Spin dynamics in thin nanometric elliptical Permalloy dots: A Brillouin light scattering investigation as a function of dot eccentricity

Abstract

Brillouin light scattering (BLS) spectra have been measured in arrays of cylindrical Permalloy dots with elliptical cross section, $200\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ wide, $15\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick, and eccentricities from 1 to 3. Several spin modes are observed and their frequencies tracked as a function of the direction of the applied $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$ magnetic field $\mathbit{H}$. The experimental data are interpreted within the framework of the recently introduced dynamical matrix method to calculate spin excitations in magnetic particles. We find that the mode frequencies strongly depend on the eccentricity of the dots and on the direction of the applied field. For fields along the principal axes the solutions can be classified into: (i) modes localized near the particle ends, (ii) modes with nodal lines perpendicular to $\mathbit{H}$ (backwardlike modes), (iii) modes with nodal lines parallel to $\mathbit{H}$ (Damon-Eshbach-like modes) and (iv) modes with both parallel and perpendicular nodal lines. In cases where the frequencies of two modes in different families are similar, some hybridization between the modes is observed. For $\mathbit{H}$ along nonsymmetry directions only the modes of type (i) remain reasonably well defined, other modes can at best be described as hybrids of modes in the above categories. Determining which of the modes is active in BLS experiments leads to excellent agreement with the experimental results.