*3.2.7 Super-spin glass formation in CoFe2O4 nanoparticles*

*Electromagnetic Materials and Devices*

is reported for an ideal spinel CFO, the bond angle is 90° of B–O–B, 120° of A–O–B and 80° of A–O–A magnetic exchange interactions. In the present case, the Rietveld analysis [19], calculated the values of bond-angle/length between A and B sites of CFO in 0.25BTO–0.75CFO nanocomposite, *i.e.*, bond angle = 91.07° for FeB–O–FeB, 133.57° for FeA–O–CoB and 76.13° of FeA–O–FeA. The values of bond length (*l*), *l*A-A = 0.3626(1) nm, *l*B-B = 0.2961(2) nm and *l*A-B = 0.34713 (2) nm. It is reported that the superexchange interactions might be related with bond-angle/length among bonds in Fe, Co and O atoms [41]. For the bond angle of 90° (FeB—O–FeB bonds), the ferromagnetic super-exchange interaction are resulted. When this bond angle is increased, the antiferromagnetic super-exchange interactions are there and generally, bond 120° of super-exchange FeA–O–FeB is the dominant interaction of magnetite. Above 120° of bond angle, the antiferromagnetic strength is increased which is maximum at 180° [42]. Hence the calculated values of bond angles for Co and Fe ions along A and B-sites are deviated with theoretical one that might be indicated the distorted spinel lattice to influence resulting magnetic behavior.

The role of hard/soft ferrites composite of *x*Li0.5Fe2.5O4-(1 − *x*)SrFe2O4 (LSF) (*x* = 0.4, 0.5, and 0.6) on the magnetic exchange-spring systems have been studied [35]. LSF thin films were prepared by MOD method. XRD result shows the polycrystalline behavior of ferrite with cubic phase of Li0.5Fe2.5O4 and orthorhombic SrFe2O4. The magnetic behavior of the three series of LSF films is investigated by measuring M-H hysteresis (**Figure 6(c)**). The Li doping into LSF enhanced the value of Ms and Mr and decreased coercivity value. At equal content of Li:Sr., the magnetic behavior is unpredicted. At annealing temperature of 800°C, the LSF55 thin film have anti S-type (diamagnetism), LSF64 has reducible magnetization, while LSF46 has a similar magnetism that seen at 700°C of annealing temperature.

coercivity, Hc(kOe) = 2.32, 2.18, and 1.54, respectively, measured for LSF55, LSF46, and LSF64 sample, annealed at 700°C. Also from **Figure 6(c)**, the magnetic hysteresis is involved two-step processes, which might have typically exchange-spring

*(a–d) ZFC-FC magnetization of CoFe2O4 nanoparticles. (e) Temperature dependent χ***′***(T)/χ***″***(T) of ac susceptibility for 4 nm CoFe2O4. (e***′***) Arrhenius law (e***″***) Vogel-Fulcher law of χ***′***(T). Adopted from* 

) = 1.21, 8.01, and 22.78,

) = 0.64, 2.13, and 14.20, with magnetic

*3.2.6 Ferromagnetism in xLi0.5Fe2.5O4-(1 − x)SrFe2O4 thin films*

The values of saturation magnetization, Ms (emu cc<sup>−</sup><sup>1</sup>

remanent magnetization, Mr (emu cc<sup>−</sup><sup>1</sup>

**104**

**Figure 7.**

*Mohapatra et al. [45].*

The magnetic CoFe2O4 nanoparticles of mean size 2–16 nm have been synthesized through a solventless thermolysis technique [44]. **Figure 7(a**–**d)** shows the ZFC/FC magnetization of 3, 4, 9 and 12 nm CoFe2O4 nanoparticles in a field of 5 Oe [45]. The ZFC magnetization of these CoFe2O4 nanoparticles has observed maxima, which represents the blocking temperature, TB. However, the FC magnetization is continuously increased below TB, but at a very low temperature, the FC magnetization slightly become constant. Expectedly, the FC magnetization below TB is abruptly increased with a decrease in temperature, which is because the superparamagnetic nanoparticles have no inter-particle interactions. This is typically a signature of super-spin glass transition [44]. The temperature dependent real χ′ (T) and the imaginary χ′′ (T) components of the *ac* magnetic susceptibility for 4 nm CoFe2O4 nanoparticles are shown in **Figure 7(e)**. The χ′ (T) curve for 1.1 Hz displays a sharp peak at the blocking temperature, TB = 179 K and the position of peak is frequency dependent. By increasing frequency from 1.1 to 999 Hz, there is shifting of peak position from 179 to 200 K that calculated the value of ∆Tm = 21 K. However, χ′′(T) in the inset of **Figure 7(e)** has also peak shifting behavior by changing peak position from 130 to 151 K with frequency 1.1–999 Hz. This is analyzed with relation: <sup>φ</sup> <sup>=</sup>∆Tm/Tm∆log(f), where ∆Tm is the difference between Tm measured in ∆log(f) frequency interval. For non-interacting nanoparticles, this parameter 'φ' is usually more than 0.13, for nanoparticle based superspin-glasses, the range is 0.005 < φ < 0.05 and for intermediate interactions, 0.05 < φ < 0.13) [46]. From **Figure 7**, the φ values calculated to be ~0.015, lies for super-spin-glass systems. The super-spin glass behavior is further studied with Neel-Arrhenius law and Vogel-Fulcher model as shown in **Figure 7(e′** and **e″)**.

#### **3.3 ZnO: diluted magnetic semiconductor**

Recently, DMS ZnO has a technological potential due to its large direct band gap (3.37 eV) and exciton binding energy about 60 meV, which is comparably high [47]. The room temperature ferromagnetism, RTFM in 3d ions doped ZnO is reported by Dietl et al*.* [48]. But the pure ZnO is also give RTFM when the crystalline product have small sized nanoparticles [49, 50]. The oxygen vacancies are located on the nanoparticles surface and responsible in major participation of RTFM [51]. Garcia et al*.* [49] found that the ZnO nanoparticles had absorbed certain organic molecules to modify the electronic structure to give RTFM without any magnetic impurity. Xu et al*.* [50] suggested singly charged oxygen vacancies that depend upon nano-size and heating condition and located mainly near on ZnO nanoparticles surface to induce ferromagnetism. During last decade, the magnetism of ZnO with TM doping is extensively studied. Sato et al*.* [52] have used local density approximation (LDA) to discuss ferromagnetic ordering which is more stable in Fe-doped ZnO. Karmakar et al*.* [53] have found antiferromagnetism, which prefers to stabilize Fe-doped ZnO without any native defects. Spaldin [54] had found ferromagnetic ordering which is not possible when Zn sites are substituted with Co or Mn, unless additional hole carriers are incorporated. However, rare earth (RE) atoms have partially filled *f*-orbitals which carry high magnetic moments and form magnetic coupling as for TM ions with partially filled *d*-orbitals [55]. Deng et al*.* [56] investigated the effect of La doping on the electronic structure and optical properties of ZnO using the

first-principle calculation. It is also recently reported that the RE Ce ions are responsible in support antiferromagnetic interactions in TM = Co, Fe doped ZnO [57].
