Time-resolved Kerr microscopy is used to study the excitations of individual micron-scale ferromagnetic thin film elements in their remnant state. Thin (18 nm) square elements with edge dimensions between 1 and 10 µm form closure domain structures with 90 degree Néel walls between domains. We identify two classes of excitations in these systems.The first corresponds to precession of the magnetization about the local demagnetizing field in each quadrant, while the second excitation is localized in the domain walls. Two modes are also identified in ferromagnetic disks with thicknesses of 60 nm and diameters from 2 µm down to 500 nm. The equilibrium state of each disk is a vortex with a singularity at the center. As in the squares, the higher frequency mode is due to precession about the internal field, but in this case the lower frequency mode corresponds to gyrotropic motion of the entire vortex. These results demonstrate clearly the existence of well-defined excitations in inhomogeneously magnetized microstructures.

We have observed localized spin-wave modes in individual thin-film ferromagnetic wires using time-resolved Kerr microscopy as a micron-scale spectroscopic probe. The localization is due to the partial demagnetization of a wire when an external field is applied in the plane of the film and perpendicular to the long axis of the wire. Spatially-resolved spectra demonstrate the existence of distinct modes at the edges of a rectangular wire.Spectral images clearly show the crossover of the two edge modes into a single mode in low applied fields, in agreement with the results of micromagnetic simulations.

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...

We have observed collective spin-wave modes in inhomogeneously magnetized Ni 0.81 Fe 0.19 thin-film stripes. The stripes, 18 nm thick and 2 m wide, are studied in an in-plane magnetic field oriented along their short axes. When the magnetic field is on the order of the shape anisotropy field, the equilibrium magnetization near the stripe edges rotates 90 deg over a length scale of order 100 nm-1 m. Time-resolved Kerr microscopy is used to detect a hierarchy of spin-wave modes in these edge regions. Using a combination of semianalytical theory and micromagnetic simulations, we show that these modes span the entire stripe but can only be detected near the edges, where the effective wave vector is small.

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