Spin-Wave Dynamics in the Presence of Magnetic Vortices

Abstract

This chapter describes spin-wave excitations in nanosized dots and rings in the presence of the vortex state. The special attention is paid to the manifestation of the competition between exchange and dipolar interactions in the spin-wave spectrum as well as the correlation between the spectrum and the stability of the vortex. The calculation method uses the dynamic matrix for an all-discrete system, the numerical diagonalization of which yields the spectrum of frequencies and spin-wave profiles of normal modes of the dot. We study in-plane vortices of two types: a circular magnetization in circular dots and rings and the Landau state in square rings. We examine the influence of the dipolar-exchange competition and the geometry of the dot on the stability of the vortex and on the spectrum of spin waves. We show that the lowest-frequency mode profile proves to be indicative of the dipolar-to-exchange interaction ratio and the vortex stability is closely related to the spin-wave profile of the soft mode. The negative dispersion relation is also shown. Our results obtained for in-plane vortices are in qualitative agreement with results for core-vortices obtained from experiments, micromagnetic simulations, and analytical calculations.Comment: in 'Vortex Dynamics and Optical Vortices', Hector Perez-De-Tejada (Ed.), InTech 2017. Available from: http://www.intechopen.com/books/vortex-dynamics-and-optical-vortices/spin-wave-dynamics-in-the-presence-of-magnetic-vortice

Spin Wave Excitations of the Interacting Two-Dimensional In-Plane Nano-Vortices

“…In the effective field we take into account the dipolar and exchange interactions. Linearization of the set of LL equations for all magnetic moments in the system leads to the eigenvalue problem for so-called dynamical matrix (see [15,16] for more details). Numerical diagonalization of this matrix yields the frequency spectrum of the spin-wave excitations, and the spin-wave profiles, i.e., the distribution of the in-plane (m r ) and out-of-plane (m k ) amplitudes of precession of the elementary magnetic moments.…”