Transverse susceptibilities of ferromagnetic spin wave interacting with phonon reservoir, II: Temperature dependence of line shapes

Abstract

A form of the transverse magnetic susceptibility of a ferromagnetic spin system with a uniaxial anisotropy energy and an anisotropic exchange interaction, interacting with a phonon reservoir, is derived in the spin-wave approximation using the TCLE method, where the phonon reservoir interacts with not only the x and y components of each spin but also its z component. The transverse magnetic susceptibility is numerically and analytically studied for the system of one-dimensional infinite spins in the lowest spin-wave approximation, by assuming a damped oscillator model of the phonon reservoir. The temperature dependence and wave number dependence of the susceptibility are numerically investigated for the half-widths and peak-heights of the line shapes in the resonance region. It is shown that as the temperature increases, the half-widths of the line shapes increase and the peak heights decrease in the resonance region, and that as the wave number increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is also shown that as the uniaxial anisotropy energy of the z direction increases or as the exchange interaction between the z components of spins increases, the half-widths of the line shapes decrease and the peak heights increase in the resonance region. It is besides shown that as the characteristic frequency of the phonon increases, the line shapes show ‘motional broadening’ at the low temperature and show ‘motional narrowing’ at the high temperature. Furthermore, the resonance frequency is shown to increase as the wave number increases or as the temperature increases. The numerical results are examined analytically.