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.

• Received 9 October 2017
• Revised 4 March 2018

DOI:https://doi.org/10.1103/PhysRevB.97.104416