Collective modes for an array of magnetic dots in the vortex state

Abstract

The dispersion relations for collective magnon modes for square-planar arrays of vortex-state magnetic dots, having closure magnetic flux are calculated. The array dots have no direct contact between each other, and the sole source of their interaction is the magnetic dipolar interaction.The magnon formalism using Bose operators along with translational symmetry of the lattice, with the knowledge of mode structure for the isolated dot, allows the diagonalization of the system Hamiltonian giving the dispersion relation. Arrays of vortex-state dots show a large variety of collective mode properties, such as positive or negative dispersion for different modes.For their description, not only dipolar interaction of effective magnetic dipoles, but non-dipolar terms common to higher multipole interaction in classical electrodynamics can be important. The dispersion relation is shown to be non-analytic as the value of the wavevector approaches zero for all dipolar active modes of the single dot. For vortex-state dots the interdot interaction is not weak, because, the dynamical part (in contrast to the static magnetization of the vortex state) dot does not contain the small parameter, the ratio of vortex core size to the dot radius. This interaction can lead to qualitative effects like the formation of modes of angular standing waves instead of modes with definite azimuthal number known for the insolated vortex state dot.

Band structure engineering of two-dimensional magnonic vortex crystals

“…Experimentally, the interaction between the vortices in twodimensional arrangements has been studied [13][14][15][16] and * cbehncke@physnet.uni-hamburg.de collective modes for five vortices have been measured [17]. The band structure of two-dimensional vortex crystals is predicted to strongly depend on the polarization pattern [18][19][20].…”

Static and dynamic properties of vortex pairs in asymmetric nanomagnets

“…[4][5][6][7][8] Most recently, systems of coupled vortices have gained much attention. This includes lateral arrays of magnetic particles with dipole-coupled vortex-cores [9][10][11][12][13] (far-field), vortex-pairs in a single magnetic particle, [14][15][16][17] and vertically stacked vortices. [18][19][20][21] All these structures have distinct features when it comes to their dynamic behavior, with the main resonant response typically being the gyroscopic resonance, in which the vortex-core moves in the particle plane in a trajectory large in radius compared to the size of the core.…”

A comparison of numerical simulations and analytical theory of the dynamics of interacting magnetic vortices

“…1,2 Vortices can interact dynamically with one another when confined in the same structure 3 or in structures that are in close proximity, where coupling in the latter case occurs via magnetostatic interactions. [4][5][6][7] Modifications of the gyrotropic resonance frequency, first predicted to arise in a 2D square array of magnetic vortices, [8][9][10] have been observed experimentally for 2D square arrays 4,11,12 and in the simpler case of a pair of closely spaced magnetic squares. 5,13 In the case of the 2D arrays, the effect is primarily a line-broadening effect of $20% for an inter-disk spacing of 20% of the disk radius, 4 whereas the gyrotropic resonance frequency splits into two distinct modes for a vortex pair, the frequencies of which depend on the vortex polarities.…”

“…16 Furthermore, recent studies have shown that signals can be transmitted from one disk to another via dipolar coupling in chains of two, 5,13,17 three, 18 or more structures lined up in a row, 19 and schemes to improve the signal transfer rate 20 and coupling efficiency in vortex chains have been investigated. 21 Several theories of vortex coupling have been proposed [8][9][10]22,23 but have not yet been compared against full micromagnetic simulations.…”