Theory of Critical Sound Attenuation in Ising-Type Magnets

The critical behaviour of sound attenuation 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 Kawasaki behaviour and Murata-Iro-Schwabl behaviour is studied as dependent on the values of ultrasonic frequency, reduced temperature, relaxation times, etc. A new high-frequency regime is discussed 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 describes the process of equilibration between spin and lattice subsystems and includes the most important features of critical sound attenuation.