# Fileset [Manuscript_Submission 3.docx](https://mdr.nims.go.jp/filesets/c3028282-f5ba-4be4-9ed7-f07f4adba060/download) ## Creator Biswajit Dalal, [Xun Kang](https://orcid.org/0000-0003-4364-6218), [Yoshitaka Matsushita](https://orcid.org/0000-0002-4968-8905), [Alexei A. Belik](https://orcid.org/0000-0001-9031-2355), [Yoshihiro Tsujimoto](https://orcid.org/0000-0003-2140-3362), [Kazunari Yamaura](https://orcid.org/0000-0003-0390-8244) ## Rights ©2022 American Physical Society [In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [Inverse exchange bias effects and magnetoelectric coupling of the half-doped perovskite-type chromites Gd0.5Sr0.5CrO3 and Gd0.5Ca0.5CrO3](https://mdr.nims.go.jp/datasets/83d39275-0aa2-4366-a7d6-dacf972d8098) ## Fulltext TitleInverse exchange bias effects and magnetoelectric coupling of the half-doped perovskite-type chromites Gd0.5Sr0.5CrO3 and Gd0.5Ca0.5CrO3 Biswajit Dalal,1,* Yoshitaka Matsushita,2 Alexei A. Belik,1 Yoshihiro Tsujimoto,1,3 and Kazunari Yamaura1,3,†1International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan2Materials Analysis Station, National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan3Graduate School of Chemical Science and Engineering, Hokkaido University, Sapporo 060-0810, Japan The Cr4+ oxidation state with two electrons in the Cr 3d shell is not often observed in perovskite-type oxides, as high pressures and temperatures are generally required to stabilize the octahedral coordination. Herein, we present a comparative study of the novel half-doped perovskite-type chromites Gd0.5Sr0.5CrO3 (GSCO) and Gd0.5Ca0.5CrO3 (GCCO). Fifty percent of the Cr occurs in the Cr4+ oxidation state following high-pressure synthesis at 6 GPa and 1200 °C. The materials were investigated using synchrotron X-ray diffraction and magnetization, heat capacity, and dielectric measurements. The diffraction patterns show that GSCO crystallizes in a monoclinic (space group: P21/c) structure with an ordered arrangement of Cr ions (+3 and +4), whereas GCCO crystallizes in an orthorhombic (Pbnm) structure without such an order. GSCO exhibits a long-range magnetic order at temperatures of <98 K, accompanied by magnetization reversal, suggesting that the magnetic ground state is ferrimagnetic. GCCO displays a weak anomaly characterized by a divergence between the zero-field-cooled and field-cooled magnetic susceptibility curves at temperatures below approximately 100 K. In addition, GSCO exhibits a crossover between conventional and inverse exchange bias effects at low temperatures (<50 K). This is likely caused by asymmetric exchange Dzyaloshinskii-Moriya interactions between the Cr ions of different valences (+3 and +4), which are arranged in a rock salt-type order. Furthermore, significant magnetoelectric coupling at the onset of the magnetic order is supported by temperature-dependent dielectric measurements. *Corresponding author: b.dalal.iitd@gmail.com†Corresponding author: YAMAURA.Kazunari@nims.go.jp 1I. INTRODUCTION Perovskite-type orthochromite RCrO3, where R is a rare-earth element, receives considerable attention owing to its potential applications and unique physical properties, such as negative magnetization, temperature- and field-induced fast spin switching, spin reorientation, field-induced switchable polarization, magnetoelectric effects, spin-driven ferroelectricity, magnetoelastic coupling, and exchange bias (EB) and giant magnetocaloric effects [1–14]. Most orthochromites crystallize in perovskite-type orthorhombic structures (space groups of Pnma or Pbnm) and exhibit canted antiferromagnetic (AFM) orders. An antisymmetric exchange Dzyaloshinskii-Moriya (DM) interaction causes a weak ferromagnetic (FM) component between the Cr3+ spins to manifest at temperatures below the AFM transition (Néel) temperature (TN) [15,16]. Superexchange interactions through the Cr3+–O–Cr3+ bond likely cause the AFM order, and complex, anisotropic interactions between R3+ and Cr3+ may cause unusual physical phenomena, e.g., the polar order of RCrO3 may be primarily caused by R–Cr exchange striction (i.e., an exchange field between the R ion and Cr sublattice) [6]. Furthermore, the onset temperatures of spin-driven ferroelectricity and long-range AFM order of all RCrO3 species remain within the range 110–290 K, regardless of the ionic radius of R3+ [7,12]. GdCrO3 undergoes a canted AFM transition at a TN of 167 K, with negative magnetization, spin reorientation, and field-induced polar order. These complex features are likely caused by interactions between two magnetic elements, Gd3+ (4f7) and Cr3+ (3d3) [2,5,6]. In addition, spontaneous spin reorientation of the ordered Cr sublattice occurs at 7 K [2,5]. The DM interactions and strong AFM coupling between Gd moments and Cr sublattices may lead to negative magnetization at a specific compensation temperature (Tcomp). Recently, an unusual EB effect and fast spin switching were observed in single-crystal GdCrO3 [17], which exhibited a giant magnetocaloric effect and temperature-induced magnetization jump [18,19]. Owing to these multiple anomalies, additional studies of GdCrO3 are required to clarify its fundamental nature. Half-doped perovskite-type transition metal oxides, such as manganite and cobaltite, were extensively investigated over recent decades owing to their strong intercorrelations among various characteristics – spin, charge, orbital, and lattice [20–24]. The first studies of half-doped manganite (La0.5Ca0.5MnO3) were conducted in the 1950s by Wollan and Koehler [25] and Goodenough [26]. The charge-exchanged AFM ground state was associated with the spatial order of the Mn3+/Mn4+ ions localized in alternate planes. The most notable discovery to date is the colossal magnetoresistance of mixed-valence manganite Pr0.5Sr0.5MnO3 [27], with significant competition between the FM metal and AFM insulator states [28]. Notably, however, there are contradictory reports regarding the origin of the colossal magnetoresistance [29–33]. In addition, half-doped manganites exhibit various phenomena, including double-exchange ferromagnetism, metal-insulator transitions, Griffiths phases, charge-order-driven ferroelectricity, strong magnetoelectric coupling, magnetodielectric and EB effects, and magnetoelectric phase separation [34–44]. Conversely, half-doped cobaltites exhibit unconventional phase transitions and unexpected properties, such as spin-state transitions, spin reorientations, valence-state and photoinduced metal-insulator transitions, and charge transfer [45–52]. The syntheses of half-doped manganites and cobaltites with perovskite structures and Mn4+ and Co4+ in octahedral coordination yield compounds with unprecedented physical properties. However, the synthesis of half-doped chromite receives less attention, likely because high pressures and temperatures are required to stabilize Cr4+ in octahedral coordination within the perovskite-type structure. We thus investigated Gd0.5A0.5CrO3, where A = Sr or Ca, using a high-pressure and -temperature method, as half-doped alkaline-earth metal ions could cause distinct magnetic phenomena. This study revealed the structural and physical properties of two half-doped chromites, Gd0.5Sr0.5CrO3 (GSCO) and Gd0.5Ca0.5CrO3 (GCCO), which were synthesized at 6 GPa and 1200 °C. Monoclinic GSCO exhibited a ferrimagnetic (FiM) ground state, whereas orthorhombic GCCO exhibited an AFM ground state. In addition, GSCO exhibited magnetization reversal, non-Griffith-like clustered FM features at temperatures of >TFiM (:FiM transition temperature), and inverse EB effects. Furthermore, temperature-dependent permittivity studies revealed magnetoelectric coupling in GSCO and GCCO. II. EXPERIMENTAL DETAILS Polycrystalline GSCO and GCCO were synthesized via a solid-state reaction using powders of Gd2O3, SrO (prepared using SrCO3 by heating at 1300 °C in oxygen), CaO (prepared using CaCO3 by heating at 1300 °C in oxygen), Cr2O3, and CrO2. The powders were thoroughly mixed in an agate mortar in a stoichiometric ratio in an Ar-filled glovebox. Each mixture was sealed in a Pt capsule and loaded into a multi-anvil press (CTF-MA1500P, C&T Factory, Tokyo, Japan), and the capsule was compressed statically and isotropically at a pressure of 6 GPa at 1200 °C for 1 h (temperature ramping required 12 min). After heating, the capsule was quenched to a temperature of <100 °C within 1 min, and the pressure was gradually released over several hours. The resulting material was a dense, polycrystalline, black pellet. A sample was finely ground for use in phase identification using a MiniFlex X-ray diffractometer (Rigaku, Tokyo, Japan) with CuKα radiation. Finely ground powders were used in synchrotron X-ray diffraction (XRD) at temperatures of 120, 300, or 750 K using a large Debye-Scherrer camera at the BL02B2 beamline at SPring-8, Sayo, Japan [53,54]. The wavelength of synchrotron XRD was 0.65297 Å, based on the standard material CeO2. Synchrotron XRD data were analyzed via the Rietveld method [55] using RIETAN-FP [56] (Dr. Fujio Izumi, Tsukuba, Japan) and the Material Analysis Using Diffraction software [57] (University of Trento, Trento, Italy). Crystal structure images were produced using the Visualization for Electronic Structural Analysis software [58] (Dr. Koichi Momma, Tsukuba, Japan). The direct-current (DC) magnetic susceptibilities (χ) of the materials were measured using a superconducting quantum interference device magnetometer (MPMS, Quantum Design, San Diego, CA, USA). To correct for the stray magnetic field of the superconducting magnet, the magnet was degaussed prior to each measurement. Measurements were conducted in the temperature range 2–350 K at various applied magnetic fields (H) under zero-field-cooled (ZFC) and field-cooled (FC) conditions. Isothermal magnetization loops were collected at various temperatures in the magnetic field range ±70 kOe. The alternating-current (ac) χ of GSCO was measured at 5–350 K using the same instrument. The electrical resistivity (ρ) of a polycrystalline material was measured as a function of temperature via a 4-probe method using a physical property measurement system (PPMS, Quantum Design). The electrical contacts on the bar-shaped material comprised Au wires and Ag epoxy. The temperature-dependent specific heat capacity (Ctotal) was measured using a thermal relaxation method under a zero field or an applied field of 90 kOe in the PPMS at temperatures of 2–300 K. We used an Apiezon-N grease to thermally connect the material to the holder stage. The dielectric properties were measured at temperatures of 5–300 K using an Alpha-A high-performance frequency analyzer (Novocontrol Technologies, Montabaur, Germany) in the frequency range 100 Hz–2 MHz at H = 0 or 90 kOe in the PPMS. During the measurement of GSCO, an extrinsic contribution to the dielectric constant was observed between 220 and 270 K, which was likely due to ice. However, the extrinsic contribution was no longer observed under a much higher vacuum [59]. The deviation between the material and system temperatures under a high vacuum became significant at <50 K. Therefore, we combined the data measured under normal and high-vacuum conditions to confirm the dielectric behavior of the material. III. RESULTS AND DISCUSSIONA. Crystal structure The crystal structures of GSCO and GCCO at room temperature (~297 K) were investigated via synchrotron XRD and data analysis using the Rietveld method, as shown in Figs. 1(a) and (b), respectively. Based on the structure of RCrO3 at room temperature, we initially refined the crystal structure of GSCO using a distorted orthorhombic model (Pbnm or Pnma). Although the observed pattern was refined to a certain extent using the Pbnm model, the analysis was unsatisfactory. Detailed inspection, particularly around the main peaks, revealed that the peak positions were not reproduced well. This indicated that GSCO could crystallize in a double-perovskite-based structure with a rock salt-type order, with Cr3+ and Cr4+ located at two different crystallographic sites. Because P21/c (no. 14), which is in a lower-symmetry subgroup of Pbnm (no. 62), is often observed in double-perovskite materials, we employed the monoclinic P21/c model. As shown in Fig. 1(a), the analysis is successful, indicating that the P21/c model better describes the crystal structure of GSCO. The refined lattice parameters, atomic coordinates, and isotropic thermal displacement parameters are shown in Table I. Notably, GdCrO3 crystallizes in an orthorhombic (Pbnm) structure, whereas SrCrO3 crystallizes in a cubic structure (Pm-3m). Therefore, GSCO is not a solid solution and exhibits different structural characteristics. The inset of Fig. 1(a) shows a structural image of GSCO. The Cr atoms are at two non-equivalent positions, suggesting the presence of two types of octahedrons, i.e., Cr1O6 and Cr2O6, with different volumes. The respective bond valence sums of Cr1 and Cr2 calculated using the parameters r0 = 1.708 (Cr3+) and 1.81 (Cr4+) and B = 0.37 [60] are 3.2 and 4.4, indicating the different valence states of the Cr ions. In contrast, GCCO is analyzed well using the orthorhombic Pbnm model, which is common in most RCrO3 species. Notably, refining the pattern of GCCO using the monoclinic model (P21/c) failed. Because the end-members GdCrO3 [6] and CaCrO3 [61] crystallize in the orthorhombic structure (Pbnm), GCCO may be regarded as a solid solution. In addition, several small peaks in the synchrotron XRD pattern indicate the presence of 3.9 wt.% orthorhombic CaCr2O4 [62]. Rietveld analysis refines the lattice parameters of GCCO and the overall scale factor simultaneously, but the structural parameters of the minor phase remain constant. The final analyzed synchrotron XRD pattern of GCCO is shown in Fig. 1(b), and detailed crystallographic data is shown in Table II. For comparison, the inset of Fig. 1(b) shows a structural image of GCCO. Furthermore, synchrotron XRD patterns were collected at various temperatures from 120 to 750 K to investigate the temperature dependences of the structural properties of GSCO and GCCO. However, neither a change in symmetry nor any additional features were observed. The synchrotron XRD patterns measured at T = 120 and 750 K are shown in Fig. S1 (Supplemental Material) [63]. The changes in the lattice parameters of GSCO and GCCO with temperature are shown in Figs. S2 and S3, respectively. All GSCO lattice parameters increase with increasing temperature, exhibiting the expected thermal behavior. The lattice parameters a and b almost converge at ~750 K [Fig. S2(a)], indicating that GSCO may approach a structural transition or thermal decomposition. In contrast, the GCCO lattice parameter b decreases with increasing temperature [Fig. S3(b)], although the cause remains unknown. This issue should be investigated in future research. B. Magnetization The temperature-dependent DC-χ of GSCO under an applied field of 0.1 kOe, as shown in Fig. 2(a), displays a clear anomaly in the FC curve at approximately 98 K [first derivative spectrum in the inset of Fig. 2(a)], revealing the onset of magnetic order. Below this temperature, the FC curve exhibits a small hump that intersects the zero line at Tcomp = 48 K. With further cooling, χ decreases until the technical limit (2 K), which is commonly known as magnetization reversal. Conversely, the ZFC curve shows a very weak response at 98 K. Notably, the FC and post-FC (when heated) curves follow the same trend, unlike those observed for GdCrO3. Furthermore, GSCO exhibits no features related to the spin reorientation that occurs in GdCrO3 [2,5]. As suggested by the GSCO structural analysis, two Cr ions with different valences located at different crystallographic sites are likely connected by AFM exchange interactions and may induce long-range magnetic order at 98 K. Early studies report a similar magnetic behavior, i.e., by the canted FiM order of the monoclinic (P21/n) double-perovskite La2Ni1.19Os0.81O6 [64]. Thus, the developed magnetic order of GSCO is likely a canted FiM order, with a transition temperature TFiM = 98 K. Under the ZFC condition, when a magnetic field is applied at the lowest temperature, the easy axes of the randomly oriented Gd moments are aligned along the magnetic field direction, and GSCO displays a positive χ. When heated from 2 K, the Gd moments are thermally disturbed and χ decreases. As the magnetizations of the sublattices (Gd and Cr) are unequal, there is no compensation phenomenon. The FC-χ curve at H = –0.1 kOe was also recorded to analyze whether the stray magnetic field plays a role in the observed magnetization reversal. The FC-χ curves measured at H = 0.1 and –0.1 kOe are plotted in Fig. 2(b). While measuring the FC–χ curve in the negative field, χ remains negative at >Tcomp and becomes positive at >TFiM (> ~200 K), suggesting a short-range magnetic correlation between TFiM and ~200 K. The sharp decrease in the 1/χ curve softens with an increasing field, possibly due to the formation of short-range FM clusters. To confirm this, we analyzed the 1/χ vs. T curves at 105 K < T < 200 K using the power-law expression of the Griffith singularity effect. , where A is a constant, is the critical temperature below which χ diverges, and λ is an exponent [32, 65]. 1/χ does not follow the power-law expression well, signifying that the possible magnetic cluster behavior is non-Griffith-like. A similar non-Griffith-like behavior is observed in the half-doped cobaltite La0.5Sr0.5CoO3, wherein AFM clusters are formed in the paramagnetic matrix [66]. Because we observe increasing magnetization of the pure paramagnetic phase by extrapolating the high-temperature Curie-Weiss (CW) line, short-range FM clusters, not AFM clusters, cause the observed non-Griffith-like behavior. Furthermore, is much lower than TFiM, which is inconsistent with the anticipated behavior of a Griffiths phase (i.e., > TFiM). However, the exact origin of this short-range magnetic order remains unclear. The ac-χ (= χ' + i χ") of GSCO was measured in an ac magnetic field of 5 Oe at frequencies in the range 2–500 Hz. The in- (χ') and out-of-phase (χ") parts of the zero-field ac-χ as functions of T are shown in Figs. 2(g) and 2(h), respectively. No sharp peak is observed at TFiM, which is consistent with the weak responses of the DC ZFC-χ curves. No additional anomalies or magnetically glassy features are detected. In contrast, GCCO exhibits a completely different magnetic behavior. Figures 3(a)–3(c) show the DC ZFC- and FC-χ curves measured under various magnetic fields (H = 0.05, 0.1, or 0.5 kOe). The ZFC- and FC-χ curves are identical, increasing continuously as the temperature decreases. No onset of magnetic order is observed, as shown in the inset of Fig. 3(b). However, there is a clear difference between the ZFC and FC curves at <100 K, as indicated by the arrows shown in Fig. 3(d). The divergence is much more pronounced in the first derivative, as shown in the inset of Fig. 3(d). The random substitution of Ca with Gd may lead to competition between the Cr3+–O–Cr3+ AFM superexchange and the Cr3+–O–Cr4+ FM double exchange interactions, causing a magnetically disordered state. However, the divergence between the ZFC and FC curves may indicate that AFM interactions are slightly dominant. Notably, β-CaCr2O4 undergoes a magnetic transition characterized by the propagation vector k = (0, 0, ~0.477) at TN = 21 K [62]. Although a small amount of β-CaCr2O4 (3.9 wt.%) is detected in GCCO, no corresponding feature is observed in the χ vs T or dMFC/dT vs T plot. The thermal remanent magnetizations (MTRM) of both materials were measured to further elucidate the onsets of the long-range magnetic order and short-range magnetic correlation. During measurement, the magnetic field was set to zero at 2 K immediately after cooling the sample from the paramagnetic state (350 K) in the presence of H (= 0.5 kOe) and the sample was then heated to measure the magnetization. Similar protocols are often used to study the spin dynamics of glassy magnetic materials. In addition, MTRM exhibits clear anomalies at the onset of the magnetic order [67, 68]. MTRM of GSCO and GCCO as functions of T are shown in Figs. 4(a) and 4(b), respectively. The magnetization reversal of GSCO is again confirmed by the MTRM measurement. However, the thermal variation of MTRM differs slightly from that observed in the DC FC-χ measurement. In addition to the sharp increase in magnetization at the onset of long-range magnetic order at TFiM, a clear anomaly is detected at approximately 150 K for GSCO [inset of Fig. 4(a)]. This indicates that a significant contribution from the short-range magnetic correlation begins at 150 K, which is >>TFiM. Conversely, GCCO exhibits an increase in magnetization at approximately 100 K [Fig. 4(b)], which highlights the presence of the magnetic anomaly. Figures 5(a) and 5(b) show the temperature-dependent 1/χ values of GSCO (H = 5 kOe) and GCCO (H = 0.1 kOe), respectively. A moderately high magnetic field was used for GSCO to avoid other dilute magnetic interactions. The solid straight lines (red) shown in both plots are guidelines to aid in identifying deviations from CW behavior. The 1/χ curves of GSCO and GCCO deviate from CW behavior at less than approximately 160 K and less than approximately 105 K, respectively. To obtain the CW parameters, we fitted the high-temperature 1/χ curves to the CW equation 1/χ = (T – Θ)/C, where C = NAμ2eff/3kB is the Curie constant, NA is Avogadro’s number, μeff is the effective magnetic moment, kB is the Boltzmann constant, and Θ is the Weiss temperature. The fitted curves of GSCO and GCCO are displayed in the insets of Figs. 5(a) and 5(b), respectively, and the respective μeff values of GSCO and GCCO are 7.04 and 6.75 μB/f. u. Because half of the Cr3+ ions transform to Cr4+ ions upon half-doping of Sr2+ (Ca2+) at the Gd site of GdCrO3, the theoretical moments should be μeff = 6.53 μB/f. u., based on the equation , where μGd = 7.90 μB, μCr3+ = 3.87 μB (spin-only due to the quenched 3d orbital), and μCr4+ = 2.82 μB (spin-only). This value is close to the experimentally observed values of GCCO and GSCO. In addition, the Θ values of GSCO and GCCO are –63 and –52 K, respectively, with the negative values indicating that AFM interactions are dominant in both materials. To further elucidate the contrasting magnetic behaviors of these two materials, we recorded isothermal field-dependent magnetization (M vs. H) curves under ZFC conditions. Prior to the measurement of each M–H curve, the material was cooled from well above the onset temperature of magnetic order to the targeted temperature under a zero magnetic field. Figure 6(a) shows the M–H curves of GSCO at temperatures of 2, 10, 40, 60, and 85 K (all less than TFiM). At T = 40, 60, or 85 K, linear changes in M vs. H are observed in the high-field regions, but weak hystereses are observed in the low-field regions. Much wider hysteresis loops are observed at T = 2 or 10 K, indicating the presence of FM and AFM correlations below TFiM. Regarding the hysteresis loops, we plotted the values of the coercive field (HC) based on the M–H curves at different temperatures in Fig. 6(b). The decrease in HC at <85 K may be related to the opposite orientation of the Gd sublattice owing to the negative internal field (i.e., the compensation phenomenon) with respect to the applied field. An enlarged view of the isotherm at T = 2 K is shown in the inset of Fig. 6(b), which indicates that the M–H loop closes within the range ±20 kOe. Figure 6(c) shows the M–H isotherms of GCCO at T = 2 or 10 K. HC is 40 Oe at 2 K, which is likely related to the AFM spin correlation. Moreover, even at 70 kOe, the M–H curves are unsaturated, which is typical for materials with AFM-exchange interactions. Nevertheless, the significant S-shapes of the M–H loops of GSCO and GCCO at T = 2 or 10 K may be due to the contributions from the much larger Gd3+ moments. To compare the magnetic properties of these two materials, we plotted the isothermal M–H curves measured at T = 2 K, as shown in Fig. 6(d), with the inset showing an enlarged view. Notably, there is a small difference in the saturation magnetizations of these compounds at 70 kOe (3.05 and 3.17 μB/f. u. for GSCO and GCCO, respectively), possibly due to the impurities in GCCO. Notably, the HC of GSCO (= 1089 Oe) is 27-fold larger than that of GCCO, which demonstrates its different magnetic nature. Generally, materials with canted FiM structures exhibit higher HC values than those of regular AFM materials. In general, a heterogeneous material with two different magnetic states, such as FM and AFM states [69,70], an FM state and a spin glass [51,52], and FM and FiM states [71], sometimes results in the EB effect. This phenomenon, which is related to the shift of the M–H loop along the magnetic field axis, has considerable applications in spintronic devices. Recently, the EB effect was also observed in a magnetically homogeneous material, i.e., FiM [14]. Because non-Griffith-like FM clusters and canted FiM states coexist in GSCO, we investigated the EB effects by measuring the FC M–H loop at several temperatures. If the cooling field (Hcool) is positive, the FC M–H loop shifts towards the negative field axis, which is widely recognized as the conventional EB effect. The EB field (HEB) is a measure of EB anisotropy and defined as HEB = (H1 + H2)/2, where H1 and H2 are the first (negative) and second (positive) coercive fields at the first and second magnetization reversals, respectively [51]. Notably, HEB should be negative in the conventional EB effect [70]. Figure 7(a) shows the FC M–H loops of GSCO at Hcool = 20 kOe at various temperatures (T = 2, 10, 15, or 20 K) below TFiM. Notably, the FC loops were measured within a maximum field (Hmax) of ±20 kOe. Contrary to the symmetric nature of a regular M–H loop at the origin (absence of EB), the FC loop shifts slightly along the field direction from the origin, suggesting that EB anisotropy is induced upon field cooling. The FC loops at T = 2 K measured in different directions of Hcool = 20 and –20 kOe are shown in Fig. 7(b). The magnitude of the shift may be small, but the loop shifts in the opposite direction. The enlarged views (within ±3 kOe) of the FC loops collected in the different directions of Hcool at T = 10, 15, 20, 30, or 50 K are shown in Figs. 7(c)–7(g), respectively. Each loop shifts alternatively, i.e., the EB anisotropy undergoes sign reversal when Hcool changes direction. Remarkably, the FC loop shifts towards the positive field axis when the material is cooled in the positive field, which contradicts the expectation of the conventional EB effect. This is known as the inverse EB (IEB) effect, and the FC loop exhibits the IEB effect at T ≤ 50 K, whereas the conventional EB effect is observed at T ≥ 70 K, e.g., an enlarged view of the FC loop within ±1 kOe at T = 90 K [Fig. 7(h)] reveals the conventional EB effect. Figure 8 shows the temperature dependences of H1, H2, HC, and HEB measured at a positive Hcool. H1 and H2 are negative between 70 and 100 K but positive at <70 K. H2 remains positive at ≥2 K and H1 becomes negative again at <20 K. Clearly, the H1 and H2 curves are not monotonous, and thus, a crossover from conventional EB to IEB effects (i.e., negative-to-positive sign inversion of HEB) is observed in GSCO, which may be related to the observed magnetization reversal. HEB approaches zero at <10 K, confirming the absence of any EB effect. Apart from the small peak at 30 kOe. In addition, the almost complete suppression of HEB at higher Hmax values may be associated with suppressed FM contributions from Cr3+/Cr4+ ions in the FiM structure. At Hmax ≥ 30 kOe, a large paramagnetic Gd3+ moment dominates the entire magnetism, which inevitably reduces the exchange anisotropy between the FM clusters and FiM state. Visualizing the origin of the EB effect, particularly the IEB effect, is rather complex, particularly in single-phase polycrystalline materials with invisible physical boundaries between the two different magnetic phases. Owing to the presence of FM clusters at high temperatures, complex interfacial magnetic interactions between these clusters and the FiM state may induce EB anisotropy, causing the traditional EB effect in GSCO. Nevertheless, the presence of FM and AFM components specific to the FiM state may be the real cause of the observed traditional EB behavior. To gain deeper insight into the IEB phenomenon, we analyzed possible mechanisms to elucidate its origin. In most earlier investigations [73–76], the phenomena of IEB manifest with increasing strength of Hcool, in addition to the conventional EB effect at lower Hcool values. The sign reversal of HEB is successfully explained for a system wherein FM nanodroplets are embedded in a charge-ordered AFM host using the following equation: –HEB J2A L(μ, Hcool, Tf) + J Hcool, where J is the surface exchange constant, A is a constant (multiplication factor), and L is the Langevin function of the magnetic moment μ of the FM nanodroplets, Hcool, and freezing temperature Tf of the interfacial spin [75]. Clearly, the competition between the surface exchange interaction and Hcool may induce the sign reversal of HEB. This equation shows that for a lower Hcool, the first term dominates, and HEB becomes negative, as J2 is always positive. For a higher Hcool, the second term may be significant, and in the case of AFM interfacial coupling, i.e., J < 0, sign reversal of HEB may be anticipated. In contrast, in this investigation, when T is varied at a fixed Hcool and the sign of Hcool is changed at a fixed T, sign inversion of HEB is observed. Because the HEB equation does not contain T-dependent terms, the above prediction is unlikely. Another possibility in achieving the IEB effect is a magnetization reversal in the FiM state at >TFiM). In the first case, the formula used is as follows: Ctotal(T) = nD Ɗ(T, ΘD) + nE Ɛ(T, ΘE), where Ɗ and Ɛ are the Debye and Einstein functions, respectively. ΘD and ΘE are the respective Debye and Einstein temperatures, and the scale factors nD and nE correspond to the numbers of vibrational modes per formula unit in the Debye and Einstein models, respectively. In the latter case, the heat capacity is approximated by Ctotal(T) = m1 Ɗ(T, ΘD1) + m2 Ɗ(T, ΘD2), where m1 and m2 are the coefficients related to the vibrational modes per formula unit and ΘD1 and ΘD2 are the characteristic Debye temperatures. In both cases, proper fitting is observed with the parameters nD = 2.34, ΘD = 859 K, nE = 2.73, ΘE = 273 K, m1 = 2.09, m2 = 2.99, ΘD1 = 888 K, and ΘD2 = 385 K. The total number of vibrational modes in both cases is approximately five (i.e., nD + nE ≈ 5 and m1 + m2 ≈ 5), which validates the presence of five atoms per formula unit of GSCO. Clattice dominates Ctotal at temperatures of >>TFiM, and thus, the fitted parameters enable the extrapolation of Clattice to the low-temperature limit, as shown by the solid and dotted lines [for Clattice (Debye) and Clattice (Debye + Einstein), respectively] displayed in Fig. 10(a). Because the observed Ctotal and Debye (only) models are very similar, we adopted Clattice (Debye) as a reference to examine the lattice contribution for further analysis. Notably, there is no similar nonmagnetic material that may be used as a reference to properly estimate Clattice of GSCO. The magnetic contribution to the heat capacity (Cm) is estimated by subtracting Clattice from Ctotal, i.e., Cm(T) = Ctotal(T) – Clattice(T). Figure 10(b) shows Cm as a function of T, revealing a sharp peak close to TFiM = 98 K. Additionally, the data show a broad peak at approximately 45 K, with another increase at <15 K. The broad peak at TFiM. Moreover, the Cm(T) curve displays several remarkable features but is too complicated to understand clearly. Finally, Sm is estimated by integrating Cm(T)/T over the studied temperature range [Fig. 10(b)]. Sm increases rapidly with increasing temperature at ≤10 K, then gradually increases with increasing temperature, and plateaus at 17 J mol–1 K–1 at >130 K. However, the saturation value of Sm is slightly smaller than the expected Boltzmann entropy [Sm = Rln(2S + 1) ≈ 19 J mol–1 K–1] based on the mean-field theory for localized Cr3+ (S = 3/2), Cr4+ (S = 1), and Gd3+ (S = 7/2, L = 0). The dashed line in Fig. 10(b) represents the Boltzmann entropy. Several factors may cause the slight discrepancy between the observed and expected Sm, one of which is the short-range AFM ordering of Gd3+ moments. In addition, the inadequate estimation of Cm at very low temperatures by extrapolating the high-temperature Clattice may be another cause of the discrepancy. Furthermore, increasing Ctotal at the lowest temperature [2 K, inset in Fig. 10(c)] hinders the proper estimation of Cm. The Ctotal/T vs T curves of GSCO at H = 0 or 90 kOe are plotted in Fig. 10(c). Even at H = 90 kOe, no noticeable suppression at ~TFiM is observed. Instead, the valley-like features centered at approximately 15 K are moderately suppressed. As shown in the inset of Fig. 10(c), Ctotal at H = 90 kOe does not increase as it does under the zero field but decreases towards zero at <5 K. Additionally, the short-range ordering of Gd3+ moments is significantly disturbed by the application of the 90 kOe field (due to the increased Gd3+ polarization). We attempted to estimate the saturation value of Sm again by determining Clattice by fitting the high-temperature region of the Ctotal (90 kOe) curve using the combination of the two Debye functions and extrapolating to T = 0 K [Fig. 10(d)]. Remarkably, the temperature dependence of Sm [inset in Fig. 10(d)] shows that Sm generally saturates at a value much closer to the Boltzmann entropy than that at H = 0 kOe. Thus, the discrepancy between the observed (H = 0 kOe) and expected Sm is likely caused by short-range AFM ordering of Gd3+ moments. To facilitate further comparative studies, we performed a detailed analysis of Ctotal of GCCO. Remarkably, the temperature dependences of the zero-field Ctotal(T) of both materials are very similar [Figs. 10(a) and 11(a) show those of GSCO and GCCO, respectively], but a clear anomaly is observed at ~100 K in the Ctotal(T) curve of GCCO. The observed anomalies and magnetization data indicate that GCCO undergoes AFM ordering at ~100 K. The solid red line shown in Fig. 11(a) represents the GCCO Clattice estimated by combining the two Debye functions. Anomalies are detected at ~100 K, but no sharp peaks are observed in the Cm(T) plot close to this temperature (not shown). Instead, a broad peak and an upturn at approximately 75 and <15 K are observed, respectively. As shown in the inset of Fig. 11(a), when the temperature is >130 K, Sm saturates at 17.5 J mol–1 K–1, which is slightly smaller than the expected Boltzmann entropy. At H = 90 kOe, Ctotal(T) displays no significant change in the magnetic transition at 100 K [C/T vs. T plot in Fig. 11(b)]. Conversely, valley-like features at 15 K, such as those observed for GSCO, are strongly influenced by the application of H. The inset in Fig. 11(b) shows an enlarged view of the Ctotal(T) curves at H = 0 or 90 kOe, revealing that they intersect at T = 5 K. D. Resistivity Figure 12(a) shows the temperature-dependent resistivities ρ(T) of GSCO and GCCO. The increase in resistivity with decreasing temperature should yield semiconductor-like behavior. In this context, measuring ρ(T) at temperatures of <70 K was impossible, because of the high resistance which was above the instrumental limit. At room temperature, ρ of GSCO is almost 14-fold higher than that of GCCO (ρ300K = 57.01 and 4.19 Ω-cm for GSCO and GCCO, respectively). No metallic behavior is observed within the investigated temperature range, and these features contrast with the electrical behaviors of half-doped manganites and cobaltites [36,50]. The resistivity data were analyzed using the Arrhenius model, ln ρ vs. 1000/T, to investigate the possible conduction mechanisms, as shown in Fig. 12(b). Owing to the nonlinear behaviors of the curves, the ρ(T) curves of both materials are not well modeled by the Arrhenius model. Instead, the linear behavior of the ln ρ vs. T–-1/4 plot [Fig. 12(c)] shows that variable-range hopping better explains the observed electronic behaviors of GSCO and GCCO. E. Dielectric behavior Several RCrO3 materials (excluding R = Sc–Pr, Pm, Eu, Dy, Yb) should exhibit significant magnetoelectric coupling at temperatures of TFiM. This was further supported by the heat capacity measurements. Remarkably, GSCO displayed a crossover from the conventional EB effect to the IEB effect upon cooling. Such a crossover could be caused by the reversal of the magnetic moment due to various competing DM interactions. In addition, significant magnetoelectric coupling with ferroelectric relaxor-like states was identified at the onsets of magnetic order of both materials. The presence of the EB effect, particularly the IEB effect, and magnetoelectric coupling yields considerable prospects for application in magnetic memory and spintronic devices. 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Atom x y z Occupancy (fixed) Biso (Å2)(fixed) Gd 0.2489(17) 0.5245(2) 0.2506(13) 0.5 0.55 Sr 0.2489(17) 0.5245(2) 0.2506(13) 0.5 0.55 Cr1 0.5 0 0.5 1 0.45 Cr2 0 0 0 1 0.45 O1 0.239(13) 0.0046(16) 0.250(9) 1 0.50 O2 0.305(6) 0.742(5) 0.049(4) 1 0.50 O3 0.238(5) 0.278(4) 0.040(3) 1 0.50During refinement, Biso of Gd and Sr, Cr1 and Cr2, and O1, O2, and O3 were constrained as equal and fixed. Gd0.5Sr0.5CrO3: monoclinic. Space group P21/c (no. 14). a = 5.40035(16) Å, b = 5.4135(3) Å, c = 9.3506(2) Å, β = 125.2400(6)°, V = 223.264(16) Å3, and Z = 4. Residuals: Rwp = 5.09%, Rp = 2.88%, S = 6.785.TABLE II Atomic positions, occupancies, and thermal displacement parameters of Gd0.5Ca0.5CrO3 (96.1 wt.%) and CaCr2O4 (3.9 wt.%) obtained using synchrotron XRD. Atom x y z Occupancy (fixed) Biso (Å2) (fixed) Gd0.5Ca0.5CrO3 Gd –0.00861(19) 0.04939(8) 0.25 0.5 0.55 Ca –0.00861(19) 0.04939(8) 0.25 0.5 0.55 Cr 0.5 0 0 1.0 0.45 O1 0.0695(8) 0.4791(6) 0.25 1.0 0.50 O2 –0.2921(7) 0.2902(6) 0.0428(4) 1.0 0.50 CaCr2O4 Ca 0.6594 0.7593 0.25 1.0 0.74 Cr1 0.6124 0.4403 0.25 1.0 0.26 Cr2 0.1010 0.4169 0.25 1.0 0.28 O1 0.1596 0.2007 0.25 1.0 0.17 O2 0.4757 0.1151 0.25 1.0 0.06 O3 0.7860 0.5285 0.25 1.0 0.11 O4 0.4262 0.4177 0.25 1.0 0.70During refinement of Gd0.5Ca0.5CrO3, Biso of Gd and Ca, and O1 and O2, were constrained as equal and fixed. Biso of Cr was fixed [62], along with Biso of all atoms of CaCr2O4. Gd0.5Ca0.5CrO3: orthorhombic. Space group: Pbnm (No. 62). a = 5.31047(2) Å, b = 5.42503(2) Å, c = 7.54208(3) Å, V = 217.2834(16) Å3, and Z = 4. CaCr2O4: orthorhombic. Space group: Pbnm (No. 62). a = 10.61746(4) Å, b = 9.08507(14) Å, c = 2.96481(19) Å, V = 285.987(19) Å3, and Z = 4. Residuals: Rwp = 4.78%, Rp = 2.82%, and S = 5.2428. FIG. 1 Rietveld refinement of the synchrotron XRD patterns of (a) GSCO and (b) GCCO collected at room temperature. The crosses and solid red lines represent the observed and calculated patterns, respectively, with the differences (solid blue lines) shown at the bottom. The vertical ticks indicate the positions of the allowed Bragg reflections. For GCCO, the upper (olive) and bottom (magenta) rows indicate the reflections of the main (GCCO) and secondary (CaCr2O4) phases, respectively. The unit cell of each material is shown as an inset. FIG. 2 (a) ZFC- and FC-χ(T) curves of GSCO measured in a magnetic field of H = 0.1 kOe. The inset shows the derivative curve of the FC curve. (b) FC-χ(T) curves of GSCO measured at H = 0.1 and –0.1 kOe. (c)–(e) ZFC- and FC-χ(T) curves measured at H = 0.5, 1, or 5 kOe, respectively. The inset of (c) displays an enlarged view of the ZFC- and FC-χ(T) curves at H = 0.5 kOe. (f) Inverse χ (1/χ) as a function of temperature and applied field. (g) In- (χˊ) and (h) out-of-phase (χ˝) parts of ac-χ(T) of GSCO measured in an ac magnetic field of 5 Oe at various frequencies. FIG. 3 (a)–(c) ZFC- and FC-χ(T) curves of GCCO measured at H = 50 Oe or 0.1 or 0.5 kOe, respectively. The inset of (b) shows the derivative curve at H = 0.1 kOe. (d) Difference between the ZFC- and FC-χ(T) curves at H = 0.1 kOe. Inset of (d) shows the derivative curve of (χFC – χZFC). FIG. 4 Thermal remanent magnetizations (MTRM) of (a) GSCO and (b) GCCO, which indicate the onset of magnetic ordering (arrows). The inset shows an enlarged view. FIG. 5 Inverse magnetic susceptibilities (1/χ) of (a) GSCO (at H = 5 kOe) and (b) GCCO (at H = 0.1 kOe) as functions of temperature. The solid red lines are guidelines for linear behavior, and the insets show the Curie-Weiss fittings of the high-temperature regions. FIG. 6 (a) Isothermal magnetization (M) of GSCO as a function of magnetic field (H) measured under the ZFC condition at several temperatures (T = 2, 10, 40, 60, or 85 K). (b) Thermal variation of the coercive field (HC), and the inset shows a magnified view of the ZFC M–H loop at T = 2 K. (c) ZFC M–H loops of GCCO measured at temperatures of 2 and 10 K. (d) Comparison of the ZFC M–H loops of GSCO and GCCO. The inset shows an enlarged view. FIG. 7 (a) M–H loops of GSCO measured at Hcool = 20 kOe. The maximum field is ±20 kOe, and the temperatures are