Inverse exchange bias effects and magnetoelectric coupling of the half-doped perovskite-type chromites ${\mathrm{Gd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{CrO}}_3$ and ${\mathrm{Gd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{CrO}}_3$

The ${\mathrm{Cr}}^{4+}$ oxidation state with two electrons in the $\mathrm{Cr}3d$ 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 half-doped perovskite-type chromites ${\mathrm{Gd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{CrO}}_3$ (GSCO) and ${\mathrm{Gd}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{CrO}}_3$ (GCCO). Fifty percent of the Cr occurs in the ${\mathrm{Cr}}^{4+}$ oxidation state after high-pressure synthesis at 6 GPa and 1200 °C. The materials were investigated using synchrotron x-ray diffraction, magnetization, heat capacity, and dielectric measurements. The diffraction patterns show that GSCO and GCCO crystallize in orthorhombic ($Pnma$) structures with different degrees of local lattice distortion. GSCO exhibits a long-range magnetic order at temperatures of $<98\mathrm{K}$, accompanied by magnetization reversal, suggesting that the magnetic ground state is ferrimagnetic. In contrast, GCCO displays antiferromagnetic characters at temperatures $<\sim 100\mathrm{K}$. In addition, GSCO exhibits a crossover between conventional and inverse exchange bias effects at low temperatures ($<50\mathrm{K}$). This is likely caused by asymmetric exchange Dzyaloshinskii-Moriya interactions between the Cr ions of different valences (+3 and +4). Furthermore, significant magnetoelectric coupling at the onset of the magnetic order is supported by temperature-dependent dielectric measurements.

Figure 1

Rietveld refinement of the synchrotron x-ray diffraction (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. The upper (olive) and bottom (magenta) rows indicate the reflections of the main and secondary phases, respectively. The lattice parameters are $a=5.41289\left(2\right)\AA , b=7.63652\left(2\right)\AA$, and $c=5.39966\left(2\right)\AA$ for GSCO ($Pnma$), and $a=5.42543\left(1\right)\AA , b=7.54252\left(1\right)\AA$, and $c=5.31059\left(1\right)\AA$ for GCCO ($Pnma$). The secondary phase is ${\mathrm{Cr}}_2{\mathrm{O}}_3$ (1.7 wt. %) for GSCO and ${\mathrm{CaCr}}_2{\mathrm{O}}_4$ (2.5 wt. %) for GCCO. The unit cell of each material is shown as an inset. Green, yellow, blue, and red balls denote Gd/Sr, Gd/Ca, O, and Cr, respectively.

Figure 2

(a) Zero-field-cooled (ZFC)- and field-cooled (FC)-$\chi \left(T\right)$ curves of GSCO measured in a magnetic field of $H=0.1\mathrm{kOe}$. The inset shows the derivative curve of the FC curve. (b) FC-$\chi \left(T\right)$ curves of GSCO measured at $H=0.1$ and −0.1 kOe. (c)–(e) ZFC- and FC-$\chi \left(T\right)$ curves measured at $H=0.5$, 1, or 5 kOe, respectively. The inset of (c) displays an enlarged view of the ZFC- and FC-$\chi \left(T\right)$ curves at $H=0.5\mathrm{kOe}$. (f) Inverse $\chi \left(1/\chi \right)$ as a function of temperature and applied field. (g) In-phase $\left({\chi }^{\prime }\right)$ and (h) out-of-phase $\left({\chi }^{\prime \prime }\right)$ parts of ac-$\chi \left(T\right)$ of GSCO measured in an ac magnetic field of 5 Oe at various frequencies.

Figure 3

(a)–(c) Zero-field-cooled (ZFC)- and field-cooled (FC)-$\chi \left(T\right)$ curves of GCCO measured at $H=50\mathrm{Oe}$ or 0.1 or 0.5 kOe, respectively. The inset of (b) shows the derivative curve at $H=0.1\mathrm{kOe}$. (d) Difference between the ZFC- and FC-$\chi \left(T\right)$ curves at $H=0.1\mathrm{kOe}$. Inset of (d) shows the derivative curve of $\left({\chi }_{\mathrm{FC}}-{\chi }_{\mathrm{ZFC}}\right)$.

Figure 4

Thermal remanent magnetizations ($M_{\mathrm{TRM}}$) of (a) GSCO and (b) GCCO, which indicate the onset of magnetic ordering (arrows). The inset shows an enlarged view.

Figure 5

Inverse magnetic susceptibilities ($1/\chi$) of (a) GSCO (at $H=5\mathrm{kOe}$) and (b) GCCO (at $H=0.1\mathrm{kOe}$) 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.

Figure 6

(a) Isothermal magnetization ($M$) of GSCO as a function of magnetic field ($H$) measured under the zero-field-cooled (ZFC) condition at several temperatures ($T=2$, 10, 40, 60, and 85 K). (b) Thermal variation of the coercive field ($H_{\mathrm{C}}$), and the inset shows a magnified view of the ZFC $M\text{−}H$ loop at $T=2\mathrm{K}$. (c) ZFC $M\text{−}H$ loops of GCCO measured at temperatures of 2, 10, 40, 60, and 85 K. (d) Comparison of the ZFC $M\text{−}H$ loops of GSCO and GCCO at 2 K. The inset shows an enlarged view.

Figure 7

(a) $M\text{−}H$ loops of GSCO measured at $H_{\mathrm{cool}}=20\mathrm{kOe}$. The maximum field is $\pm 20\mathrm{kOe}$, and the temperatures are $<T_{\mathrm{FiM}}$. (b) Hysteresis loops measured at $T=2\mathrm{K}$ and $H_{\mathrm{cool}}=20$ or $-20\mathrm{kOe}$. (c)–(h) Magnified views of the field-cooled (FC) $M\text{−}H$ loops measured at $H_{\mathrm{cool}}=\pm 20\mathrm{kOe}$ and $T=10$, 15, 20, 30, 50, or 90 K, respectively.

Figure 8

Thermal profiles of $H_1, H_2, H_{\mathrm{C}}$, and $H_{\mathrm{EB}}$ obtained from the field-cooled (FC) $M\text{−}H$ loops of GSCO at $H_{\mathrm{cool}}=20\mathrm{kOe}$ and $H_{max}=\pm 20\mathrm{kOe}$. Notably, the sign reversal of $H_{\mathrm{EB}}$ from negative to positive occurs upon cooling.

Figure 9

(a) Field-cooled (FC) $M\text{−}H$ loops of GSCO measured at $T=15\mathrm{K}$ at $H_{\mathrm{cool}}=20\mathrm{kOe}$ and $H_{max}=\pm 20,\pm 25,\pm 30$, or $\pm 70\mathrm{kOe}$. (b) Enlarged view of the loops. (c) $H_{\mathrm{C}}$ and $H_{\mathrm{EB}}$ as functions of $H_{\max }$ ($H_{\mathrm{cool}}=20\mathrm{kOe}$) at $T=15\mathrm{K}$.

Figure 10

(a) Temperature dependence of the specific heat capacity ($C_{\mathrm{total}}$) of GSCO under a zero field. The solid and dashed curves show the lattice heat capacities ($C_{\mathrm{lattice}}$) obtained by fitting to the high-temperature region with combinations of two Debye functions or Debye and Einstein functions, respectively. (b) Temperature dependences of the magnetic heat capacity ($C_m$), which is obtained by subtracting $C_{\mathrm{lattice}}$ from $C_{\mathrm{total}}$, and the magnetic entropy ($S_m$). The dash-dotted straight line represents the theoretical $S_m$. (c) $C_{\mathrm{total}}/T$ vs $T$ plots of GSCO at $H=0$ and 90 kOe. The inset shows the $C_{\mathrm{total}}$ vs $T$ plots. (d) $C_{\mathrm{total}}$($T$) of GSCO at $H=90\mathrm{kOe}$. The solid red curve represents $C_{\mathrm{lattice}}$ obtained by fitting to the high-temperature region with a combination of two Debye functions. The inset displays the $S_m$ vs $T$ curve.

Figure 11

(a) Specific heat capacity of GCCO as a function of temperature. The red solid curve shows a fitting to a combination of Debye functions, and the inset shows the thermal profile of $S_m$ of GCCO and the theoretical value. (b) $C/T$ vs $T$ plots of GCCO at $H=0$ or 90 kOe. The inset shows the $C_{\mathrm{total}}$ vs $T$ plots.

Figure 12

(a) Temperature dependences of ρ of GSCO and GCCO. (b) Alternative plot of the data. (c) Variable-range-hopping plot of the data. The red solid lines are guidelines.

Figure 13

(a)–(b) Temperature dependences of the dielectric constants (${\varepsilon }_r$) of GSCO and GCCO, respectively, as recorded at several frequencies in the range 100 Hz–2 MHz ($f=100$ Hz, 300 Hz, 903 Hz, 2.71 kHz, 8.15 kHz, 24.51 kHz, 73.68 kHz, 221.43 kHz, 665.48 kHz, and 2 MHz). The insets show representative differential curves (at 2.71 kHz). The blue and red dashed lines in the insets indicate the temperature corresponding to the onset of magnetic order of each material. (c)–(d) Temperature-dependent dielectric losses $\left(tan\delta \right)$ of GSCO and GCCO, respectively. The insets show representative differential curves (at 2.71 kHz).