The dynamics of an inhomogeneously broadened $S=1\mathrm{}$ system strongly coupled to a bottle-necked lattice are analyzed in the context of the usual rate-equation formalism. The center of the $\Delta M_S=\pm 1$ resonance is characterized by an equally spaced three-level system, while the wings of the resonance are viewed as an almost equally spaced level system in which resonant phonons are noninteracting. Calculations of phonon heating under rf saturation of the spin transitions show the phonon linewidths to be noticeably less than the EPR bandwidth; conservation conditions which relate the various phonon excitations are also obtained and extended to a general multilevel system. Determinations of the normal unbottlenecked spin-relaxation rate and the intrinsic phonon decay times are possible at early times in the decay to equilibrium, while an analytic expression for the final asymptotic decay rate of the coupled system is obtained in the limit of a large phonon lifetime. Numerical solutions to the rate equations at early times are also presented and discussed in terms of the strong competition between resonant phonons for the spin-excitation energy.

• Received 2 October 1970

DOI:https://doi.org/10.1103/PhysRevB.3.635