Many-state relaxation model for the Mössbauer spectra of superparamagnets

The stochastic relaxation theory of Anderson and Sack is applied to the M\"ossbauer spectra superparamagnetic particles with uniaxial anisotropy by including all possible values of the component of the magnetization along the quantization axis explicitly in the calculation. It is shown that for particles with a large number of states the M\"ossbauer line shape can be expressed directly in terms of the solution of a differential equation. Explicit solution of this equation in the low-temperature (high anisotropy barrier) approximation leads to effective relaxation rates between the two discrete allowed orientations of the magnetization. These rates are equivalent to those derived by Brown only if the relaxation matrix elements are assumed to have a certain rather arbitrary dependence on the temperature and magnetization.