Spin switching and unusual exchange bias in the single-crystalline $\mathrm{GdCr}{\mathrm{O}}_3$ compensated ferrimagnet

An unusual exchange bias (EB) effect in single-crystalline $\mathrm{GdCr}{\mathrm{O}}_3$ compensated ferrimagnet (fM), composed of two antiferromagnetically coupled Gd and Cr sublattices, presenting two opposite ferromagnetic (FM) moments, is reported. It is shown that the temperature- or field-induced fast reversal of the net FM moment in $\mathrm{GdCr}{\mathrm{O}}_3$ may be identified as a switching between two opposite spin configurations, attendant with abrupt drop in Zeeman energy $\approx k_{\mathrm{B}}(7\times {10}^{-4}\mathrm{K})$ per formula unit. It was found that the FM moment reversal is exchange biased in the narrow temperature interval above the compensation temperature $T_{\mathrm{comp}}=144\mathrm{K}$. Namely, the EB field emerges and diverges upon approaching $T_{\mathrm{comp}}$ at temperatures $T>T_{\mathrm{comp}}$ while unexpectedly it collapses to zero below $T_{\mathrm{comp}}$. This is in contrast to experimental results obtained for compensated fMs $R\mathrm{Fe}{\mathrm{O}}_3(R=\mathrm{Nd}$, Sm, Er) orthoferrites showing EB in a narrow range, both above and below $T_{\mathrm{comp}}$. We suppose that breakdown of EB in $\mathrm{GdCr}{\mathrm{O}}_3$ may be linked to the lack of anisotropy of the spin-only Gd $S$-ion magnetic moment dominating below $T_{\mathrm{comp}}$.

Figure 1

(a) Temperature dependence of magnetization of $\mathrm{GdCr}{\mathrm{O}}_3$ single crystal measured along the $c$ axis upon field cooling (FC) and subsequently on warming (FCW) at external magnetic field of 100, 50, and 12 Oe. Two possible spin configurations above and below the spin-switching (magnetization-reversal) temperature $T_{\mathrm{sw}}$ are shown. The upper inset shows FC and FCW magnetizations around the compensation point $T_{\mathrm{comp}}=144\mathrm{K}$. The lower inset shows the spin switching at 50 Oe of external magnetic field directed along the $c$ axis in the sample 2 with much larger demagnetization factor $4\pi N=4.27$. (b) Spin switching around $T_{\mathrm{comp}}$ at higher magnetic fields. (c) The $T_{\mathrm{sw}}-H_{\mathrm{sw}}$ boundary between phases with different spin configurations, with $H_{\mathrm{sw}}$ field values corrected for the demagnetization field. The lines represent fit with $H_{\mathrm{sw}}\propto T/(T-T_{\mathrm{comp}})$ dependence.

Figure 2

(a) Remanent magnetization $M_{\mathrm{r}}$, measured along the $c$ axis upon cooling at $H=0$, after FC with $H=10\mathrm{kOe}$ to temperature (1) $T=130\mathrm{K}<T_{\mathrm{comp}}$ and (2) $T=160\mathrm{K}>T_{\mathrm{comp}}$. The $M_{\mathrm{r}}$ obtained with different cooling protocol shows the alternating sign. A sharp fall in $M_{\mathrm{r}}$ at $T_{\mathrm{sw}}=32\mathrm{K}$ indicates a transition from the single-domain state to the multidomain one with $M\approx 0$. The lines are the best fit with Eq. (1). (b) $M$ vs $H$ curves along the $c$ axis at several temperatures. The extrapolated lines intersect, in accordance with Eq. (1), at $H=-H_{\mathrm{I}}=-5.6\mathrm{kOe}$ and $M=M_{\mathrm{Cr}}=-1.22\mathrm{emu}/\mathrm{g}$.

Figure 3

Magnetization hysteresis loops of $\mathrm{GdCr}{\mathrm{O}}_3$, in an extended scale, measured between ±10 kOe and with cooling field 10 kOe along the $c$ axis at temperatures $T<T_{\mathrm{comp}}=144\mathrm{K}$ (a)–(c) and at $T$ > $T_{\mathrm{comp}}$ (d)–(f). Arrows indicate the fields of the first and the second magnetization reversals, $H_1$ and $H_2$, respectively, and EB field $H_{\mathrm{EB}}$. The ascending and descending loop branches around $H_1$ are also indicated (e). (g) The magnetization loop at $T_{\mathrm{comp}}$. (h) The calculated $C_{\mathrm{Gd}}/T$ and measured $M$($H$) slopes in the temperature range between 50 and 160 K.

Figure 4

Temperature variation of (a) coercive fields $H_1$ and $H_2$ at the first and second magnetization reversals, respectively [the $H_{\mathrm{sw}}$ vs $T$ dependence shown in Fig. 1 is also presented for comparison], (b) average coercive field $H_{\mathrm{C}}$ [the lines are fit with $H_{\mathrm{C}}\propto T/(T-T_{\mathrm{comp}})$ law], and (c) exchange bias field $H_{\mathrm{EB}}$ for $\mathrm{GdCr}{\mathrm{O}}_3$ with applied magnetic field along the $c$ axis. Exchange bias exists in the narrow temperature interval (marked by shadow area) above $T_{\mathrm{comp}}$, and EB collapses to zero at $T<T_{\mathrm{comp}}$.

Figure 5

Magnetization loops of $\mathrm{GdCr}{\mathrm{O}}_3$ measured between ±10 kOe at 150 K with two opposing small cooling fields $H_{\mathrm{cool}}=+20\mathrm{Oe}$ (a) and −20 Oe (b). The field $H_{\mathrm{EB}}$ changes sign with altering the $H_{\mathrm{cool}}$ sign. (c) The $H_{\mathrm{EB}}$ vs $H_{\mathrm{cool}}$ dependence at 150 K.