Surface anisotropy and spin wave resonance in submicron amorphous wires

The influence of surface magnetic anisotropy on ferromagnetic resonance (FMR) in submicron wires is investigated both theoretically and experimentally. An analytical formula for resonance fields of radial spin waves in a long axially magnetized circular cylinder is obtained. Three types of surface anisotropy with the easy direction along one of the cylindrical coordinates are considered. For sufficiently strong surface anisotropy with hard direction parallel to the cylinder axis the surface spin wave mode is observed. The theoretical results are verified by FMR measurements at six microwave frequencies from 9 to 69 GHz on glass-covered amorphous FeCrSiB wires with diameters from 541 to 1032 nm. From the bulk spin wave resonances the exchange stiffness constant about 6.5 10⁻⁷ erg/cm is obtained. The frequency dependence of the surface mode resonance field indicates that a perpendicular surface anisotropy with anisotropy constant K_s = 6.2 erg/cm² is present at the metal/glass interface.