Interactions of Spin Waves with a Magnetic Vortex

Abstract

We have investigated azimuthal spin-wave modes in magnetic vortex structures using timeresolved Kerr microscopy. Spatially resolved phase and amplitude spectra of ferromagnetic disks with diameters from 5 µm down to 500 nm reveal that the lowest order azimuthal spin wave mode splits into a doublet as the disk size decreases. We demonstrate that the splitting is due to the coupling between spin waves and the gyrotropic motion of the vortex core.PACS numbers: 75.30. Ds, 75.75.+a, 75.40.Gb The magnetic ground state of a soft ferromagnetic particle is determined by a balance between magnetostatic and exchange energies. In the case of disks with negligible magnetocrystalline anisotropy, the stable configuration for radii of several hundred nanometers and thicknesses of the order of 20 -50 nm is a vortex with a core diameter on the order of the exchange length [1,2]. The magnetization outside of the core circulates around the central axis, reducing the total magnetostatic energy. This comes at the cost of a large exchange energy near the vortex core, inside of which the magnetization rotates out of the plane of the disk. Because the vortex state represents the simplest type of domain configuration that can be created in a uniformly magnetized particle, its excitation spectra is of fundamental interest. Recent experimental work has identified two classes of excitations in magnetic vortices. First, low-order magnetostatic spin waves can be observed by either time-resolved Kerr microscopy [3,4,5,6] or Brillouin scattering [7,8]. A second type of excitation is associated with the translational degree of freedom of the vortex core itself [3,9,10]. This has a much lower characteristic frequency than the other spin-wave modes, and it is for this reason that the two types of excitations are often treated as distinct. For example, the radial spin wave modes of a particle can be calculated accurately even if the position of the vortex core is regarded as fixed [4,5].In this Letter we report on a study of the dynamics of the lowest order azimuthal spin wave modes in ferromagnetic disks with diameters between 500 nm and 5 µm. In larger diameter disks, these are degenerate as expected for a system with cylindrical symmetry. We demonstrate that this degeneracy is lifted in smaller disks (with diameters less than 2 µm and thickness to diameter ratio > 0.005) due to the motion of the vortex core. The relative phases of the two modes are determined by the polarity of the vortex core, and the magnitude of the splitting is of the same order as the vortex gyrotropic frequency. These results demonstrate a significant coupling between vortex dynamics and magnetostatic spin waves.Two sets of permalloy disks were fabricated on Si substrates using electron-beam lithography and electronbeam evaporation of permalloy (Ni 0.81 Fe 0.19 ). The first set of disks were used primarily for investigations of the vortex gyrotropic mode and were 50 nm thick with diameters D from 500 nm to 2 µm. The disks used for the detailed investigation of azimuthal...

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

“…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.…”

“…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. Our letter reports on broadband measurements of the vortex dynamics in circular Permalloy (Py) dots excited by applying in-plane stratifying field with the variable angle between the bias and excitation fields.…”

Vortex dynamics in Permalloy disks with artificial defects: Suppression of the gyrotropic mode

“…Especially the so-called gyrotropic mode, a sub gigahertz characteristic excitation of the magnetic vortex core itself, is of enormous interest. [8][9][10][11][12][13][14] The numerous efforts to study the gyrotropic mode in depth stem partly from the importance to understand the fundamental magnetic properties of these magnetic nanostructures, and partly from the technological challenge to achieve a controllable and reproducible switching behavior of the vortex core. Another possibility to influence the behavior of a vortex core is the insertion of artificial defects, e.g., small holes, into the magnetic structures.…”

Mode degeneracy due to vortex core removal in magnetic disks

“…[9][10][11] In some recent papers, the attempts to manipulate the structure of spin-wave modes in confined magnetic elements by modification of the elements' physical properties have been reported. [10][11][12] A particular attention has been paid to diskshaped elements due to their simplicity. The response of these elements to the external excitation with pulsed and continuous magnetic fields has been studied both experimentally and theoretically.…”