Brillouin light scattering investigation of dynamic spin modes confined in cylindrical Permalloy dots (original) (raw)
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Spin wave eigenmodes of square permalloy dots studied by Brillouin light scattering
Journal of Magnetism and Magnetic Materials, 2007
The frequencies of spin wave eigenmodes of square permalloy nano-elements with relatively large aspect ratio (thickness 20 nm, width 275 nm), fabricated by deep ultraviolet lithography, were measured experimentally using Brillouin light scattering (BLS). The measurements were done in a wide range of bias magnetic fields applied along one of the in-plane sides of the square element. The experimental data have been reproduced using both micromagnetic and analytical calculations, which allowed us to reliably identify the spatial structure of the excited spin wave eigenmodes. It is demonstrated that both purely dipolar sinusoidal and dipole-exchange localized spin wave eigenmodes contribute to the formation of the discrete BLS spectrum of the nano-element. r
Spin wave modes in submicron cylindrical dots
Journal of Applied Physics, 2003
The dynamic properties of a squared array of cylindrical Ni 81 Fe 19 dots with thickness Lϭ50 nm, radius Rϭ100 nm, and separation 2R have been investigated by Brillouin light scattering. The sample was prepared by means of electron-beam lithography and evaporation in ultrahigh vacuum. The lateral confinement of spin waves within each dot causes a marked discretization of the spin wave spectrum. Several discrete peaks were measured in the saturated state as a function of both the incidence angle of light and the applied magnetic field. The detected modes are classified as surface dipolar and bulk magnetostatic modes at frequencies higher and lower than the Kittel uniform mode, respectively.
Theory of spin wave modes in tangentially magnetized thin cylindrical dots: A variational approach
Physical Review B, 2006
We present a theoretical study of the quantized spin wave spectrum in tangentially magnetized cylindrical thin magnetic dots. Low-energy spin waves in magnetic dots may be subdivided into four families: Damon-Eshbach like, backward like, mixed, and end modes. Frequencies and mode profiles are found using a variational approach based on carefully chosen trial functions. The variational method has the advantage that it can be used for large dots that are not practical to treat using numerical finite-element methods. Results for small dots generated using the variational method compare well with micromagnetic results. The variational method is demonstrated with an analysis of data obtained from experimental Brillouin light scattering data from saturated thin cylindrical Permalloy dots. Our approach allows for the definition of parameters describing important contributions to the spin wave energies. As an example, we show that a variational parameter ⑀ provides a measure of spin wave localization near the dot border for one class of modes.
Microelectronics Journal, 2009
The spin-wave modes in nanoscale permalloy stripes are studied using Brillouin light scattering for the case where an external magnetic field is applied transversely to the length of the stripes. By adjusting the magnitude of this external field, the overall magnetization may be varied between the approximately transverse and longitudinal orientations. The observed spin-wave frequencies are analysed using a recently developed microscopic dipole-exchange theory that is particularly appropriate when the magnetization displays strong spatial inhomogeneity. Comparison between theory and experiment for the two sizes of stripes studied gives fairly good agreement, allowing the magnetic parameters of permalloy to be deduced. A small magnetic anisotropy of the easy-plane type is shown to play an important role.
Journal of Physics: Condensed Matter, 2004
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 inplane 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.
Journal of Applied Physics, 2007
A microwave assisted Brillouin light scattering ͑BLS͒ technique based on resonant excitation of spin waves in a 200 nm thick permalloy film by a micrometric size coplanar antenna has been studied. It has been demonstrated that the BLS intensity and signal-to-noise ratio have been improved by three orders of magnitude with respect to the conventional light scattering by thermal magnons. The analysis of the amplitude, shape, and frequency position of Stokes and anti-Stokes lines in the BLS spectra, for nonzero angles of the light incidence, indicates the presence of a strong hybridization of standing spin-wave resonances with propagating spin waves due to partial nonsymmetric pinning on the film surfaces. Direct optical probing has shown that the excited hybrid spin-wave modes are localized strictly in the vicinity of the microwave antenna.
Journal of Physics: Condensed Matter, 2007
The magnetic Brillouin scattering of arrays of permalloy stripes with rectangular 29 nm × L cross section (L = 500, 1000, 1500 nm) is studied versus the amplitude and the direction of the applied magnetic field and of the transferred wavevector. A simple model provides a satisfactory agreement of the full set of experimental results: each stripe is viewed as a continuous film showing an in-plane anisotropy due to the demagnetizing effects induced by lateral surfaces. We introduce an anisotropy field H a = a M, where M stands for the magnetization and where the coefficient a can be evaluated directly, at least approximately. In addition, we give an account of the previously studied magnetic mode quantization and of the observed variations in the Stokes/anti-Stokes asymmetry in patterned arrays as well as in continuous films.
Physical Review B, 2004
A double-peaked structure was observed in the in-situ Brillouin Light Scattering (BLS) spectra of a 6Å thick epitaxial Fe/GaAs(001) film for values of an external magnetic field H, applied along the hard in plane direction, lower than a critical value Hc ≃ 0.9 kOe. This experimental finding is theoretically interpreted in terms of a model which assumes a non-homogeneous magnetic ground state characterized by the presence of perperpendicular up/down stripe domains. For such a ground state, two spin-wave modes, namely an acoustic and an optic mode, can exist. Upon increasing the field the magnetization tilts in the film plane, and for H ≥ Hc the ground state is homogeneous, thus allowing the existence of just a single spin-wave mode. The frequencies of the two spin-wave modes were calculated and successfully compared with the experimental data. The field dependence of the intensities of the corresponding two peaks that are present in the BLS spectra was also estimated, providing further support to the above-mentioned interpretation.