Stochastic theory of spin-phonon relaxation

Abstract

Spin-phonon relaxation is interpreted as a quantum stochastic process. Time-dependent magnetization correlation functions are written in general exponential form, and the phase-modulation terms occurring in them are evaluated approximately to second order with respect to the coupling parameter. The spin-phonon interaction is described by the isotropic model of Huber and Van Vleck. A physical parameter corresponding to an effective Larmor precession frequency is introduced and determined from the zero-frequency longitudinal susceptibility, which is made consistent with the thermodynamic derivative of the magnetization. Longitudinal and transverse dynamic susceptibilities are calculated for all frequencies. At low frequencies they agree with the usual Lorentzian model as expected from the asymptotic exponential decay of the correlation functions. The high-frequency spectra differ from the Lorentzian form and contain information on the short-time history of spin-phonon collisions.