Exchange-bias reversal in magnetically compensated $\mathrm{ErFe}{\mathrm{O}}_3$ single crystal

An exchange-bias (EB) effect observed in single crystal $\mathrm{ErFe}{\mathrm{O}}_3$ compensated ferrimagnet, exhibiting the EB field $H_{\mathrm{EB}}$ increasing and diverging upon approaching compensation temperature $T_{\mathrm{comp}}=45\mathrm{K}$, and changing sign with crossing $T_{\mathrm{comp}}$, is reported. The EB sign may be changed to the opposite one by varying the field-cooling protocol, depending on whether $T_{\mathrm{comp}}$ is crossed with decreasing or increasing temperature. Namely, a different EB sign with the same $|H_{\mathrm{EB}}|$ and coercive field $H_{\mathrm{C}}$ values is obtained approaching a given $T$ with increasing and decreasing temperature and the $H_{\mathrm{EB}}\left(T\right)$ dependence completed in one way is a mirror image of that completed in another way.

Figure 1

(a) Temperature dependence of magnetization of $\mathrm{ErFe}{\mathrm{O}}_3$ single crystal measured at 100 Oe along both the $a$ and $c$ axes for zero-field-cooling (ZFC), field-cooling (FC), and field-cooling-warming (FCW) modes. The inset shows the “butterfly” behavior (hallmark of the first-order transition) around the compensation point $T_{\mathrm{comp}}$ in an extended scale. (b) Remanent magnetization $M_{\mathrm{r}}$ recorded at $H=0$ after FC in 10 kOe. (c) Jump in slope $\mathit{dM}/\mathit{dT}$ at $T_{\mathrm{comp}}$ for FC magnetization at 10 kOe.

Figure 2

Angular dependence of the magnetization of $\mathrm{ErFe}{\mathrm{O}}_3$ measured for several temperatures along the applied magnetic field $H=100\mathrm{Oe}$ in the $ac$ plane.

Figure 3

Magnetization hysteresis loops of $\mathrm{ErFe}{\mathrm{O}}_3$, in an extended scale, measured in the field up to 10 kOe applied along the $a$ axis at $T<T_{\mathrm{comp}}=45\mathrm{K}$ [(a), (c)] and at $T>T_{\mathrm{comp}}$ [(b), (d)] after different cooling procedures: FC in 10 kOe from 300 to 10 K and then warming to the given $T$ (abbreviated in the figure as FCW), and FC in 10 kOe from 300 K to given $T$ (abbreviated in the figure as FC). The possible spin configurations for the case of low applied fields depending on cooling protocol are shown.

Figure 4

(a), (b) Temperature variation of coercive fields $H_1$ and $H_2$ at the first and second magnetization reversals, respectively, obtained following different cooling procedures: FC in 10 kOe from 300 to 10 K and then warming to the given $T$ (abbreviated in the figure as FCW), and FC in 10 kOe from 300 K to given $T$ (abbreviated in the figure as FC). (c), (d) Average coercive field $H_{\mathrm{C}}$ (c) and exchange-bias field $H_{\mathrm{EB}}$ (d) around the compensation point $T_{\mathrm{comp}}$, obtained for the FCW and FC protocols. Remarkably, both the coercive $H_1$ and $H_2$ fields, and the EB field obtained with FCW exhibit the mirror behavior of those obtained with FC.