Nonasymptotic Effects in Critical Sound Propagation Associated with Spin-Lattice Relaxation

The nonasymptotic critical behavior of sound attenuation coefficient has been studied in an elastically isotropic Ising system above the critical point on the basis of a complete stochastic model including both spin-energy and lattice-energy modes linearly coupled to the longitudinal sound mode. The effect of spin-lattice relaxation on the ultrasonic attenuation is investigated. The crossover between weak-singularity behavior $t^{-2 \alpha}$ and strong singularity behavior $t^{-(z \nu +\alpha)}$ is studied. A new high-frequency regime with singularity of the type $t^{-z \nu +\alpha}$ is discovered in the magnetic systems. This new regime corresponds to an adiabatic sound propagation and is very similar to the ones in binary mixture and liquid helium. A new frequency-dependent specific-heat being the harmonic average of the bare lattice and critical spin specific-heats is introduced. It was shown that such specific-heat descibes the process of equilibrization between spin and lattice subsystems and includes the most important features of critical sound attenuation. In some regions of coupling constants the acoustic self-energy can be very well approximated solely by this quantity.