Spin dynamics and sound propagation near the spin-glass transition

Sound propagation in two models—the random-uniaxial-anisotropy model and the random-bond Ising model—of the spin-glass transition is studied. Both models give similar results for sound speed and damping. The sound speed decreases linearly with ($T-T_g$) and the sound damping diverges as ${(T-T_g)}^{-1\mathrm{}}$ when the spin-glass transition is approached from above $T_g$. At the spin-glass temperature $T_g$, the sound speed has a ${\omega }^{\frac{1}{2}}$ dependence on frequency, and the sound damping has a ${\omega }^{\frac{-1\mathrm{}}{2}}$ dependence. The effect of an external magnetic field on the sound speed is studied. The behavior of the order-parameter fluctuations in the spin-glass phase is obtained by comparing our results with data on sound speed in a 5 at.% sample of CuMn.