Theory of three-magnon interaction in a vortex-state magnetic nanodot

TL;DR

This paper develops a vector Hamiltonian formalism to analyze three-magnon interactions in vortex-state magnetic nanodisks, revealing selection rules, mode dependencies, and validating predictions with experiments and simulations.

Contribution

It introduces a theoretical framework using VHF for three-magnon interactions in vortex disks, accounting for core effects and mode selection rules.

Findings

Selection rules for three-magnon splitting in vortex disks.

Dependence of interaction efficiency on mode numbers.

Agreement between theory, experiment, and simulations.

Abstract

We use vector Hamiltonian formalism (VHF) to study theoretically three-magnon parametric interaction (or three-wave splitting) in a magnetic disk existing in a magnetic vortex ground state. The three-wave splitting in a disk is found to obey two selection rules: (i) conservation of the total azimuthal number of the resultant spin-wave modes, and (ii) inequality for the radial numbers of interacting modes, if the mode directly excited by the driving field is radially symmetric (i.e. if the azimuthal number of the directly excited mode is $m = 0$). The selection rule (ii), however, is relaxed in the "small" magnetic disks, due to the influence of the vortex core. We also found, that the efficiency of the three-wave interaction of the directly excited mode strongly depends on the azimuthal and radial mode numbers of the resultant modes, that becomes determinative in the case when several splitting channels (several pairs of resultant modes) simultaneously approximately satisfy the resonance condition for the splitting. The good agreement of the VHF analytic calculations with the experiment and micromagnetic simulations proves the capability of the VHF formalism to predict the actual splitting channels and the magnitudes of the driving field thresholds for the three-wave splitting.