Calculation of nonlinear magnetic susceptibility tensors for a ferromagnet

We derive the equations of motion from which nonlinear field- and frequency -dependent magnetic susceptibilities defined by M = <(chi)over left right a rrow>((1))H + <(chi)over left right arrow>((2))HH + <(chi)over left right a rrow>((3))HHH may be calculated for a Heisenberg ferromagnet. Explicit expr essions are given, in the circular polarization frame, for the second- and third-order effects that arise for a single-frequency input wave, namely se cond-harmonic generation, optical rectification, third-harmonic generation and intensity-dependent susceptibility. Illustrative graphs are presented f or a few of the coefficients and the paper concludes with a brief discussio n of the implications for multistability of a magnetic Fabry-Perot resonato r.