Magnetic normal modes of nanoelements

Micromagnetic calculations are used to determine the eigenfrequencies and precession patterns of some of the lowest-frequency magnetic normal modes of submicron patterned elements. Two examples are presented. 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. Other resonant frequencies are compared with the frequencies of spinwaves with discrete wave vectors. For a normally magnetized 50 nm diameter × 15 nm thick cobalt disk, 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.