Dipolar localization of quantized spin-wave modes in thin rectangular magnetic elements

Abstract

Dipole-exchange spectrum of quantized spin wave modes of a tangentially magnetized rectangular thin-film magnetic element is calculated using the method of tensorial Green's functions. The strong inhomogeneity of the internal bias magnetic field along the magnetization direction leads to the localization of spin wave modes either at the edges ͑exchange localization͒ or at the center ͑dipolar localization͒ of the element. The mode intensity distributions along the other in-plane direction are determined by the dipolar boundary conditions and have the usual cosinusoidal form. The approximate theory developed in the paper gives a quantitative description of the resonance fields and qualitative description of the spatial distributions of quantized spin wave modes in a thin square permalloy element ͑in plane sizes 50ϫ50 m 2 , thickness 0.1 m͒ recently observed by space-resolved Kerr spectroscopy. The theory shows also that the mode localization in this case ͑in the element center͒ is of the dipolar nature.

Engineering spin-wave channels in submicrometer magnonic waveguides

“…The effective width felt by the centre modes is on the one hand smaller than the real width of the waveguide, i.e. w * < w, but the "magnetic wall" boundary condition is on the other hand not applicable to the model system, 44 suggesting that the centre modes in this system with the narrow antenna are not equivalent in nature to those reported in previous research. 21,24,[31][32][33] The edge and centre modes are degenerate in energy, yet spatially confined to different channels and of distinct dispersion relations.…”

“…The positions of the nodes are determined by the effective width w * of the waveguide felt by the centre mode, which is further associated with the boundary condition of the waveguide. 43,44 In our micromagnetic simulations, no boundary conditions were artificially imposed a priori on the lateral surfaces. In the theoretical calculations, the value of w * could not be chosen arbitrarily, otherwise the agreement with the simulations would not be accomplished.…”

Large-amplitude coherent spin waves excited by spin-polarized current in nanoscale spin valves

“…It was recently demonstrated [14] that a spinpolarized current can excite motion of magnetization in metallic nanomagnets with precession cone angles over 30° -values far exceeding those achievable in typical FMR experiments performed on bulk and thin-film samples. There are two reasons why it is possible to have such large-amplitude current-driven motions of magnetization in nanomagnets: (i) suppression of Suhl instability processes [15,16] due to quantization of the magnon spectrum in the nanomagnet [17][18][19][20][21][22][23][24][25][26][27][28], and (ii) efficient amplification of spin waves by spin transfer torque that can act approximately as negative magnetic damping [1,2].…”

Calculations of three-dimensional magnetic normal modes in mesoscopic permalloy prisms with vortex structure

“…Several studies on magnetic excitations in various thinfilm elements have been reported, including wires, [3][4][5][6][7] rectangles, 4,[8][9][10] circular disks 2,[11][12][13][14][15][16][17][18][19] and squares [20][21][22][23][24] with closure domains, rings, 25 and several other elementary shapes. In all examples listed above, the samples studied were essentially two-dimensional ͑2D͒, i.e., thickness effects are not important as far as the profile of the dynamic mode is concerned.…”