The effect of nonlocal conductivity on the transmission of microwave radiation through ferromagnetic metals in the field-normal configuration

Abstract

Procedures are described for the numerical calculation of the electric-field distributions generated in a model ferromagnetic metal slab of thickness d by incident microwave radiation when a static magnetic field is directed along the slab normal and the mean free path ℓ of the charge carriers becomes comparable to, or greater than, the skin depth δ. The model metal is characterized by a local, frequency-dependent permeability; a spherical Fermi surface; and a nonlocal relationship between the current density and the electric-field distribution. The two limiting cases of specular and diffuse scattering of the charge carriers at the slab faces are considered. Electric-field distributions, transmission amplitudes, and surface impedances have been calculated for a wide range of ℓ and d using parameters that simulate nickel. For diffuse surface scattering, the transmission of the magnetically active mode increases at both ferromagnetic resonance (FMR) and cyclotron resonance (CR). A most striking result is the total absence of structure in the magnetic-field dependence of the transmission amplitude near fields corresponding to FMR or to CR for the case of specular scattering. It is demonstrated that very simple formulae provide a good estimate of the free-space transmission amplitudes for both specular and diffuse surface scattering when [Formula: see text] and d/ℓ ≥ 1.