Magnetic relaxation and anisotropy effects on high-frequency permeability

Initial longitudinal permeability μ_i and rf signal propagation as a function of angular frequency ω are examined in terms of spin-lattice interactions that manifest themselves as relaxation time τ and anisotropy energy density K₁. Domain-wall resonance is analyzed as a classical damped harmonic oscillation forced by longitudinal coupling between magnetization vectors and an alternating magnetic drive field. Gyromagnetic effects from transverse drive fields are reviewed in the context of Snoek´s permeability-frequency limits. To explain the observed overlap of longitudinal and transverse regions the physical connection between the longitudinal relaxation frequency and the gyromagnetic resonance frequency is described. Guidelines for extending the permeability and frequency limits of unmagnetized ferrites are: 1) for high μ_i, employ large-grain multiple-domain ferrites with low-K₁/high-τ combinations and 2) for high ω, create small-grain single-domain media with high K₁ and low τ. At microwave frequencies, the lower edge of the gyromagnetic resonance region can overlap the decay of μ_i, except in cases where the very high anisotropy of hexagonal ferrites is used for millimeter wavelengths.