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

TL;DR

This paper calculates the dispersion relations of collective magnon modes in arrays of vortex-state magnetic dots, revealing complex behaviors influenced by dipolar and non-dipolar interactions, with implications for understanding their dynamic properties.

Contribution

It introduces a formalism to analyze collective magnon modes in vortex-state magnetic dot arrays, accounting for non-dipolar interactions and revealing non-analytic dispersion relations.

Findings

Array dots exhibit positive or negative dispersion modes.

Non-dipolar interactions can significantly influence mode properties.

Dispersion relation becomes non-analytic as wavevector approaches zero.

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.