Electromagnetic Theory of dc Effects in Ferromagnetic Resonance

Effects of magnetoresistance and extraordinary Hall effect on the propagation of electromagnetic waves through very thin sheets of ferromagnetic conductors are studied. These contributions to the conductivity produce electric fields varying like products of current and magnetization and introduce nonlinear interactions, which are particularly large in the neighborhood of ferromagnetic resonance. Detailed first-order dc electric fields are obtained for the configuration of a very thin ferromagnetic sheet very close to a conducting wall. The results predict signals strictly proportional to incident microwave power, and mostly inversely proportional to film thickness, becoming independent of thickness for the thinnest films. Their magnetic field or frequency dependence gives typical resonance curves modulated by slowly varying amplitudes. The maxima and zeros of these amplitudes are very sensitive to the local field configuration. Once this latter is well known, however, these effects can be employed to study conveniently the high-frequency conduction and magnetic properties of the thinnest films.