Observation of Spin-Glass Behavior in Spinel Compound CoGa2O4

In this work, the synthesis process, crystal-structure, and comprehensive physical properties of spinel compound CoGa 2 O 4 have been investigated. The competition between antiferromagnetism (AFM) and ferromagnetism (FM) are considered to be the crucial elements for resulting in spin-glass (SG) behavior due to magnetic frustration. The observed SG behavior is determined by the temperature dependence of magnetization M(T) curves under the ZFC (zero-eld-cooled) and FCC (eld-cooled) processes, where form the intense irreversibility divergence. Moreover, the corresponding tting parameters (the freezing temperature T 0 = 9.32 K, the ipping time τ 0 = 4.49 × 10 -10 s, and the dynamical exponent zν = 4.46) strongly indicate the existence of the SG behavior. Meanwhile, as another specic characteristic for SG, in our present work, frequency (f) and magnetic eld (H) have a strong inuence on the peaks of AC susceptibility. From where, with the increase of f and H, the freezing temperature follows a corresponding peak shift. All the above phenomena and relevant analyses of magnetic frustration behavior conrm the typical SG behavior in CoGa 2 O 4 system.


Introduction
Since the typical spin glass (SG) behavior has been found in magnetic materials, the sub-stable magnetic alloy material and magnetic compounds have been extensively studied due to its interesting structure and properties [1,2]. The research of SG plays a crucial role in many comprehensive study of interdisciplines, meanwhile, it also provides mathematical tools to solve practical problems in memory elements, microwave components, computing machinery, functional materials, and biology science [3][4][5].
As is known to all, the SG behavior is usually existed in the antiperovskite compounds with a formula AXM 3 (A = Ga, Al, Cu, In, Sn, Zn, Ge etc.; X = C, N; M = Ni, Mn, Fe, etc) such as SnCFe 3 [6] and GaNMn 3 [7].
However, to date, there are no report on the SG behavior in CoGa 2 O 4 spinel compound, and thus the work seems more necessary and meaningful.
In this paper, the spinel structure CoGa 2 O 4 has been prepared by solid state method. The distribution of the cations at the tetrahedral and the octahedral sites can be re ected by the structural formula (Co 1 − [8,9]. It can be seen that, Co 2+ ions and Ga 3+ ions are both divided into A and B-sites. We report and verify the spin glass behavior of the prepared sample, from where, the SG behavior in CoGa 2 O 4 is con rmed to be resulted from the magnetic frustration and atomic disorders according to the systematical measurements. The temperature dependence of magnetization M(T) and magnetic susceptibility χ(T) are measured at several xed frequencies. The isothermal remanent magnetization (M IRM ) are also performed and described in the following sections. We illustrate a detailed investigation of the magnetic property and structural characteristic of the sample. As all results shown, the competition between AFM and FM interactions should be responsible for the SG behavior of CoGa 2 O 4 [10,11]. CoGa 2 O 4 with the chemical formula of (Co 1 − x Ga x )[Co x Ga 2−x ]O 4 was analyzed by standard solid state reaction method in air atmosphere. The powder of materials Co 2 O 3 (100%) and Ga 2 O 3 (99.8%) were used as starting materials, and homogeneous mixed by the ball milling. The mixture was sintered at 1300 ℃ in the mu e for 12 h. When the sample is cooled to room temperature at a rate of 3 K/min, the sample is basically prepared. After quenching to room temperature, the products were pulverized, mixed, pressed into pellets, and annealed again in order to obtain homogeneous samples.
The phase identi cation of the prepared sample was measured by X-ray diffraction at room temperature (XRD, Rigaku D/max-2550V/PC, Cu Kα (λ = 1.5406 Å)) with the angle from 20° to 90°. Scanning electron microscope (SEM) was used to characterize the microstructure, and Energy Dispersive X-Ray spectroscopy (EDX) was used to analyze the element composition. All the magnetic measurements were performed by a Quantum Design superconducting quantum interference device based on magnetic property measurement system (SQUID-MPMS 3). Meanwhile, two speci c peaks at 781.3 eV and 797 eV are attributed to Co 3+ , and the other two peaks at 786.6 eV and 803.2 eV are associated with Co 2+ [18][19][20]. Figure 3(c) shows the XPS spectrum of Ga 2p. The observed energy peaks of Ga 2p 1/2 and Ga 2p 3/2 are located at 1144.5 eV and 1117.7 eV respectively [21,22]. In the case of Fig. 3(d) for O 1s spectra, the peak with binding energy of 531.05 eV is related to oxygen bonding [23,24]. Through the analyses above, all of the measurement results of XPS spectrum show that the prepared sample contains all the elements, which are well consistent with other related investigations. destroyed under a large external magnetic eld [26]. As plotted in Fig. 4(a), an obvious irreversibility appears below T wi , which are the typical characteristic of spin glass behavior. Below T wi , the value of M FC remains almost a constant, meanwhile, M ZFC almost drops to zero as the temperature decreases.

Results And Discussion
According to previous reports, at low temperature, the difference between M FC and M ZFC curves may be resulted from the competition between magnetic couplings [27]. As shown in Fig. 4(b), the magnetic hysteresis loops (M-H) for CoGa 2 O 4 sample are performed at 300 K and 5 K respectively. All M(H) curves have a linear relationship with magnetic eld in high eld, which is consistent with spin glass system.
According to the obtained results, neither of them reach saturation even up to 50 kOe. For another prominent case, M is bigger than 300 K at 5 K because of thermal disturbance has a susceptible effect on the magnetic moment.
In order to further con rm the spin-glass behavior, we characterized the temperature dependence of AC magnetic susceptibility under the changing frequency and magnetic eld process. Figure 5(a) and 5(b) display AC magnetic susceptibility χ(T) for CoGa 2 O 4 at AC eld of H AC = 2 Oe under different xed frequencies (f = 1, 10, 100, 500, and 1000 Hz), respectively. It can be found that both χ'(T) and χ''(T) present strongly frequency-dependent peaks, obviously, the positions of these peaks shift to higher temperatures and the magnitudes decrease with increasing f, which indicate a typical spin glass behavior. Generally, ∆T f /[T f ∆(log 10 f)] can determine the dependence of peak shift on frequency, and the typical value for spin-glass system is between 0.0045 and 0.08. Under the AC magnetic eld, the energy of the applied magnetic eld becomes smaller in one direction, and H AC changes rapidly in the opposite direction with the increase of f. Meanwhile, the system needs a higher temperature eld T f (f) to reach a stable state. In fact, the value of relaxation time τ around the transition temperature can be written as follows [28]: Here, T 0 represents the freezing temperature, τ stands for the relaxation time τ = 1/(2πf), τ 0 stands for the characteristic ipping time of the magnetic moments, T f is the frequency dependent of the peak position in χ'(T), and zv is the dynamical critical exponent. Acknowledged from the previous reports on spin glass, the parameters of τ 0 and zv for typical spin glass are located as follows, where τ 0 is in the range of 10 − 10 -10 − 13 s and zv is 4-13, respectively. In this paper, the parameters of T 0 = 9.32 K, τ 0 = 4.49×10 − 10 s, and zv = 4.64 obtained by tting formula (1) further suggest the typical spin-glass behavior [6]. Figure 5(c) and 5(d) present the χ'(T) and χ''(T) for CoGa 2 O 4 under several bias DC magnetic elds respectively, with AC magnetic eld H AC = 2 Oe and f = 10 Hz. It is clearly shown that the values of T f transfer to a lower temperature and the value of peak decreases with H DC increase. There is a typical dependence and linear relationship between the value of T f (H) and H 2/3 , which is expected for the 3D-Heisenberg SG behavior [29]. magnetic elds from 300 to 5 K. It is necessary to emphasize the measurement process that under the premise of cooling the sample to the required temperature in the zero eld, then apply a magnetic eld for about 600 s and measure the remanent magnetization with decaying time. It is obviously seen from the Fig. 6 that M IRM is mainly a straight line and is nonzero in different elds, which proves the distinct existence of spin frustration in CoGa 2 O 4 and also a typical SG behavior. The data of experiment under different elds can be obtained by tting the following formula [28,30]: M IRM (t) = M 0 -αln(t), (2) As shown in the inset of Fig. 6, the relationship between tting parameters M 0 and α is depicted.
Obviously both parameters increase rapidly and then tend to saturate, which further proves the SG behavior of CoGa 2 O 4 [31,32].
In  [33]. The spin magnetic moments of the spin up and spin down with asymmetric distribution imply the net magnetization in the sample [28]. The calculated magnetic characteristics of CoGa 2 O 4 are consistent with the measured magnetic properties.
We note that the CoGa 2 O 4 sample also behaves a SG behavior with the reliable parameters: decreases with increasing f, which indicates a strong dependence on frequency and associates with a typical SG behavior in CoGa 2 O 4 . Generally, the existence of SG is closely associated with the competition between FM and AFM interactions which results from the multicon guration of spins or spin frustration.  [1,28], where the local FM cluster and atomic disorder caused by the atomic de ciency were observed. And thus, based on these discussions, the origin of SG behavior in our present work should be closely dependent upon the spin frustrations and disorder occupations of the mixed sites. That is to say, the observed SG behavior in CoGa 2 O 4 may be attributed to the atomic disorders introduced by the Ga/Co de ciency which affects the characteristic parameters of the SG state remarkably.
In summary, the structure and magnetic properties of the compound CoGa 2 O 4 were investigated systematically. The results of XRD, EDX, and XPS con rmed that the pure CoGa 2 O 4 sample was prepared, and exhilaratingly, SG was also observed in CoGa 2 O 4 from magnetic measurements. To further elaborate the SG, the following work is completed, for instance, M(T) curves with different applied eld/frequency, eld dependent AC susceptibility, and M IRM at xed magnetic elds. The characteristic parameters T 0 = 9.32 K, τ 0 = 4.49×10 − 10 s, and zv = 4.64 obtained from AC magnetic susceptibility indicate that CoGa 2 O 4 is a SG system. Meanwhile, the curves of M(T), χ'(T), and χ''(T) change regularly with the variation of magnetic and frequency. These phenomena can be explained by different magnetic competition and disorder. In other words, the competition between FM and AFM leads to the existence of SG, which is characterized by spin frustration and disorder. On this basis, the spin glass behavior of CoGa 2 O 4 may be also caused by the competition between competing magnetic orders.