Experimental and theoretical study of quantized spin-wave modes in micrometer-size permalloy wires -: art. no. 134429

Using Brillouin light scattering measurements, we have studied the properties of the spin waves in various arrays of Permalloy wires showing widths of 0.5, 1, and 1.5 mum. When the transferred in-plane wave vector kappa (parallel to), specified by the experimental setup, is perpendicular to the wires, a sampling of the Damon-Eshbach surface mode branch giving rise to a set of discrete dispersionless modes is observed. We attribute this behavior to a lateral quantization of the wave vector q(parallel to) of the magnetic excitations. The frequency separation between two adjacent modes is found to decrease when the width D of the wires increases. However, this frequency dependence does not simply follow the expected one assuming the usual naive relation q(parallel to ,n) = n pi /D, which would not allow one to give account of the behavior of the lowest mode n = 0. We have performed numerical calculations of the dynamical magnetization response functions of these rectangular cross section wires using the method of finite elements. The magnetic parameters used in these calculations were derived from the experimental Brillouin spectra of the unpatterned films. Both our experiments and our calculations agree with the results expected from the unpatterned film assuming the following discrete values: q(parallel to ,0) = 0, q(parallel to ,n) = pi (n + beta)/D. The zero value observed for the lowest mode n = 0 simply results from the calculation and does not need for an additional hypothesis as previously proposed.