Ferromagnetic resonance in periodic domain structures

Abstract

We have recalculated the Smit and Beljers FMR mode frequencies for thin multi-domain magnetic platelets (disks) with uniaxial magnetocrystalline anisotropy K taking the finite aspect ratio of the domains into account. The magnetic anisotropy axis (z-axis) was taken to be perpendicular to the disk plane; the external magnetic field H was applied in the disk plane. The demagnetization energy coefficients of the periodic magnetic structures were found by the method of Kaczér and Murtinová. Below magnetic saturation the normalized FMR frequencies are: (a) for stripe domain arrays with H normal to the walls, Ω2+= (1−p)(1+2r−2p)−h2, Ω2−= (1−p)2−h2; (b) for bubble domain arrays, Ω2+= (1−p)(1+r−3p/2)−(1−r−p/2)(1−p)−1h2, Ω2−= (1+r−3p/2)[1−p−(1−p)−1h2], with HA=2K/M, Ω=ω/γHA,h=H/HA, r=2πM/HA and p=NzzM/HA. As the domain aspect (width/height) ratio tends toward zero, p→0 and the Ω2+, − expressions reduce respectively to (a) the stripe resonance expressions given by Smit and Beljers, (b) the first two bubble resonance expressions found in Kaczér and Gemperle. Our attempts to correlate these results with published experimental data are inconclusive; often the samples were too thick to support simple domain structures or relevant information was not provided.