Effects of random fields on the phase diagram of ${\mathrm{Mn}}_{0.875}$${\mathrm{Zn}}_{0.125}$${\mathrm{F}}_2$

Phase transitions in ${\mathrm{Mn}}_{1-x}{\mathrm{Zn}}_x{\mathrm{F}}_2$, $x=0.125\mathrm{}$, were investigated using thermal-expansion, magnetostriction, and ultrasonic-attenuation measurements. The phase diagram was determined for 4.2 $\mathrm{K}\le T\le T_N$ and $0\le H\le 140$ kOe, where $T_N=58.4\mathrm{}$ K is the Néel temperature. The magnetic field $\overrightarrow{\mathrm{H}}$ was parallel to [001]. The random field $H_R$ induced by $H$ influences the shape of the $\lambda$ anomaly at the paramagnetic-antiferromagnetic transition, and depresses the transition temperature $T_c^{\parallel }$. Some evidence for an irreversible behavior near $T_c^{\parallel }$ is found for $H\ne 0$. The paramagnetic—spin-flop boundary $T_c^{\perp }\mathrm{}\left(H\right)\mathrm{}$ exhibits a large "bulge" towards high $T$. At 4.2 K, the spin-flop field $H_{\mathrm{sf}}$ is 78 kOe, which is lower than that predicted by mean-field theory. The discrepancy is explained by considering the effect of the random fields. As $T$ increases from 4.2 K, $H_{\mathrm{sf}}$ first increases but then decreases as $T$ approaches the bicritical temperature $T_b=55\mathrm{}$ K. It is possible that the latter portion of the spin-flop line is actually one of two second-order lines which surround an intermediate phase. The Néel temperature is in reasonable agreement with mean-field theory.