The exchange-bias (EB) effect with sign reversal was found in $\mathrm{LuF}{\mathrm{e}}_{0.5}\mathrm{C}{\mathrm{r}}_{0.5}{\mathrm{O}}_3$ ferrite-chromite, which is a weak ferrimagnet below $T_{\mathrm{N}}=265\mathrm{K}$, exhibiting antiparallel orientation of the ferromagnetic (FM) moments of the Fe and Cr sublattices due to opposite sign of the Fe-Cr Dzyaloshinskii vector, as compared to that of the Fe-Fe and Cr-Cr. The weak FM moments of the studied compound compensate each other at temperature $T_{\mathrm{comp}}=230\mathrm{K}$, leading to the net magnetic moment reversal and to observed negative magnetization, at moderate applied fields, below $T_{\mathrm{comp}}$. Both vertical and horizontal shifts from the origin were gotten in the field-cooled magnetization hysteresis loops. The EB sign was found to be positive below $T_{\mathrm{comp}}$ and negative above $T_{\mathrm{comp}}$, with nonmonotonic dependence on cooling field $H_{\mathrm{cool}}$. It sharply increases at small values of magnetic fields up to $H_{\mathrm{cool}}\sim 1\mathrm{kOe}$, then remains almost unchanged in the range 1–30 kOe and strongly decreases with further increase of $H_{\mathrm{cool}}$. This unusual behavior results from the competition of various Dzyaloshinskii-Moriya interactions between $\mathrm{F}{\mathrm{e}}^{3+}$ and $\mathrm{C}{\mathrm{r}}^{3+}$ ions.

中文翻译：

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与弱铁氧体LuFe0.5Cr0.5O3中的磁化反转相关的反向交换偏置效应

发现具有符号反转的交换偏向（EB）效应 $\mathrm{卢夫}{\mathrm{Ë}}_{0.5}\mathrm{C}{\mathrm{[R}}_{0.5}{\mathrm{Ø}}_3$ 亚铁酸盐-亚铁酸盐，是下面的弱铁氧体 ${Ť}_{\mathrm{ñ}}=265\mathrm{ķ}$与Fe-Fe和Cr-Cr相比，由于Fe-Cr Dzyaloshinskii矢量的相反符号，Fe，Cr亚晶格的铁磁（FM）矩呈现反平行取向。所研究化合物的弱FM矩在温度下相互补偿${Ť}_{\mathrm{补偿}}=230\mathrm{ķ}$导致净磁矩反转并在以下中等施加磁场下观察到负磁化 ${Ť}_{\mathrm{补偿}}$。在磁场冷却的磁滞回线中获得了从原点开始的垂直和水平偏移。在下面发现EB信号为正${Ť}_{\mathrm{补偿}}$ 和上面的负数 ${Ť}_{\mathrm{补偿}}$，对冷却场具有非单调依赖性 $H_{\mathrm{凉爽的}}$。当磁场强度较小时，它会急剧增加，直至$H_{\mathrm{凉爽的}}〜\mathrm{1个}O$，然后在1–30 kOe的范围内几乎保持不变，并随着进一步的增加而大大降低 $H_{\mathrm{凉爽的}}$。这种不寻常的行为是由于各种Dzyaloshinskii-Moriya之间的竞争所致。$\mathrm{F}{\mathrm{Ë}}^{3+}$ 和 $\mathrm{C}{\mathrm{[R}}^{3+}$ 离子。