Figure 1 depicts the XRD patterns of Bi0.5Sr0.5Fe0.5Cr0.5O3 at 23°C. The diffraction data reveals the same structure with a hexagonal R3c unit cell, which is similar with BiFeO3 previously reported. Since Sr ionic has a smaller size than Ba and the ionic size of Cr is smaller than Fe, this leads to the lattice parameters change. To discuss the structural parameter changes, the structure was refined using Rietveld, and the data was fitted to the experimental pattern. The lattice parameters were refined using the high-resolution synchrotron XRD data shown in Table 1. It is found that the lattice parameters, both a and c decrease because Sr and Cr substitute Bi and Fe, respectively. The in-plane lattice parameter a is reduced to 0.557262 nm, and the out-of-plane lattice parameter c is reduced to 1.35006 nm. No additional reflections and impurities are detected in the room-temperature XRD data of bulk Bi0.5Sr0.5Fe0.5Cr0.5O3.
Figure 2 illustrates the Fe 2p and Cr 2p XPS spectra of bulk Bi0.5Sr0.5Fe0.5Cr0.5O3. Fe3+ ions have binding energies. Figure 2(a) shows the Cr 2p XPS spectrum. The energies 576.2 eV and 586.2 eV correspond to Cr 2p1/2 and Cr 2p3/2, respectively. It demonstrates that the Cr ions in BSFCO are mainly Cr3+.The Fe 2p3/2 and Fe 2p1/2 peaks at about 711.7 eV, Fe 2p3/2 and 725.3 eV, and Fe 2p1/2 with a satellite at 719.6 eV[22–23]. Therefore, it can be deduced that the Fe ions in the bulk BSFCO are primarily Fe3 + in Fig. 2(b), with a few Fe2+ ions present to compensate for oxygen vacancies that cannot be determined.
2.The Mössbauer spectrum and magnetization of bulk BSFCO
Mössbauer data for bulk BSFCO samples at 300K(a)and 80K(b) are shown in Fig. 3(a) Mössbauer spectroscopy is used to demonstrate the bulk paramagnetic behavior at room temperature: the data show no magnetism. Mössbauer data at 300 K can be fitted to a doublet profile. It is a paramagnetic/antiferromagnetic material with an isomer shift of 0.16(0) mm/s, which is a property of the Fe3+ cation. The property of quadrupole splitting indicates the presence of a distorted octahedral environment, which agrees with bond distances refined from X-ray diffraction.
The low-temperature Mössbauer data in Fig. 3(b) show that the transition at 80 K is to a magnetically ordered or frozen state. The 80-K spectrum was fitted to a six-line magnetic profile (in green) and a double magnetic profile (in black). The double magnetic profile indicates that there is some paramagnetism at 80 K. The quadrupole interaction at 80 K is 0.40(7) mm/s. Meanwhile, the width of the spectrum at 80 K is wider than that at 300 K. This is due to the fact that the hyperfine field of Fe is dispersed with 50% Cr3+ instead of Fe3+ .
ZFC-FC curves are measured to investigate the magnetization of bulk BSFCO at low temperatures as shown in Fig. 4. Figure 4 shows the magnetization curves of bulk BSFCO at zero field and cooling field at H = 1 T and T = 300 K. The bulk magnetic behavior of Bi0.5Sr0.5Fe0.5Cr0.5O3 is revealed by magnetization measurements and plotted as a M-T curve. The ZFC and FC curves split around 130 K, while the FC curve (H = 1 T) has a plate-like peak and magnetization decreases rapidly below 25 K. Fitted by the Curie-Weiss law
[χ(T ) = C=(T -ΘCW )], which yields a Curie constant of 2.66 emu K/mol and a Weiss temperature Θ of -130 K. The negative ΘCW suggests an antiferromagnetic coupling and TN is about 25 K as evinced by the FC curve. The plate-like curve suggests the existence of competing interactions among its ferromagnetic property, antiferromagnetic property, and spin glass exit, consequently it may not be linked to spin glass-like freezing with long range order, but a transition to short range order.
To confirm these magnetic properties, the hysteresis loops of magnetization were collected from − 1 T to 1 T at 2 K after ZFC and FC under H = 1 T from 300 K, as shown in Fig. 5. The M-H loop under ZFC state is symmetric around zero, whereas the existence of exchange bias was proved by the shift of FC loops towards negative field. HEB and HC parameters are defined as HEB = (H1 + H2)/2 and HC =-(H1-H2)/2, respectively, where H1 and H2 are the left and right coercivity fields. HEB was about 1150 Oe under the FC condition. HC obtained from the FC loop is about 460 Oe and it is slightly higher than HC obtained from ZFC (410 Oe). The different value results from the function of the exchange anisotropy.
It is shown in Fig. 6, with the reduction of HEB and HC by subsequent magnetization reversals, namely, the so-called training effect. This effect indicates that the exchange anisotropy slowly decreases. From the M-H loops (Fig. 6), it is observed that the ZFC magnetizations at 1 T, 3 T, and 5 T are much smaller than their FC counterparts. So FC can enlarge the content of the FM region and tFM. The increase of tFM under FC conditions reduces strain anisotropy, which arises from different magnetic states among the FM layer, the AF layer, and disordered spin glass; meanwhile, the strain anisotropy could cause the decrease of HC.
Because HFC can improve tFM, we can deduce that changing HFC can affect tFM and the ratio of HCFC and HEBFC, as shown in Fig. 7. By connecting each data point, which represents the sample being cooled from 300 K to 2 K from 1 T to 1 T, the sample was cooled from 300 K to 2 K from 1 T to 1 T. Figure 7 shows a hysteresis loop. With an increase in HFC, both HCFC and HCFC decrease. When HFC increases from 1 T to 6 T, HEB decreases by 16% at 2 K. It is not difficult to conclude from the above analysis that strain anisotropy could decrease because an increase in tFM may result in a decrease in HCFC. To demonstrate the relationship between tFM and HEB in bulk BSCFO, the dependence of tFM on HFC must be confirmed. From the M-H loop, the magnetization of the FM layers is almost saturated under an applied field of 1 T. Msat, defined as (M1T-M-1T)/2, is proportional to the volume fraction of the FM region. Msat increases with HFC when tFM emerges, so the Msat-HFC curve plotted in Fig. 7 scales the variation of tFM with HFC. HEB and 1/Msat have a quasi-linear relationship, as illustrated in Fig. 8. As shown in Fig. 8, HEB decreases as tFM increases, which is consistent with the trend in exchange bias films. The result demonstrates the presence of FM coupling at the FM/AF interface in BSCFO. The AF coupling at the interface would result in a competition between the exchange energy and the Zeeman energy. It would weaken the relationship between HEB and 1/tFM. This trend deviates from the linear prediction. It is worth noting that HFC changes the thickness tAF of the AF layer, which has an impact on HEB.
This implies that the majority of the regions in the system are AF, but tFM remains constant after sample fabrication without being affected by HFC. The interfacial spins of FM and/or AF layers with HFC will have an effect on HEB change. The spontaneous FM and AF layers in BSCFO remain constant, allowing tFM to be tuned after fabrication utilizing external forces. The mutual interactions of charge, spin, and lattice degrees of freedom in this bulk material can result in a delicate balance of different ground states. Magnetic field, electric field, laser light, pressure, and other forces can disrupt the equilibrium and cause it to transition to a new state.
Figure 9 illustrates schematic diagrams of the AFM/FM structure for bulk BSCFO at various magnetic fields. Since the FM increases as magnetic fields increase, some AFM structures can be tuned into FM structures. FM structure can be influenced with AFM by interfacial coupling, so the magnetization can be changed to a greater extent under a PM background, as shown in Fig. 9 (①②③④). It is identified from above that external fields have an effect on the interaction between the AF and FM layers. Furthermore, it benefits FM phase enhancement, as increasing HFC can increase the ration of FM content and tFM while decreasing HEB. This indicates that, in the presence of certain external factors, the sensitivities of order parameters can be used to tune the exchange bias. Some recent studies suggest that short disorder is beneficial to FM clusters/microstructure in La1.5Sr0.5CoMnO6 and Mn2PtGa materials. The exchange anisotropic coupling of the embedded phase between FM and AFM layers has resulted in SEB. Thus, it's reasonable to assume that the SEB in bulk BSFCO is due to the coupling between the AFM layer, spin glass, and FM layer. To summarize, the analysis of exchange bias in these types of materials may lead to unusual events, which could aid in the creation of multifunctional spintronic devices.