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

TL;DR

This paper investigates how spin-lattice relaxation influences sound attenuation near critical points in isotropic Ising systems, revealing new regimes and a frequency-dependent specific heat that captures the equilibration process.

Contribution

It introduces a comprehensive stochastic model for critical sound attenuation, discovering a new high-frequency regime and a novel specific heat concept related to spin-lattice interactions.

Findings

Identified a new high-frequency singularity regime $t^{-z u +eta}$.

Proposed a frequency-dependent specific heat that models spin-lattice equilibration.

Showed that the acoustic self-energy can be approximated by this specific heat in certain conditions.

Abstract

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.