Ultrasonic Attenuation in the Simple Cubic Antiferromagnet near the Néel Temperature

Abstract

Ultrasonic attenuation in an insulating simple cubic Heisenberg antiferromagnet near the magnetic phase transition point is investigated on the basis of Mori’s theory of irreversible processes. The sound wave is assumed to couple mainly to the spin-energy-density fluctuation which decays via a fast non-diffusive relaxation process arising from the spin-lattice interaction. Firstly, the relaxation time of the spin-energy-density fluctuation, τ, and then the sound attenuation coefficient, α_q, is calculated. The calculations of τ and α_q applied to RbMnF₃ agree quantitatively with the experimental results. The contribution of the longitudinal thermal-phonons to 1/τ is found to be 1/7 of that of the transverse thermal-phonons. The present calculations for RbMnF₃ involve none of adjustable parameters. The sound attenuation coefficient of MnF₂ also is discussed.