Resonant and nonresonant effects of paramagentic spins on acoustic modes

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Abstract
The resonant and nonresonant effects of paramagnetic spins on acoustic velocity and attenuation are treated self-consistently and on the same footing. The acoustic waves are treated using elastic continuum theory and generalized Bloch equations are used for the spins although the same results can be obtained more formally using quantum-mechanical equations of motion and time-dependent correlation functions. Detailed formulas are derived for angular dependence and magnitudes of both resonant and nonresonant effects. Nonresonant velocity and attenuation changes are related to adiabatic and isothermal regimes and the transition between the two regimes. We suggest that nonresonant experiments can be used to measure spin decay rates and spin-phonon coupling constants in regimes or substances where resonant techniques cannot be used.