Transverse Susceptibilities of Ferromagnetic Spin Wave Interacting with Phonon Reservoir

Abstract

A form of the transverse magnetic susceptibility of a ferromagnetic system interacting with a phonon reservoir is derived in the spin-wave approximation using the TCLE method in which the admittance of the system is directly calculated from time-convolutionless equations with external driving terms, and is investigated numerically and analytically for the system of one-dimensional infinite spins. It is confirmed that the effects of the initial correlation and memory for the spin system and phonon reservoir, which are represented by the interference terms in the TCLE method, increase the peak heights of the power spectra in the resonance region and cause the power spectra to decrease in the low-frequency region. It is shown that as the damping of the phonon reservoir becomes rapid, the half-widths of the line shapes in the resonance region decrease and the peak heights increase for small wave numbers, and thus the line shapes show ‘motional narrowing’ for small wave numbers but not for large wave numbers. For the case of an acoustic phonon reservoir, it is shown that as the wave number increases, the half-widths decrease and the peak heights increase, except in the vicinity of 0 and π. For a damped oscillator model of the phonon reservoir, it is shown that as the characteristic frequency of the phonon increases, the half-widths increase and the peak heights decrease, and thus the line shapes show ‘motional broadening’. It is also shown that as the magnitude of the spin becomes large, the peak heights increase and the half-widths increase for small wave numbers but decrease for large wave numbers. Furthermore, the resonance frequency is shown to increase as the wave number increases or as the magnitude of the spin becomes large. The numerical results are examined analytically.