A Brillouin light scattering study and theoretical interpretation of spin-wave modes in arrays of in-plane magnetized micron-size rectangular Ni 80 Fe 20 elements are reported. It is shown that two-dimensional spinwave eigenmodes of these elements can be approximately described as products of one-dimensional spin-wave eigenmodes of longitudinally and transversely magnetized long finite-width permalloy stripes. The lowest eigenmodes of rectangular elements are of dipole-exchange nature and are localized near the element edges, while the higher eigenmodes are of a mostly dipolar nature and are weakly localized near the element center. The frequency spectra and spatial profiles of these eigenmodes are calculated both analytically and numerically, and are compared with the results of the Brillouin light scattering experiment.
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.
We have observed several localized modes in the spin-wave spectrum of a permalloy microstripe (length 90 μm, width 1 μm, thickness 0.033 μm) magnetized along its width. The mode frequencies increase from 4.5 to 8 GHz with increasing applied field (0–1.1 kOe). These modes are interpreted as multiple spin–wave eigenstates in effective potential wells created by a strongly inhomogeneous internal magnetic field in the stripe near its edges.
The magnetic field dependences of the frequencies of standing spin-wave
modes in a tangentially magnetized array of thin rectangular permalloy dots
(800 × 550 nm) were measured experimentally by a Brillouin light scattering technique and calculated
theoretically using an approximate size-dependent quantization of the spin-wavevector
components in the dipole-exchange dispersion equation for spin waves propagating in a
continuous magnetic film. It was found that the inhomogeneous internal bias magnetic field
of the dot has a strong influence on the profiles of the lowest spin-wave standing modes. In
addition, the dynamic magnetization distributions found for both longitudinally and
transversely magnetized long magnetic stripes gives a good approximation for mode
distributions in a rectangular dot magnetized along one of its in-plane sides. An
approximate analytic theory of exchange-dominated spin-wave modes, strongly localized
along the dot edge that is perpendicular to the bias magnetic field, is developed. A
good quantitative agreement with the results of the BLS experiment is found.
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