Paramagnetic-to-Antiferromagnetic Phase Boundaries of FeF2from Ultrasonic Measurements

The attenuation of longitudinal ultrasonic waves in Fe${\mathrm{F}}_2$ exhibits a $\lambda$ anomaly at the paramagnetic-to-antiferromagnetic (P-AF) transition, both in zero and in finite magnetic fields. The P-AF phase boundaries in the $H-T$ plane were determined in magnetic fields up to 200 kG directed along the [001] and [110] directions. These boundaries are well described by the relation $T_N-T=C{H}^2$, where $C=10.0\mathrm{}\times {10}^{-11\mathrm{}}$ °K/${\mathrm{G}}^2$ for $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[001\right]\mathrm{}$, and $C=2.0\mathrm{}\times {10}^{-11\mathrm{}}$ ${\mathrm{°}\mathrm{K}/\mathrm{G}}^2$ for $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[110\right]\mathrm{}$. The Néel temperature is $T_N=(78.35\mathrm{}\pm 0.03)$ °K. The experimental results for the P-AF phase boundaries are in reasonable agreement with the results of detailed calculations carried out in the molecular field approximation. These calculations include the effects of the anisotropy on $T_N$, and on the coefficient $C$ for fields parallel and perpendicular to the preferred axis. The more general problem of the effect of a single-ion anisotropy on the response of a spin to an effective magnetic field is also considered. A thermodynamic relation, derived by Skalyo et al., for the P-AF phase boundary with $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[001\right]\mathrm{}$ is fairly well satisfied. An unusual behavior was observed for longitudinal waves propagating along [110] with $\overrightarrow{\mathrm{H}}$ along [001]. In this configuration, the magnitude of the $\lambda$ anomaly in the attenuation, at the P-AF phase boundary, increased rapidly with $H$.