Figure 1. (a) XRD spectra and Rietveld refinement at room temperature for CoGa2O4. Inset shows the Rietveld refinement XRD pattern. (b) The crystal structure of CoGa2O4.
In order to further gain the insight of element composition and state of CoGa2O4, XPS spectrum of the sample is illustrated in Fig. 3. Figure 3(a) presents the survey XPS spectrum of CoGa2O4 sample, where the survey XPS spectrum contains the peaks of O 1s, Ga 2p, and Co 2p, and confirms the existence of Co, Ga, and O in the CoGa2O4 composite. As shown in Fig. 3(b), the Co 2p spectrum is exhibited, in which the binding energies of the Co 2p1/2 and Co 2p3/2 have four peaks at 803.2 eV, 797 eV, 786.6 eV, and 781.3 eV. Meanwhile, two specific peaks at 781.3 eV and 797 eV are attributed to Co3+, and the other two peaks at 786.6 eV and 803.2 eV are associated with Co2+ [18–20]. Figure 3(c) shows the XPS spectrum of Ga 2p. The observed energy peaks of Ga 2p1/2 and Ga 2p3/2 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.
Figure 4(a) shows the temperature dependence of magnetization M(T) curves for CoGa2O4 at different magnetic fields under the processes of zero field cooled (ZFC) and field cooled (FC). It is not difficult to identify that the compound adopts a characteristic of spin glass behavior since the MZFC and MFC curves exhibit significant divergence at lower temperatures. The observed spin glass behavior of the sample may be due to the disorder of atoms and the competition of different magnetic spin-orders [25]. Meanwhile, with increasing the applied magnetic field, both the peak position of weak irreversibility Twi (defined as the temperature where MZFC = MFC) and strong irreversibility Tsi (defined by the maximum value of magnetization) curves shift to lower temperature. It is shown that the spin glass state is gradually destroyed under a large external magnetic field [26]. As plotted in Fig. 4(a), an obvious irreversibility appears below Twi, which are the typical characteristic of spin glass behavior. Below Twi, the value of MFC remains almost a constant, meanwhile, MZFC almost drops to zero as the temperature decreases. According to previous reports, at low temperature, the difference between MFC and MZFC curves may be resulted from the competition between magnetic couplings [27]. As shown in Fig. 4(b), the magnetic hysteresis loops (M-H) for CoGa2O4 sample are performed at 300 K and 5 K respectively. All M(H) curves have a linear relationship with magnetic field in high field, 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 confirm the spin-glass behavior, we characterized the temperature dependence of AC magnetic susceptibility under the changing frequency and magnetic field process. Figure 5(a) and 5(b) display AC magnetic susceptibility χ(T) for CoGa2O4 at AC field of HAC = 2 Oe under different fixed 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, ∆Tf/[Tf∆(log10f)] 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 field, the energy of the applied magnetic field becomes smaller in one direction, and HAC changes rapidly in the opposite direction with the increase of f. Meanwhile, the system needs a higher temperature field Tf(f) to reach a stable state. In fact, the value of relaxation time τ around the transition temperature can be written as follows [28]:
τ = τ0[Tf(f)/T0-1]−zv, Tf > T0 (1)
Here, T0 represents the freezing temperature, τ stands for the relaxation time τ = 1/(2πf), τ0 stands for the characteristic flipping time of the magnetic moments, Tf 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 τ0 and zv for typical spin glass are located as follows, where τ0 is in the range of 10− 10-10− 13 s and zv is 4–13, respectively. In this paper, the parameters of T0 = 9.32 K, τ0 = 4.49×10− 10 s, and zv = 4.64 obtained by fitting formula (1) further suggest the typical spin-glass behavior [6]. Figure 5(c) and 5(d) present the χ'(T) and χ''(T) for CoGa2O4 under several bias DC magnetic fields respectively, with AC magnetic field HAC = 2 Oe and f = 10 Hz. It is clearly shown that the values of Tf transfer to a lower temperature and the value of peak decreases with HDC increase. There is a typical dependence and linear relationship between the value of Tf (H) and H2/3, which is expected for the 3D-Heisenberg SG behavior [29].
The isothermal remanent magnetization MIRM(t) was measured under ZFC process with different magnetic fields 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 field, then apply a magnetic field for about 600 s and measure the remanent magnetization with decaying time. It is obviously seen from the Fig. 6 that MIRM is mainly a straight line and is nonzero in different fields, which proves the distinct existence of spin frustration in CoGa2O4 and also a typical SG behavior. The data of experiment under different fields can be obtained by fitting the following formula [28, 30]:
MIRM(t) = M0 – αln(t), (2)
As shown in the inset of Fig. 6, the relationship between fitting parameters M0 and α is depicted. Obviously both parameters increase rapidly and then tend to saturate, which further proves the SG behavior of CoGa2O4 [31, 32].
In Fig. 7, we have exhibited PODS and total DOS for spin-up (↑) and spin-down (↓) states for CoGa2O4 and the figure is formed by the s, p, d and Total states. It can be concluded from the figure that the conduction band in CoGa2O4 is about 15 eV wide and is formed by the Co 3d states, Ga 4s, 4p states and O 2p states. The width of the valence band is about 15 eV and consists of two sub-band, it is also clear in the band structure: the one between − 8 and 0 eV is the O 2p states and Co 3d states. The other one is between − 15 and − 13 eV is created by Co 3d states. The band between − 20 and − 18 eV is due to the Ga 4s states [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 CoGa2O4 are consistent with the measured magnetic properties.
We note that the CoGa2O4 sample also behaves a SG behavior with the reliable parameters: ∆Tf/[Tf∆(log10f)] ~ 0.025, T0 = 9.32 K, τ0 = 4.49×10− 10 s, and zv = 4.64. As the result shown that the characteristic parameter varying with the different fixed frequencies: the magnitude of ∆Tf/[Tf∆(log10f)] decreases with increasing f, which indicates a strong dependence on frequency and associates with a typical SG behavior in CoGa2O4. Generally, the existence of SG is closely associated with the competition between FM and AFM interactions which results from the multiconfiguration of spins or spin frustration. The similar case have been reported in other analogous spinel ferrites as well as antiperovskite compounds [Zn0.8− xNixCu0.2Fe2O4 and SnNCo3] [1, 28], where the local FM cluster and atomic disorder caused by the atomic deficiency 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 CoGa2O4 may be attributed to the atomic disorders introduced by the Ga/Co deficiency which affects the characteristic parameters of the SG state remarkably.