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 $mu$m form closure domain structures with 90 degree Neel 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 $mu$m 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.
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