Hyperfine field at an impurity in a ferromagnetic host

A simple model is developed for calculating the hyperfine field at an impurity site by describing the host magnetic ions in terms of a spin-dependent spherical potential around the impurity. The model is used to estimate the effects of zero-point motion and lattice relaxation around the impurity on the hyperfine field. Both these effects are found to be important. The temperature dependence of the hyperfine field is investigated by including the non-linear dependence of the hyperfine field on the average bulk magnetisation, lattice vibrations and thermal expansion. Application to the case of muon spin rotation in ferromagnetic Gd and Dy gives results in qualitative agreement with experiments.