Electromagnetic Effects of Spin Wave Resonance in Ferromagnetic Metals

It was shown experimentally by Rado and Weertman that under suitable conditions there is an observable effect of exchange interactions on the ferromagnetic resonance in metals. The present paper provides an electromagnetic theory of this "spin wave resonance" experiment and satisfactorily explains the exchange shift as well as the width and shape of the absorption line. A combined solution is obtained of Maxwell's equations and the equation of motion of the magnetization vector M the latter equation including the exchange term due to the nonuniform orientation of M in the skin depth. It is shown that the triple refraction caused by the exchange effect necessitates the introduction of new boundary conditions. The final result, which is checked numerically and by an approximate calculation, is an expression for the measurable surface impedance and the "equivalent isotropic permeability" derived therefrom. This result is discussed and generalized, the properties of thermal spin waves in metals are briefly considered, and previous theories of exchange effects in ferromagnetic resonance are shown to be inadequate.