Survey of Ferromagnetic Resonance in Small Ferrimagnetic Ellipsoids

This paper discusses the response of the magnetization in a small ferrimagnetic ellipsoid, magnetized in an arbitrary direction and excited by spatially uniform microwave magnetic fields, when a typical spin wave is present. The generalized Kittel frequency is given, and possible frequency generation processes appropriate to the ellipsoidal geometry are treated. If the ellipsoid is magnetized at an angle to a principal axis,time-varying components of demagnetizing field at the fundamental frequency occur in the longitudinal direction, as well as transverse components varying at this frequency. Previous analyses have not included such a possibility and certain interesting solutions have, therefore, been missed. In particular, it is found that subharmonics as well as harmonics may be created when the driving field exceeds a certain threshold power. The particular case of the half-frequency resonance is considered and the conditions for the minimum threshold are given. The generalized Suhl spin-wave spectrum is found, together with the coupling relations between the uniform precession and the spin wave. The Suhl first and second order instability thresholds, for the general ellipsoid, are formulated, and a zero order coupling is established for certain transient states of the magnetization. In addition, direct parametric coupling between a longitudinal pumping field and both the uniform precession and the spin waves is discussed.