Approximate method for ferromagnetic resonance in metals

Abstract

We present a useful new approximate calculation of ferromagnetic resonance in isotropic metal plates. The key step in this calculation is a transformation, previously applied to magnetoelastic insulators, which permits the separation of the resonant and nonresonant senses of polarization. As a result, we are able to reduce the dispersion relation resulting from simultaneous solution of the Landau-Lifshitz equation and of Maxwell's equations from a quartic, for arbitrary directions of the magnetization, to a quadratic. Assuming a simple (but arbitrary) spin-pinning boundary condition on the surface rf magnetization. the surface impedance Z can then be obtained from a linear equation. Near resonance, at X or K band, we find that Z agress with values from the exact calculation to within a fraction of 1% for all magnetization directions. The resonant frequency and linewidth both agree with the exact calculation to better than 1 Oe.