Sound Velocity Measurements of Nuclear-Ordered Solid ${}^3\mathrm{He}$ along the Melting Curve

We have measured the temperature dependence of the 10.98 MHz longitudinal sound velocity of solid ${}^3\mathrm{He}$ in the nuclear-ordered $U2D2\mathrm{}$ phase and in the paramagnetic phase along the melting curve. The temperature dependence of the sound was attributed to the contributions from the nuclear spin system and the molar volume change along the melting curve. The sound velocity increased with temperature as $T^4$ in the $U2D2\mathrm{}$ phase and the sound anisotropy due to the exchange interaction was found to be about $10\%$ among single-domain crystals investigated. The average value of the Grüneisen constant of the spin wave velocity in the ordered phase was ${\overline{\gamma }}_c=16\mathrm{}$ and is compared to the calculated value of the multiple-exchange model.