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

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