High Frequency Modes in Vortex-State Nanomagnets

Abstract

The magnon mode excitation spectrum is obtained from a linearized set of Landau-Lifshitz equations for vortex ground state cylindrical nanomagnets in an external magnetic field. It is shown that there is a rich spectrum of doublet states, and the splitting can be amplified in an external magnetic field.

Radiation of spin waves from magnetic vortex cores by their dynamic motion and annihilation processes

“…[2][3][4] Both theoretical and experimental studies have thus been increased in numbers for the exploration of the spatial and temporal characteristics of spin waves excited in micrometer-scale magnetic elements. [5][6][7][8][9][10][11][12][13][14][15][16][17] It is known that the characteristic properties of spin waves are determined by the intrinsic material parameters of exchange and dipole interactions and an external magnetic field as well as the size and shape of a system. [5][6][7][8][9] Fundamentally, it has been of great interest how the frequencies and spatial configurations of their eigenmodes are governed by these parameters.…”

“…[5][6][7][8][9][10][11][12][13][14][15][16][17] It is known that the characteristic properties of spin waves are determined by the intrinsic material parameters of exchange and dipole interactions and an external magnetic field as well as the size and shape of a system. [5][6][7][8][9] Fundamentally, it has been of great interest how the frequencies and spatial configurations of their eigenmodes are governed by these parameters. From a technological point of view, a logical operation using spin waves is also of a great interest because they can deliver information with the controllable phases of spin waves being propagating in magnetic media, which is applicable for a new generation of logic devices.…”

Spin waves in circular soft magnetic dots at the crossover between vortex and single domain state

“…For in-plane magnetic excitation field the azimuthal spin waves m = ±1 and the gyrotropic mode are expected to be excited [13,16,17] because only these spin modes have non zero 3 average in-plane magnetization and can interact with the uniform rf driving field. Previous studies were mainly focused on resonant response in the absence of bias magnetic field [6][7][8][9]11,12,14,15] when the static vortex was localized in the dot center.…”

“…The lowest frequency excitation corresponds to the gyrotropic mode when the vortex moves as a whole around an equilibrium position [7][8][9], meanwhile the higher frequency modes correspond to the spin waves excited mainly outside of the vortex core [10][11][12][13][14][15][16][17][18][19]. The spin wave having radial or azimuthal symmetry with respect to the dot center are described by integers (n, m), which indicate number of nodes in the dynamic magnetization along radial (n) and azimuthal (m) directions.…”

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

“…They also have been observed experimentally by use of Brillouin light scattering [37,38] and time resolved Kerr microscopy with Fourier filtering [34][35][36]. Theoretical analysis [39][40][41][42] and numerical simulations were also used for investigations of these modes. For these modes, because of the absence of angular nodes, the contribution of the volume magnetic charges is maximal, thus their frequencies are usually higher than for non-radial modes with m>1 [35,39,42].…”