x *= 0.20 and 0.30, respectively. The upper insets show the corresponding temperature dependence of Rxx. The lower insets show schematic drawings of the corresponding*

sized. Pairing a TI with MI keeps the integrity of the surface states. Various materials can be used to create a TI, such as (Bi*x*Sb1-*x*)2 Te3. The choice of *x* can ensure protection from time-reversal symmetry. **Figure 14a** and **b** show the sheet

resistance measurements of a (Bi*x*Sb1-*x*)2Te3 film that was grown on a MI (Tm3Fe5O12, TIG) for *x* = 0.2 and *x* = 0.3, respectively. The lower inset of both figures show the broken symmetry of the topological surface states of both configurations. The sheet resistance in both figures shows a linear portion, attributed to the normal Hall effect, and a hysteresis loop portion. The different slopes indicate opposite carriers in each sample. The hysteresis portion indicates strong magnetic uniaxial anisotropy in the TI owing to highly spin-polarized electrons on the TI's surface. This uniaxial anisotropy is maintained at room temperature and

become hundreds of times stronger at very lower temperatures [10].

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

switching to happen in TI/conductive ferromagnet structures.

up to T = 400 K [57].

**Figure 14.**

**53**

*chemical potential position. Source: [57], p. 2.*

The results from running the two different models of simulations were very close and are shown in **Figure 13**. The blue dots show the linear nature of the relationship between *H*<sup>c</sup> and *H*DLT, when *H*FLT = 0. This is similar to the experimental *H*<sup>c</sup> vs. *J*<sup>c</sup> data. The simulation showed that when *H*DLT is -400 Oe, *H*<sup>c</sup> increases to about 2.0 kOe, and when *H*DLT is 400 Oe, *H*<sup>c</sup> decreases to about 0.95 kOe. This same change was experimentally observed when *J*<sup>c</sup> changed between -10<sup>7</sup> A cm�<sup>2</sup> and 10<sup>7</sup> A cm�<sup>2</sup> . Thus, we can conclude that *H*DLT in the Pt/BaM is about 400 Oe at *J*<sup>c</sup> = 10<sup>7</sup> A cm�<sup>2</sup> . The red and olive dots in **Figure 13a** and **b** show the same relationship when *H*FLT = *H*DLT/2 and *H*FLT = *H*DLT, respectively. The red dots show that the effect of *H*FLT is negligible when *H*FLT = *H*DLT/2, while the olive dots show a deviation for strong negative charge currents that was not observed experimentally. The red and olive portions of both figures prove that the majority of the SHE generated torque is due to DLT, with FLT having a relatively small effect in comparison. The experimental results, along with the simulation data, show that SOT in Pt/BaM films can reduce the required switching field by as much as 500 Oe.

Further improvements and enhancements in the switching efficiency can be achieved by using materials with higher spin-orbit coupling, resulting in stronger SOT. Topological insulators exhibit such requirements and will be the topic of the next section. (All figures, experimentation setup, and results were taken from [51] with appropriate permissions).

#### **3.4 Magnetization switching with topological insulators**

Topological insulators (TI) are of great interest in spintronic-related studies. A TI is a material with nontrivial symmetry-protected topological order that behaves as an insulator in its interior but whose surface contains conducting states. What differentiates a TI from other materials with conducting surfaces is that its surface

#### **Figure 13.**

*(a) and (b) Coercivity vs. DLT field (H*DLT*) estimated for three different field-like torque (FLT) fields (H*FLT*) through macrospin and full micromagnetic simulations, respectively. Large blue spheres, H*FLT *= 0; small red spheres, H*FLT *= H*DLT*/2; and small olive spheres, H*FLT *= H*DLT*. The dash line in (a) and (b) is the H*<sup>c</sup> *at I = 0. All the measurements were done at room temperature. Source: [51], p. 4.*

#### *Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

*J*<sup>c</sup> 6¼ 0 and *H*FLT = 0. Simulations are then performed at given *H*DLT values to find the corresponding *H*<sup>c</sup> values. This is because a flip in the direction of *H*DLT breaks the symmetry, thereby affecting *H*c. A flip in the direction of *H*FLT on the other hand does not affect *H*<sup>c</sup> as *H*FLT is orthogonal to *H*a, *H*, and *m*. The third step considers non-zero values of *H*DLT and repeats the simulations to find *H*<sup>c</sup> for given

The results from running the two different models of simulations were very close and are shown in **Figure 13**. The blue dots show the linear nature of the relationship between *H*<sup>c</sup> and *H*DLT, when *H*FLT = 0. This is similar to the experimental *H*<sup>c</sup> vs. *J*<sup>c</sup> data. The simulation showed that when *H*DLT is -400 Oe, *H*<sup>c</sup> increases to about 2.0 kOe, and when *H*DLT is 400 Oe, *H*<sup>c</sup> decreases to about 0.95 kOe. This same change was experimentally observed when *J*<sup>c</sup> changed between -10<sup>7</sup>

same relationship when *H*FLT = *H*DLT/2 and *H*FLT = *H*DLT, respectively. The red dots show that the effect of *H*FLT is negligible when *H*FLT = *H*DLT/2, while the olive dots show a deviation for strong negative charge currents that was not observed experimentally. The red and olive portions of both figures prove that the majority of the SHE generated torque is due to DLT, with FLT having a relatively small effect in comparison. The experimental results, along with the simulation data, show that SOT in Pt/BaM films can reduce the required switching field by as

Further improvements and enhancements in the switching efficiency can be achieved by using materials with higher spin-orbit coupling, resulting in stronger SOT. Topological insulators exhibit such requirements and will be the topic of the next section. (All figures, experimentation setup, and results were taken from [51]

Topological insulators (TI) are of great interest in spintronic-related studies. A TI is a material with nontrivial symmetry-protected topological order that behaves as an insulator in its interior but whose surface contains conducting states. What differentiates a TI from other materials with conducting surfaces is that its surface

*(a) and (b) Coercivity vs. DLT field (H*DLT*) estimated for three different field-like torque (FLT) fields (H*FLT*) through macrospin and full micromagnetic simulations, respectively. Large blue spheres, H*FLT *= 0; small red spheres, H*FLT *= H*DLT*/2; and small olive spheres, H*FLT *= H*DLT*. The dash line in (a) and (b) is the H*<sup>c</sup> *at I = 0.*

. Thus, we can conclude that *H*DLT in the Pt/BaM is about

. The red and olive dots in **Figure 13a** and **b** show the

combinations of *H*DLT and *H*FLT values.

*Magnetic Materials and Magnetic Levitation*

A cm�<sup>2</sup> and 10<sup>7</sup> A cm�<sup>2</sup>

much as 500 Oe.

**Figure 13.**

**52**

400 Oe at *J*<sup>c</sup> = 10<sup>7</sup> A cm�<sup>2</sup>

with appropriate permissions).

**3.4 Magnetization switching with topological insulators**

*All the measurements were done at room temperature. Source: [51], p. 4.*

states are time-reversal symmetry-protected. Due to the very strong spin-orbit coupling of TIs [10, 52], if a charge current is supplied to their surface, the surface states induce spin polarity and therefore generate a spin current, owing to the SHE. The SHE in TIs is several times stronger than in heavy metals such as Pt, and it can become hundreds of times stronger at very lower temperatures [10].

Theoretically, the very strong SHE in a TI can generate SOT that is much stronger than its counterpart in heavy metals. This strong SOT can then be exploited for magnetization switching by pairing it with a ferromagnet, similar to what was discussed in the previous section. Using a conductive ferromagnet, however, can completely suppress the surface states of a TI [49–56], preventing the generation of spin currents, therefore making it impossible for SOT magnetization switching to happen in TI/conductive ferromagnet structures.

Here, the usefulness and importance of magnetic insulators are again emphasized. Pairing a TI with MI keeps the integrity of the surface states. Various materials can be used to create a TI, such as (Bi*x*Sb1-*x*)2 Te3. The choice of *x* can ensure protection from time-reversal symmetry. **Figure 14a** and **b** show the sheet resistance measurements of a (Bi*x*Sb1-*x*)2Te3 film that was grown on a MI (Tm3Fe5O12, TIG) for *x* = 0.2 and *x* = 0.3, respectively. The lower inset of both figures show the broken symmetry of the topological surface states of both configurations. The sheet resistance in both figures shows a linear portion, attributed to the normal Hall effect, and a hysteresis loop portion. The different slopes indicate opposite carriers in each sample. The hysteresis portion indicates strong magnetic uniaxial anisotropy in the TI owing to highly spin-polarized electrons on the TI's surface. This uniaxial anisotropy is maintained at room temperature and up to T = 400 K [57].

In another experiment, the authors used a Bi2Se3/BaM heterostructure to explore the effect of topological surface state in switching the magnetization of a magnetic insulator [10]. The BaM layer used had similar characteristics to the BaM layer used in the Pt/BaM experiment. The BaM film was 5-nm-thick and had a uniaxial anisotropy axis perpendicular to the surface, as shown by the two hysteresis loops in **Figure 15a**. The blue hysteresis loop was measured when the external field was applied perpendicular to the BaM film's surface. The red loop was measured when an external field was applied along the BaM film plane. The two loops together confirm the perpendicular orientation of the anisotropy axis of the BaM film.

A Hall bar was fabricated on the Bi2Se3/BaM bilayer film. **Figure 15c** shows that, similar to the Hall bar setup of the Pt/BaM experiment discussed in the previous section, the AHE contribution to the Hall bar resistance, *R*AHE, scales with the

#### **Figure 14.**

*(a) and (b) Hall traces of TIG/(BixSb1x)2 Te3 for* x *= 0.20 and 0.30, respectively. The upper insets show the corresponding temperature dependence of Rxx. The lower insets show schematic drawings of the corresponding chemical potential position. Source: [57], p. 2.*

**53**

**Figure 15.**

*(a) Magnetization (M) vs. field (H) loops for the Bi2Se3/BaFe12O19 sample. (b) Saturation magnetization (M*s*) and coercive field (H*c*) as a function of T. (c) and (d) R*AHE *vs. field (H) loops measured at T = 300 K and T = 3 K. Source: [10], p. 4.*

perpendicular magnetization *M*<sup>⊥</sup> of the BaM film and therefore can be used as an easy way to probe *M*<sup>⊥</sup> of the BaM film during experimentation. While **Figure 15c** shows the *R*AHE response in room temperature settings, **Figure 15d** shows *R*AHE when T = 3 K. The figure shows a hysteresis loop that is very close to the one in **Figure 15c**. The hysteresis loop widths are very similar, indicating that the same field strength *H* is required to saturate the magnetization of the BaM film when T = 3 K and when T = 300 K. The value of *R*AHE is slightly higher when T = 3 K than when T = 300 K, indicating that the saturation of the BaM film increases slightly as T decreases. The effect of the temperature change on the values of the saturation magnetization of the BaM film and the coercive field required to saturate it are both shown in **Figure 15b**.

**Figure 16c, d**, and **e** shows the results of the same experiment performed at decreasing temperatures. The figures clearly indicate that the current required for magnetization switching becomes smaller as temperature decreases. This is due to

*SOT-induced switching in Bi2Se3/BaM. (a) Experimental configuration. (b to e) AHE resistance (R*AHE*) measured as a function of charge current (I*dc*) at different fields (H) and temperatures (T), as indicated. The*

the enhancement of the topological surface states in Bi2Se3 as T decreases. **Figure 17** further demonstrates the effect of SOT on the magnetization switching of the BaM film. The experiment was performed at T = 3 K; the external field was applied at 45 degrees angle out of the plane of the film as shown in the inset of the figure. The blue hysteresis loop is the result of applying a negative charge current that generated a SOT acting against *H*. The result is a wider hysteresis loop when compared with the normal hysteresis loop of the BaM film shown in **Figure 15**. This is due to the SOT acting against *H*, therefore hindering the magnetization switching and requiring a stronger external field to switch the magnetization of the BaM film. The red hysteresis loop shows the result of applying a positive charge current, which caused SOT that was in the direction of the external magnetic field, significantly decreasing the switching field required as shown by the much narrower hysteresis loop. This confirms the strength and significance of SOT in TIs

*arrows in (b) to (e) indicate the current sweeping directions. Source: [10], p. 5.*

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

**Figure 16.**

**55**

and how it can be used to assist in magnetization switching.

**Figure 16a** shows the SOT switching experiment configuration. An external field *H* was applied along the *x* direction to aid in the SOT switching of *M*<sup>⊥</sup> in the BaM film. *M*<sup>⊥</sup> was initially along the positive *z* direction. **Figure 16b** shows the experimentation results when T = 200 K and *H* = -15 kOe. The blue data points show the effect of sweeping a DC charge current *I*dc from positive to negative. When the supplied current was positive, the SOT direction was also in the positive *z* direction, so we see no change in *R*AHE. When *I*dc is <0, however, the SOT direction flips to the negative *z* direction. When the torque generated by the polarized spin accumulation at the Bi2Se3/BaM becomes strong enough, the magnetization within the BaM film switches to the negative *z* direction, as indicated by the change in *R*AHE value from positive to negative. Sweeping *I*dc from negative to positive generates SOT in the +z direction when *I*dc > 0; when the SOT is strong enough, it flips the magnetization of the BaM film again, indicated by the red points in the figure. The result from both cases is a hysteresis loop in *R*AHE that can be seen in the figure.

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

**Figure 16.**

perpendicular magnetization *M*<sup>⊥</sup> of the BaM film and therefore can be used as an easy way to probe *M*<sup>⊥</sup> of the BaM film during experimentation. While **Figure 15c** shows the *R*AHE response in room temperature settings, **Figure 15d** shows *R*AHE when T = 3 K. The figure shows a hysteresis loop that is very close to the one in **Figure 15c**. The hysteresis loop widths are very similar, indicating that the same field strength *H* is required to saturate the magnetization of the BaM film when T = 3 K and when T = 300 K. The value of *R*AHE is slightly higher when T = 3 K than when T = 300 K, indicating that the saturation of the BaM film increases slightly as T decreases. The effect of the temperature change on the values of the saturation magnetization of the BaM film and the coercive field required to saturate it are both

*(a) Magnetization (M) vs. field (H) loops for the Bi2Se3/BaFe12O19 sample. (b) Saturation magnetization (M*s*) and coercive field (H*c*) as a function of T. (c) and (d) R*AHE *vs. field (H) loops measured at T = 300 K*

**Figure 16a** shows the SOT switching experiment configuration. An external field *H* was applied along the *x* direction to aid in the SOT switching of *M*<sup>⊥</sup> in the BaM film. *M*<sup>⊥</sup> was initially along the positive *z* direction. **Figure 16b** shows the experimentation results when T = 200 K and *H* = -15 kOe. The blue data points show the effect of sweeping a DC charge current *I*dc from positive to negative. When the supplied current was positive, the SOT direction was also in the positive *z* direction, so we see no change in *R*AHE. When *I*dc is <0, however, the SOT direction flips to the negative *z* direction. When the torque generated by the polarized spin accumulation at the Bi2Se3/BaM becomes strong enough, the magnetization within the BaM film switches to the negative *z* direction, as indicated by the change in *R*AHE value from positive to negative. Sweeping *I*dc from negative to positive generates SOT in the +z direction when *I*dc > 0; when the SOT is strong enough, it flips the magnetization of the BaM film again, indicated by the red points in the figure. The result

from both cases is a hysteresis loop in *R*AHE that can be seen in the figure.

shown in **Figure 15b**.

**54**

*and T = 3 K. Source: [10], p. 4.*

*Magnetic Materials and Magnetic Levitation*

**Figure 15.**

*SOT-induced switching in Bi2Se3/BaM. (a) Experimental configuration. (b to e) AHE resistance (R*AHE*) measured as a function of charge current (I*dc*) at different fields (H) and temperatures (T), as indicated. The arrows in (b) to (e) indicate the current sweeping directions. Source: [10], p. 5.*

**Figure 16c, d**, and **e** shows the results of the same experiment performed at decreasing temperatures. The figures clearly indicate that the current required for magnetization switching becomes smaller as temperature decreases. This is due to the enhancement of the topological surface states in Bi2Se3 as T decreases.

**Figure 17** further demonstrates the effect of SOT on the magnetization switching of the BaM film. The experiment was performed at T = 3 K; the external field was applied at 45 degrees angle out of the plane of the film as shown in the inset of the figure. The blue hysteresis loop is the result of applying a negative charge current that generated a SOT acting against *H*. The result is a wider hysteresis loop when compared with the normal hysteresis loop of the BaM film shown in **Figure 15**. This is due to the SOT acting against *H*, therefore hindering the magnetization switching and requiring a stronger external field to switch the magnetization of the BaM film. The red hysteresis loop shows the result of applying a positive charge current, which caused SOT that was in the direction of the external magnetic field, significantly decreasing the switching field required as shown by the much narrower hysteresis loop. This confirms the strength and significance of SOT in TIs and how it can be used to assist in magnetization switching.

generating higher SOT. (All figures, experimentation setup and results were taken

Magnetic insulators with perpendicular anisotropy have become an important class of materials in the development of spintronic devices. For magnetic domain devices, the low-damping and large anisotropy features can enable high-speed domain-wall motion with a small current threshold, fueling the development of domain-wall memory and logic devices. Moreover, low-damping is significant for SOT oscillator applications, where the current threshold for self-oscillations decreases with damping. Recent experiments show that spin waves can be used to control magnetic domains through spin-orbit torques [60, 61]; this effect can be amplified and become more efficient in magnetic insulators. The strong magnetic anisotropy also allows the engineering of spin-wave dispersion relation without the need for large bias magnetic fields [62]. This will expand the horizon for magnonic and spin-wave devices, allowing the development of new magnon-photon coupling devices for quantum transduction and microwave photonic systems [63, 64].

Department of Electrical and Computer Engineering, Auburn University, Auburn,

© 2020 The Author(s). Licensee IntechOpen. 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,

from [10] with appropriate permissions).

*Perpendicular Magnetic Insulator Films for Spintronics DOI: http://dx.doi.org/10.5772/intechopen.92277*

**3.5 Summary and outlook**

**Author details**

USA

**57**

Laith Alahmed and Peng Li\*

\*Address all correspondence to: peng.li@auburn.edu

provided the original work is properly cited.

**Figure 17.** *Effects of I*dc *on R*AHE *hysteresis loops at T = 3 K in Bi2Se3/BaM. Source: [10], p. 6.*

#### **Figure 18.**

*SOT efficiency (η) as a function of T in Bi2Se3/BaM and Pt/BaM. The data were all measured at a field applied at an angle of 45 degrees away from the film normal direction. The data on Pt/BaM were measured with a Hall bar structure that had the same dimension as the Bi2Se3/BaM Hall bar. Source: [10], p. 6.*

The efficiency of SOT switching can be calculated using the following expression [58]:

$$\eta = \frac{H\_{\rm SW}(I\_{\rm dc} > 0) - H\_{\rm SW}(I\_{\rm dc} < 0)}{2|I\_{\rm dc}|/(wt)} \tag{6}$$

where *H*SW is the switching field, w is the Hall bar width, and t is Bi2Se3 or Pt thickness. The increase of SOT efficiency as the temperature decreases is demonstrated in **Figure 18**. The blue data points show *η* of Bi2Se3/BaM as a function of temperature. Note that the Debye temperature of Bi2Se3 is about 180 K [59]. When T is > > Debye, the efficiency is proportional to *T*�<sup>1</sup> , but when the temperature is < < Debye (at T = 100 K), the efficiency is proportional to *T*�<sup>5</sup> . Pt/BaM SOT efficiency is also shown as a function of temperature on the same plot (red points). The data show that decreasing the temperature has a negligible effect on the efficiency in Pt/BaM bilayers. The exponential improvement in SOT efficiency of Bi2Se3/BaM is caused by the fact that the surface conductance in TIs increases with decreasing temperatures, while the bulk conductance decreases. This means that the decrease in T enhances the TSS in TIs, resulting in a higher charge current to spin current conversion efficiency, increasing the spin polarity in TIs and therefore generating higher SOT. (All figures, experimentation setup and results were taken from [10] with appropriate permissions).
