Effects of random fields on the phase transitions and phase diagram of ${\mathrm{Mn}}_{0.75}$${\mathrm{Zn}}_{0.25}$${\mathrm{F}}_2$

The magnetic phase transitions and phase diagram of ${\mathrm{Mn}}_{0.75}$ ${\mathrm{Zn}}_{0.25}$ ${\mathrm{F}}_2$ are investigated by dilatometric, ultrasonic-attenuation, and magnetization measurements. The random fields, generated by the magnetic field $H$, affect all three phase boundaries: the spin-flop line $H_{\mathrm{sf}}\mathrm{}\left(T\right)\mathrm{}$ separating the antiferromagnetic (AF) phase from the spin-flop (SF) phase; the boundary $T_c^{\parallel }\mathrm{}\left(H\right)\mathrm{}$ between the paramagnetic (P) and AF phases; and the P-SF boundary $T_c^{\perp }\mathrm{}\left(H\right)\mathrm{}$. At $T=0\mathrm{}$, $H_{\mathrm{sf}}=58.2\mathrm{}\pm 0.3$ kOe. At high temperatures the boundary $H_{\mathrm{sf}}\mathrm{}\left(T\right)\mathrm{}$ is reentrant, in disagreement with the mean-field prediction. Near the P-AF transitions the differential thermal expansion and differential magnetostriction exhibit hysteresis effects when the transition field is above about 12 kOe. In low fields the P-AF transitions are quite sharp, in agreement with earlier data. In high fields the P-AF transitions are smeared if the sample is cooled at constant $H$ or if $H$ is reduced at constant $T$. The P-AF transitions at high $H$ are sharper if the sample is warmed in a field after it has been cooled in zero field. The hysteretic behavior at high $H$ is consistent with recent theory. The transition temperature $T_c^{\parallel }$ is depressed substantially by the random fields. The crossover exponent obtained from the low-field results for $T_c^{\parallel }$ is $\phi =1.25\mathrm{}\pm 0.07$, which agrees with the Fishman-Aharony prediction. The Néel temperature is 46.0 K. The P-SF transition temperature $T_c^{\perp }$ increases with increasing $H$ up to 131 kOe. This increase of $T_c^{\perp }$ is much larger than in pure Mn${\mathrm{F}}_2$, but is consistent with other data in siterandom uniaxial antiferromagnets. The phase diagram in the bicritical region is qualitatively different from that in pure Mn${\mathrm{F}}_2$. Also, we do not observe the two separate critical lines which surround the intermediate phase suggested by Aharony.