Spin-Wave Eigenmodes of a Saturated Magnetic Square at Different Precession Angles

Abstract

Using low-loss dielectric magnetic films in combination with space-resolved Brillouin light scattering spectroscopy we have studied nonlinear modification of eigenmode spatial distributions in saturated magnetic squares. We have found that, as the angle of magnetization precession increases, the eigenmode spatial distributions experience significant qualitative changes due to a nonlinear coupling between forming them standing spin waves. We show that the found nonlinear eigenmodes cannot be described by means of the linear theoretical approach even qualitatively.

Nonlinear mode conversion in monodomain magnetic squares

“…As shown in Ref. 23 this method gives very good agreement with the experimentally measured frequencies.…”

“…24 For this geometry the BLS intensity is proportional to the square of the precession angle of the magnetization, ͉͉ 2 averaged over the probing laser spot, which in these experiments had a diameter of about d =60 m. A detailed description of the used experimental setup can be found elsewhere. 23 Note that the absolute value of the opening angle was not experimentally determined, due to the complexity of the calibration process of the BLS setup. However, the technique gives the possibility of mapping the distribution of the opening angle over the sample in spinwave modes with wave vectors up to / d.…”

“…22 Recently, we have suggested the use of low-loss dielectric films of yttrium iron garnet ͑YIG͒ in combination with space-resolved Brillouin light scattering ͑BLS͒ spectroscopy as a method for experimental modeling of nonlinear magnetization dynamics in small magnetic elements. 23 Using this technique, we have observed a modification of the spatial profiles of spin-wave eigenmodes in magnetic squares at large angles of magnetization precession. Here we present a deep analysis of the observed phenomenon based on the complex Ginzburg-Landau equation.…”

Two-wave mixing in nonlinear magnetization dynamics: A perturbation expansion of the Landau-Lifshitz-Gilbert equation

“…[1][2][3] Recently there has been a renewal of this interest because it has become possible to generate large amplitude precessional motion in metals through a variety of techniques. [4][5][6][7][8][9][10][11] There have been a number of experiments 8,12,13 which have shown an interesting nonlinear mixing of two signals in magnetic materials. These experiments were done in ultra-small geometries where the microwave magnetic field could be varied over several orders of magnitude, from less than one Oe up to several hundred Oe.…”

Non-linear response of driven spin excitations

“…We did point out that the method looked promising for the study of non-linear dynamics. Recently, non-linear modification of eigenmode spatial distribution was reported in a rather large saturated magnetic square studied with BLS spectroscopy [9]. A technique based on magneto-optical Kerr effect was also developed to detect the non-linear ferromagnetic resonance in thin films [10].…”