Iron-based oxides with higher Fe valence states like Fe⁴⁺ exhibit intriguing physical properties. For example, charge disproportionation is found to occur in CaFeO₃ and CaCu₃Fe₄O₁₂,^[1,2] which leads to crystal structural phase transition accompanied with metal-insulator transformation. In addition, Cu–Fe intermetallic charge transfer takes place in RCu₃Fe₄O₁₂ (R = La, Pr, Nd, Bi),^[3–9] giving rise to a first-order isostructural phase transition and a series of sharp variations in magnetism and electrical transport properties. BaFeO₃ usually crystallizes into a hexagonal phase by the high-temperature anneal method in oxygen flow.^[10] Recently, a simple cubic perovskite phase of BaFeO₃ is reported to have been prepared when a lower-temperature reaction method is adopted through using ozone as an oxidizing agent,^[11] although only a limited thickness of powder sample (ca. 50 nm) can be obtained by this method.

In the 1950s, Meiklejohn and Bean^[12] discovered the so-called exchange bias (EB) effect in the Co core and CoO shell structure. In general, this effect can occur when a sample is cooled in a magnetic field across the a critical temperature of a magnetic phase transition because the magnetic hysteresis will shift from the center point vertically or horizontally.^[13] The EB effect promises to have potential applications in spin valves,^[14] ultra high-density recording,^[15] permanent magnets, etc.^[16] Therefore, it has received much attention in many different material systems such as ferromagnetic (FM)–antiferromagnetic (AFM) bilayers,^[17] nanostructured compounds (nanowires^[18] and nanoparticles^[19]), strongly correlated oxides,^[20] heterostructures, etc.^[21] Moreover, it is found that the competition between the FM interaction and the AFM interaction in a spin glassy system can significantly induce the EB effect.^[22,23]

In this work, an oxygen deficient iron compound Ba_0.8Sr_0.2FeO^2.81 with a simple cubic perovskite structure is prepared. The random distribution of Fe³⁺ and Fe⁴⁺ causes competition between the FM interaction and AFM interaction, resulting in a spin glassy behavior which can be well explained by a critical slowing down model. More interestingly, a large exchange bias effect is observed in this compound.

The Ba_0.8Sr_0.2FeO^2.81 was prepared by a solid-state anneal method. The stoichiometric powders BaCO₃ (99.99%), SrCO₃ (99.99%), and Fe₂O₃ (99.99%) used as starting materials were thoroughly mixed and ground in an agate mortar. The mixture was then heated in a tube furnace at 1323 K in O₂ flow for 24 h. The powder x-ray diffraction (XRD) was measured by a Huber diffractometer with Cu radiation at 40 kV and 30 mA at room temperature. The diffraction angle is selected in a range from 5° to 100° in steps of 0.05°. The XRD data were analyzed by Rietveld refinement with the GSAS program.^[24] The oxygen content was evaluated by thermogravimetric (TG) analysis on a Setaram TG-DTA system. The sample was heated up to 950 K in Ar flow with a heating speed of 10 K/min. Temperature dependence of magnetic susceptibility and field dependence of magnetization were measured by using a superconducting quantum interference device magnetometer (Quantum Design, SQUID-VSM). The alternating current (ac) magnetization, specific heat, and electrical transport properties were measured on a physical property measurement system (Quantum Design, PPMS-9 T).

Figure 1(a) shows the XRD pattern of Ba_0.8Sr_0.2FeO^2.81 measured at room temperature. The Rietveld analysis demonstrates that the compound crystallizes into a simple cubic perovskite structure with space group Pm-3m. The lattice parameter we refined is a = 3.93943(1) Å. This value is slightly smaller than that of BaFeO₃ (∼3.971 Å), due to the partial introduction of Sr at the A site. To identify the oxygen content, we perform TG measurement as shown in Fig. 1(b). The compound is thermally stable below ∼550 K. Above this temperature, there exists a remarkable weight loss, indicating the occurrence of oxygen release. Above 800 K, the product becomes stable again on heating up to 950 K, the maximum temperature that is used for TG measurement. According to the TG loss, as well as the final product (Ba_0.8Sr_0.2FeO_2.5 identified by XRD), the oxygen content is determined to be 2.81 ± 0.02, suggesting the presence of a mixed Fe^3.62+ valence state. Therefore, the perovskite B site should be occupied by randomly distributed Fe³⁺ and Fe⁴⁺ in the current Ba_0.8Sr_0.2FeO^2.81.

Fig. 1.

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	Fig. 1. (a) The XRD pattern and the Rietveld refinement result of Ba0.8Sr0.2FeO2.81, where black circle and red line represent the observed and fitted data, respectively. Bottom blue line represents their difference,and pink ticks denote allowed Bragg reflections; (b) TG measurement result of Ba0.8Sr0.2FeO2.81.

Figure 2(a) shows the temperature dependence of direct current (DC) magnetic susceptibility of Ba_0.8Sr_0.2FeO^2.81 measured at 0.1 T using zero-field-cooling (ZFC) and field-cooling (FC) mode. Obviously, the ZFC curve displays a kink around 50 K. However, there is a large separation between the ZFC and FC susceptibility curves below this temperature. This feature can usually be caused by a canted long-range AFM ordering or a spin glassy effect.^[25] However, when the specific heat as a function of temperature is measured (see Fig. 2(b)), one cannot find any anomaly in the whole temperature region we measured (2 K–100 K), ruling out the possibility of long-range spin ordering in Ba_0.8Sr_0.2FeO^2.81. Therefore, the compound should experience a spin glassy transition at a critical temperature . Note that the specific heat below 10 K can be well fitted by the formula . The fitting gives , and , indicating that both FM interaction and AFM interaction play a role in specific heat, which is in agreement with the magnetic measurement result. As mentioned earlier, there exist random Fe³⁺ and Fe⁴⁺ ions in the cubic perovskite Ba_0.8Sr_0.2FeO^2.81. The 180° Fe³⁺–O–Fe³⁺ superexchange pathways can contribute to the AFM interaction, whereas the contribution to FM can be made by the Fe³⁺–O–Fe⁴⁺ double exchange. The competition between the FM interaction and the AFM interaction is thus responsible for the spin glassy behavior observed in Ba_0.8Sr_0.2FeO^2.81. Note that the field dependence of magnetization of Ba_0.8Sr_0.2FeO^2.81 presented in the inset of Fig. 2(a) is also consistent with the spin glassy feature.

Fig. 2.

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Fig. 2. (a) Plots of temperature dependence of DC magnetic susceptibility measured at 0.1 T. The inset shows plots of magnetization versus magnetic field, measured at different temperatures for Ba0.8Sr0.2FeO2.81. (b) Temperature dependence of specific heat, measured between 2 and 100 K. Inset shows fitting result (red curve) using function . (c) Temperature dependence of resistivity. Inset shows fitting result (red line) using hopping model of small polarons as described in the text.

Figure 2(c) shows the temperature dependence of resistivity measured on a pellet of Ba_0.8Sr_0.2FeO^2.81. As the temperature decreases, the resistivity increases sharply, suggesting semiconducting or insulating electrical transport properties. Different electrical conductivity modes are attempted to fit the resistivity data. Like some manganites composed of mixed Mn³⁺ and Mn⁴⁺,^[26,27] the hopping model of small polarons can well reproduce the electrical transport of Ba_0.8Sr_0.2FeO^2.81 in a temperature range between 250 K and 300 K. The inset of Fig. 2(c) shows the fitting result by using the function ). Here the E_A represents the activation energy, and K is the Boltzman constant. The E_A we fitted is 224 meV. This value is slightly less than that obtained from the hexagonal BaFeO_2.86 (300 meV) and BaFeO_2.9 (260 meV),^[28] which is probably due to the more straight Fe–O–Fe bonding in the current Ba_0.8Sr_0.2FeO^2.81 with a cubic perovskite structure.

To further characterize the spin glassy state of Ba_0.8Sr_0.2FeO^2.81, the AC magnetization values are measured at different frequencies. As shown in Fig. 3, a frequency-dependent cusp that shifts toward higher temperatures with the increasing of frequency is found to occur near the freezing temperature T_f (see the upper-left inset), providing convincing evidence for the formation of spin glass. Moreover, the spin glassy behavior of Ba_0.8Sr_0.2FeO^2.81 can be well described by the critical slowing down model^[29] with the formula , where is the relaxation time, the parameter zv is the dynamic critical exponent, and the maximum relaxation time . The bottom-right inset of Fig. 3 presents the fitting result, yielding the parameters s and . These values are comparable to those observed in other spin glassy systems, like Eu_0.4Sr_0.6S, Sr₂FeCoO₆,^[30–32] etc.

Fig. 3.

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	Fig. 3. Plots of AC magnetization versus temperature, measured between 2 K and 100 K for Ba0.8Sr0.2FeO2.81. The upper-left inset shows enlarged view for the shift. Bottom right inset shows fitting by using critical slowing down model as described in the text.

Since the spin glassy behavior caused by the competition between the FM interaction and the AFM interaction is highly likely to induce a large exchange bias effect, the FC magnetization curves are measured at 2 K. For these measurements, the sample is cooled from 300 K to 2 K through the T_g under different positive cooling fields (0 T–7 T). Figure 4(a) shows the related measurement results. The asymmetrical magnetic hysteresis loops that deviate from the origin point can be well observed. Specifically, the magnetization curves shift towards the negative magnetic field axis and the positive magnetization axis, revealing the remarkable exchange bias effect. To quantitatively characterize the exchange bias effect of Ba_0.8Sr_0.2FeO^2.81, the EB field ( ) and the remnant magnetization shift ( ) are calculated. Here, the H_L and H_R respectively present the left and right cooling field intercept, and M_U and M_D are upside and downside magnetization intercept, as illustrated in the inset of Fig. 4(a), measured at a cooling field H_CF = 2 T. Figure 4(b) shows the calculated H_EB and M_E as a function of H_CF. The values of H_EB sharply increase at lower cooling fields ranging from 0 T to 2 T, and then gradually decrease at higher cooling fields. The maximum value of H_EB we obtained at 2 T is 5.6 kOe ( ), which is significantly higher than those for most of other compounds.^[33–35] Similarly, the M_E also sharply increases to /f.u. with field increasing up to 2 T. Above this cooling field, it decreases slightly.

Fig. 4.

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	Fig. 4. (a) Plots of field dependence of magnetization measured at 2 K after cooling at different fields from 300 K to 2 K for Ba0.8Sr0.2FeO2.81. Inset shows the enlarged view for the magnetic hysteresis loop measured at a 2-T cooling field. (b) Plots of HEB and ME as a function of HCF obtained at 2 K.

The magnitudes of H_EB and M_E are dependent on factors such as FM and AFM cluster size or thickness, interfacial roughness, and exchange coupling strength between the FM interaction and the AFM interaction.^[13,36–38] In the current Ba_0.8Sr_0.2FeO^2.81 composed of disordered FM and AFM domains, at H_CF = 0 T, the spin glassy state caused by the competition between the FM interaction and the AFM interaction froze at T_g. When the applied cooling field increases up to 2 T, the magnetic anisotropy sharply increases due to the pinning effect of FM domains. Consequently, the values of H_EB and M_E increase drastically in a cooling field range from 0 T to 2 T. Meanwhile, when the cooling field exceeds 2 T, the FM cluster size will develop considerably. Consequently, the exchange coupling effect becomes too weak to pin the FM spins, resulting in the H_EB and M_E decreasing at higher H_CF.

In summary of the present study, an oxygen deficient perovskite Ba_0.8Sr_0.2FeO_3-δ with simple cubic Pm-3m space group is synthesized. The oxygen content is determined to be 2.81 ± 0.02 by TG measurement. The electrical transport behavior can be well fitted by the hopping model of small polarons, and the activation energy we obtained is 224 meV. In magnetism, both DC and AC magnetic susceptibility measurements reveal the spin glassy features of Ba_0.8Sr_0.2FeO^2.81 with a glassy transition temperature at about 50 K. The spin glassy behavior can be attributed to the competition between the FM interaction and the AFM interaction originating from the Fe³⁺–O–Fe⁴⁺ double exchange and Fe³⁺–O–Fe³⁺ superexchange pathways, respectively. On using a positive magnetic field to cool Ba_0.8Sr_0.2FeO^2.81 from 300 K to 2 K through T_g, a large negative exchange bias effect is observed. Moreover, the exchange bias field increases sharply as H_CF increases up to 2 T, due to the FM pinning effect. The maximum H_EB that we obtained at 2 K is 5.6 kOe, which is located at a higher level than those observed in other compounds.