Critical Attenuation of Sound in Gadolinium

We present ultrasonic attenuation measurements in the vicinity of the Curie temperature. Longitudinal waves along the $c$ axis exhibit a large critical attenuation, whereas transverse waves show only a spurious attenuation peak. Along the $a$ axis, the critical attenuation for longitudinal waves is much smaller. In a nonsymmetry direction, both longitudinal and transverse waves show large critical attenuation. All these results can be explained by assuming that the spin-phonon coupling is of the volume magnetostrictive type. For longitudinal waves propagating along either the $c$ or the $a$ axis, we find the following attenuation law for the frequency range 30-180 Mc/sec and $\frac{(T-T_c)}{T_c}>1\mathrm{}\times {10}^{-3\mathrm{}}:\alpha \propto {\omega }^2{(T-T_c)}^{-1.2\mathrm{}\pm 0.1}$. For temperatures nearer to $T_c$, the attenuation remains finite. Theories of this effect can account quantitatively for the frequency dependence but not for the temperature dependence.