Spin-Lattice Relaxation Effects in Critical Sound Propagation

Abstract

The nonasymptotic critical properties of sound propagation are studied in compressible Ising system above Τ. In the present paper we analyse a model where in addition to the coupling to two order-parameter fluctuations tle sound mode couples linearly to the fluctuations of spin-energy and lattice-energy densities. Both subsystems exchange energy with the rate determined by the bare spin-lattice relaxation time: The total energy may be conserved or not. The crossover between insulator-like behaviour t -2 α a n d In typical ultrasonic experiments near the magnetic phase transition temperature we observe strong anomalies of sound attenuation in magnetic metals such as some rare-earth metals, whereas in magnetic insulators only very weak anomaly is observed [1,2]. Many theories have been proposed to describe the strong anomaly in various substances [3][4][5][6]. They assume that the sound mode is coupled to two spin fluctuations above Τ . On the other hand, the weak anomalies have been qualitatively explained by postulating the dominance of the linear coupling to the spin-energy density [7]. In our recent study we have investigated a model where both couplings were present [8]. Inn this paper we present more extensive discussion of the problem including also the lattice energy mode and transfer of energy between spin and lattice subsystems. We consider the acoustic phonon Q coupled to the scalar spin S and to the fluctuations of energy of spin and lattice subsystems. The Hamiltonian of the elastically isotropic system may be specified as (449) m e t a l -l i k e b e h a v i o u r t i t -( z v ± α ) i n u l t r a s o n i c a t t e n u a t i o n i s i n v e s t i g a t e d