Spectral analysis of the precessional switching of the magnetization in an isotropic thin film

We study how a magnetic field step triggers the precessional switching of the magnetization in an isotropic thin film. Using a variational approach, we make an analytical estimate of the switching frequency. We compare it to more general analytical models, and to the results obtained numerically by direct integration of the equations of motion. We show that the periodic motions of the three magnetization components can be described satisfactorily with truncated Fourier expansions, indicating a relatively high spectral purity of the magnetic response. Our analytical expressions are simple enough to be physically transparent at first sight, in contrast to the results of the more elaborate models that treat also anisotropy.