Velocity of Sound in MnF2near the Néel Temperature

The anomalous change of the velocity of sound near the Néel point was measured in Mn${\mathrm{F}}_2$ for the longitudinal waves propagating along the [110], [100], and [001] directions. The measured result did not show any dispersion. The anomaly as a function of temperature was described by the power-law formula, $\frac{\Delta V}{V_0}\sim {|T-T_N|}^{-\zeta }$, with the critical exponent $\zeta$ equal to 0.12 for $T>\mathrm{}{T}_N$, and 0.02 for $T<\mathrm{}{T}_N$, for all these longitudinal waves. A significant anisotropy was found, however, in the magnitude of the anomalous change. These results were well explained by a theoretical treatment, by which a relative value of the derivatives of the dominant exchange interaction $J_2$ was deduced to be $\left|\frac{\left(\frac{\partial J_2}{\partial z}\right)}{\left(\frac{\partial J_2}{\partial x}\right)}\right|={2.7}_7$, a value in good agreement with other experimental results. Finally, combining present sound-velocity data with those on attenuation, the existence of a relaxation time of 3×${10}^{-9\mathrm{}}$ sec is suggested over the temperature range of $T-T_N\gtrsim 2\times {10}^{-2\mathrm{}}°$K in the paramagnetic phase, and implications of this relaxation time are discussed.