III. RESULTS AND DISCUSSION

Figure 1(a) shows the XRD pattern of NiCr₂O₄/Cr₂O₃ composite. Two sets of diffraction pattern corresponding to NiCr₂O₄ (cycle) and Cr₂O₃ (diamond) can be indexed without other impurity. EDS data in Fig. 1(c) and the right inset table confirm the stoichiometry with 1:4. Considering the phase formation temperature of NiCr₂O₄ is higher than that of Cr₂O₃, we speculate that Ni cations react with part of Cr cations to form NiCr₂O₄ phase leaving the other Cr cations develop to Cr₂O₃ phase. In other words, with the special chemical synthesis method and thermal treatment, Ni cations doped in Cr cations separate the phases into ferrimagnetic NiCr₂O₄ and antiferromagnetic Cr₂O₃ phases by a local arrangement of the Ni and Cr cations. To confirm this, the XRD pattern of pure NiCr₂O₄ synthesized by the same method is shown in Fig. 1(b). In addition, the micrograph shown in the left inset of Fig. 1(c) displays the morphology of NiCr₂O₄/Cr₂O₃ composite. As analyzed and calculated, NiCr₂O₄ particles with grain size of about 50 nm are embedded in Cr₂O₃ of about 250 nm. It can further confirm that the NiCr₂O₄ phase is separated out from the Cr₂O₃ phase. They also prove that the ferrimagnetic NiCr₂O₄ and antiferromagnetic Cr₂O₃ can be coexistent in the system synthesized by the co-precipitation method.

FIG. 1.

(a) XRD pattern of the NiCr₂O₄/Cr₂O₃ system. (b) XRD pattern of the pure NiCr₂O₄ phase. (c) EDS spectrum of NiCr₂O₄/Cr₂O₃ system. The left inset is the SEM micrograph and the right inset is the proportion values of elements.

The temperature dependent magnetization under different magnetic field with zero-field-cooled (ZFC) and field-cooled (FC) processes are plotted in Fig. 2. From Fig. 2(a), we can find that magnetization curves have a steep increase near 75 K accompanied with a clear peak in ZFC around 68 K associated with the ferrimagnetic transition and a subtle anomaly in FC at 30 K marked with the spiral magnetic order. It is very qualitatively similar to the previous data about NiCr₂O₄. ^{Reference Ptak, Maczka, Gagor, Pikul, Macalik and Hanuza12,Reference Suchomel, Shoemaker, Ribaud, Kemei and Seshadri13} The magnetization curves with high applied field of 40 kOe showed in Fig. 2(b) exhibit a broad cusp near 305 K corresponding to the antiferromagnetic orders of Cr₂O₃. In addition, as temperature decreases below the temperature about 65 K, the ZFC curve does not follow the same path as the FC curve. The irreversibility between ZFC and FC curves reveals that there are some frozen moments in the sample. Since NiCr₂O₄ can be separated from Cr₂O₃, an intermediate structural disorder layer including anisotropy can be formed because of the chemical roughness and the intermixing at the interfaces. Thus, some uncompensated spins at the interfaces are also frozen along the field cooling direction after FC process. With increasing magnetic field, the spiral magnetic order temperature shifts appreciably toward to lower temperature side ^{Reference Tadic, Savic, Jaglicic, Vojisavljevic, Radojkovic, Prsic and Nikolic16} and the peak involving ferrimagnetic transition is gradually flat, which is probably due to the modification of the interface spins. As discussed above, the interface between NiCr₂O₄ and Cr₂O₃ forms into structure disordered layer. The intermediate layer with limited thickness modifies the establishment of long range ordering unlike the original domain in ferrimagnetic and antiferromagnetic phase. The modification results in the asymmetric atomic arrangement and breaks the exchange bonds of magnetic cations. More important, this structural modification can produce competing or pinning interactions between the randomly oriented spins and then the interactions further generate some novel magnetic effects.

FIG. 2.

Temperature dependence of magnetization with ZFC and FC processes at (a) H _FC = 2 kOe and (b) H _FC = 40 kOe.

Magnetic hysteresis loops have been measured after ZFC and FC processes at 10 K. During ZFC process, the sample was cooled from 350 to 10 K without applied field and for FC process the sample was cooled with a 30 kOe field. After that, hysteresis loops were measured between ±50 kOe. In Fig. 3(a), ZFC magnetic hysteresis loop shows a strict central symmetry at zero field but FC magnetic hysteresis loop exhibits a shift of the loop. Inset of Fig. 3(a) is the whole loops of ZFC and FC processes. We can find that the loops are not saturated evidently even though at high field. However, the system can be considered effectively saturated if the ascending and descending branches of the loop coincide for high fields. We define the field as H _irr, above which the loop is closed. In the inset, it shows that the magnetization is reversible in high fields and the loops is closed at H _irr, which is about 35 kOe. Ascending and descending branches also have the coincident tendency above the H _irr. In other words, the maximum of measuring field is high enough to make hysteresis loop saturate effectively. In addition, ferrimagnetic NiCr₂O₄ is commonly easier to get saturation than antiferromagnetic Cr₂O₃. It is reasonable that the NiCr₂O₄/Cr₂O₃ system is effectively saturated at higher field than NiCr₂O₄. Therefore, those can give the true signature of the observed EB effect, rejecting the minor loop effect. In our system, a negative H _EB ≈ 2037 Oe and a positive M _shift ≈ 0.129 emu/g can be found. Here, H _EB is defined as H _EB = (H _C1 − H _C2)/2, where H _C1 and H _C2 are the absolute values of left and right coercive fields in the hysteresis loop, respectively. M _shift is calculated by the mathematical formulae, M _shift = (M ₊ − M ₋)/2, in which M ₊ and M ₋ are the absolute values of positive and negative remanent magnetization. Meanwhile, a coercivity enhancement ∆H _C ∼ 355 Oe is also observed and H _C is defined as H _C = (H _C1 + H _C2)/2. Spin disorder at the interface can reduce the antiferromagnetic anisotropy and further influence the coupling strength. With field cooling, interfacial uncompensated spins including frozen and rotatable with different coupling strength can be existed. ^{Reference Gruyters and Schmitz17,Reference Qiu, Yang, Zhou, Chantrell, O’Grady, Nowak, Du, Bai and Sun18} During magnetic reversal, the rotatable antiferromagnetic spins can couple with the adjacent ferrimagnetic moments and follow the ferrimagnetic spin rotation, which can explain the enhancement of H _C. As a pinning center, the frozen antiferromagnetic spins can pin the adjacent ferrimagnetic moment leading to the appearance of H _EB. In addition, M _shift is another good evidence proving the existence of net uncompensated spins. Some uncompensated spins are pinned along the external field direction and could not rotate following the applied field, which give rises to the appearance of M _shift in FC hysteresis loop. Certainly, the value of M _shift is depend on the number of pinned spins. Temperature dependence of H _EB and M _shift is shown in Fig. 3(b). For each measurement, the sample was cooled down from 350 K to the measuring temperature with a 30 kOe field and then the magnetization loops were obtained. As a result, with temperature increasing, H _EB and M _shift decrease and the values finally tend to zero at 70 K, which is consistent with the irreversible temperature in Fig. 2. Besides, H _EB has a similar temperature dependence behavior to M _shift. It indicates that they have close correlation and the similar origination. Not only resulting in the generation of M _shift, the interfacial frozen uncompensated spins can also act as the pinning layer, execute a microscopic torque on ferrimagnetic spins and then bring about the appearance of H _EB. In the inset of Fig. 3(b), nearly linear relationship between M _shift and H _EB can be noted. It directly reveals the equivalence of the parameters and the value of H _EB is determined by the quantity of uncompensated pinned spins on the interfacial layer. The decreasing tendency does not present any anomaly, which can also exclude the influence of spiral magnetic order on EB effect.

FIG. 3.

(a) The ZFC and FC hysteresis loops measured at 10 K cooled from 350 K without applied field and a 30 kOe field, respectively. Inset is the whole loops of ZFC and FC processes. (b) Temperature dependence of H _EB and M _shift after field cooling in 30 kOe from 350 K and the inset shows the variations in H _EB with M _shift.

In addition, cooling field dependence of H _EB and M _shift is exhibited in Fig. 4. The sample was cooled down from 350 to 10 K with different field (0.5 kOe ≤ H _FC ≤ 30 kOe). After reaching 10 K, magnetization loops were measured between ±50 kOe. When cooling field increases from 0.5 to 10 kOe, there is an abrupt increase of H _EB and M _shift. After the initial increase, both of them nearly reach the saturation values. The beginning increase in cooling field just like a stronger applied force induces a growing number of pinned spins along the field direction and also induces the increase in M _shift and H _EB. When cooling field is going on increasing from 10 to 30 kOe, it is high enough to make more pinned spins along the applied field direction and the number of pinned spins varies little with the field. That implies that H _EB and M _shift obtain the saturated values, and so does the EB effect. From the inset of Fig. 4, the uniform field dependence of H _EB and M _shift also represents their close relationship and similar origination, which proves the critical role of frozen uncompensated spins in EB effect. Moreover, the EB effect has also been found in single NiCr₂O₄ phase. ^{Reference Barman, Bora and Ravi19,Reference Singh, Chakraborty, Srikanth, Chandra, Mitra and Kumar20} Compared with the EB effect of polycrystalline NiCr₂O₄ and the nanoparticle phase, the values of H _EB and H _C in NiCr₂O₄/Cr₂O₃ system are evidently improved. The improvement should be related to the different mechanisms inducing the appearance of EB effect.

FIG. 4.

The cooling field dependence of H _EB and M _shift, and the inset is the dependence of H _EB on M _shift.

One of the interesting characteristics of EB is training effect, which is manifested as the evolution of magnetic hysteresis loop when the system is field-cycled several times successively at a specific temperature. Typically, a gradual decrease of H _EB and M _shift with increasing number (n) of subsequent loop cycling can be observed. For the training effect measurements, the sample was first cooled from 350 to 10 K under H = 30 kOe. Subsequently, the magnetic hysteresis loops were measured and cycled 9 times, consecutively. As plotted in Fig. 5, training effect is evident in NiCr₂O₄/Cr₂O₃ system. The first cycle loop shows a prominent EB effect presenting an asymmetric magnetization reversal characteristic. After that, the subsequent magnetization cycles tend to symmetric gradually. The central part of first, second, and ninth loops are shown in Fig. 5. During the training procedure, both H _EB and M _shift decrease with the field cycling accompanied with a dramatic decrease in H _C1 and M ₊ in comparison with the variation of H _C2 and M ₋. The systematic decrease of H _EB (including H _C1 and H _C2) and M _shift with n is shown in Fig. 6. Figure 6(a) proves the decrease tendency of H _EB and M _shift. The inset of Fig. 6(a) displaying the linear relationship between H _EB and M _shift is consistent with the inset of Figs. 3(b) and 4. The pinned uncompensated spins at ferrimagnetic/antiferromagnetic interfaces still play a crucial role during training effect. When field cycles are applied continuously, some pinned uncompensated spins try to alter their direction repeatedly along the external field, which results in the depinning at the interfaces between ferrimagnetic and antiferromagnetic phase. Thus, the number of pinned uncompensated spins is gradually decreasing under continuous cycle magnetization and it gives rise to the decrease of M _shift. In addition, the decrease tendency of interfacial coupling interaction leads to the decrease in H _EB. Therefore, Both H _EB and M _shift are closely connected with the decreasing fraction of pinned uncompensated spins. As shown in Fig. 6(b), it is not difficult to find that the training effect of H _EB is mainly due to the decrease of H _C1 dependent on n, while H _C2 just has the uniform tendency with far less evident dependent on n. Furthermore, in spite of the reduction of H _EB, H _C also has a shrink with field cycling as plotted in the inset of Fig. 6(b). The different dependence on n of H _C1 and H _C2 indicates the different mechanism of magnetization reversal during the left and right branches hysteresis. It is in good agree with the NiO–Fe heterostructure, where coherent rotation is observed at H _C2 while wall propagation and domain nucleation dominate in the vicinity of H _C1. ^{Reference Hochstrat, Binek and Kleemann21}

FIG. 5.

The first, second and ninth hysteresis loops at 10 K after field cooling from 350 K with 30 kOe.

FIG. 6.

(a) Field cycle dependence of H _EB and M _shift at 10 K, and the inset presents the variations of H _EB with M _shift. (b) Field cycle dependence of H _C1 and H _C2 at 10 K, and the inset is the cycle number dependence of H _C.

Figure 7 shows the dependence of H _EB on n and the best fitting (solid line) with n ≥ 2. H _EB of the second hysteresis loop (∼1600 Oe) is decreased about 20% compared with that of the first loop (∼2037 Oe) while the subsequent loops show a more gradual continuous decrease. The distinct character difference of H _EB between n = 1 and n ≥ 2 is a signal that training effect in our system is considered to two different explanation. For n = 1, magnetization reversal asymmetry may exist, which is correlated with the antiferromagnetic magnetic symmetry due to the onset of biaxial anisotropy. As can be seen in the report by Hoffman, ^{Reference Hoffmann22} the symmetry of anisotropy in antiferromagnet is crucial for understanding of training effect in EB system. Multiple antiferromagnetic easy anisotropy axes can exist and initially stabilize the noncollinear arrangement of antiferromagnetic spins, which then relaxes into a collinear arrangement after the first magnetization reversal. However, the subsequent field cycles should arise from the conventional mechanism based on the thermally driven depinning of uncompensated spins. The instability of EB system results in a reduction of pinning upon repeated field cycling, which is due to the irreversible changes in the magnetic microstructure of antiferromagnet. ^{Reference Paccard, Schlenker, Massenet, Montmory and Yelon23} To unveil the detailed mechanism, thermal activation and athermal contribution are used to distinct the first and subsequent loops in training effect, recently. The existence of the two types in interfacial domain states after FC has been reported by Chan et al. ^{Reference Chan, Parker, Crowell and Leighton24} So, we can explain our training effect through the two types.

FIG. 7.

Field cycle dependence of H _EB (open square) and the corresponding best fit (solid line) to the data for n ≥ 2. The inset is H _EB versus n ^−1/2 for NiCr₂O₄/Cr₂O₃ system.

For many cases, training effect has been found to obey the empirical n ^−1/2 law. The relationship between H _EB and n observed in experimentally is usually expressed by: $H_{{\rm{EB}}}^n - H_{{\rm{EB}}}^\infty = {\kappa \mathord{\left{\vphantom {\kappa {\sqrt n }}} \right\kern-\nulldelimiterspace} {\sqrt n }}$ /, where $H_{{\rm{EB}}}^\infty$ is H _EB in the limit of infinite loops and κ is an experimental constant about material dependent decay. ^{Reference Chan, Parker, Crowell and Leighton24} As can be seen, the fitting curve in Fig. 7 is in good agree with our experimental data with n ≥ 2 but fails with n = 1. The fitting parameters are $H_{{\rm{EB}}}^\infty = 1299\,{\rm{Oe}}$ and κ = 406. According to the thermal activation theory, ^{Reference Dias, Menéndez, Liu, Haesendonck, Vantomme, Temst, Schmidt, Giulian and Geshev25} thermal fluctuations can reduce the stability of antiferromagnetic anisotropy energy and the interfacial exchange energy. As a driving force, ferrimagnetic magnetization reversal can overcome high interfacial pinning energy. Consequently, the reversal of ferrimagnetic moment influences the interfacial ferrimagnetic/antiferromagnetic coupling and leads to the loss of interfacial exchange energy during training cycles. The reduction of interfacial coupling energy is reflected by the decrease of H _EB due to the depinning of frozen antiferromagnetic spins. Nevertheless, athermal effect can come from the spin-flop-like coupling and the initial spin configuration cannot be restored. Straight line fitting of H _EB versus n ^−1/2 in the inset of Fig. 7 further presents a clear illustration to separate the two effects into athermal and thermal training effect shown as “∆H _Ather” and “∆H _Ther,” respectively. Antiferromagnetic phase at the interfaces breaks the adjacent ferrimagnetic phase into small size domains which interact with frozen and rotatable uncompensated spins. The first loop is athermal accompanied with the strong magnetization reversal asymmetry. The subsequent loops have a more gradual loop number dependence and we interpret this contribution as a conventional mechanism due to thermally activated depinning.