Micromagnetic calculations are used to determine the eigenfrequencies and precession patterns of some of the lowest-frequency magnetic normal modes of submicron patterned elements. For a Permalloy-like ellipse, 350 nm ¿ 160 nm ¿ 5 nm thick in zero field, the lowest frequency normal mode at 4 GHz corresponds to precession in the "ends" of the ellipse. This mode is not predicted by quantization of wavevectors in the confined geometry. The eigenmodes of a normally magnetized 50 nm diameter ¿ 15 nm thick cobalt disk are calculated. The calculated eigenfrequencies increase linearly with applied field, mimicking the behavior of the experimental critical current for spin transfer instabilities in an experimental realization of this disk.
Journal of Applied Physics
eigenfrequencies, magnetic normal modes, nano-elements, submicron patterned elements