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, 350nm×160nm×5nm thick in zero field, the lowest frequency normal mode at 4GHz 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 50nmdiameter×15nm 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.