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Nonlinear Eigenoscillations of Spins in a Parallel-Plane Ferromagnetic Resonator

机译:平行平面铁磁谐振器中自旋的非线性本征振荡

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Inhomogeneous, with respect to thickness, spin eigenoscillations of arbitrary amplitude in a ferromagnetic resonator (a film placed in a normal saturating magnetic field) are investigated theoretically. Nonlinear boundary conditions are derived for the case of arbitrary character and degree of the spin pinning on the surface. The solutions to the nonlinear dynamical equations for magnetization that describe standing waves in angle variables (precession angle-azimuthal angle) are found. The analysis of solutions on the phase plane makes it possible to determine their mode composition and formulate simple algorithms for calculating profiles and spectra. The considered nonlinear oscillations must be excited at high excitation levels when spin-wave resonance (SWR) is investigated experimentally. The existence of the series of modes with a finite excitation threshold (in the case of hard excitation) is indicated. When the excitation level of the fundamental inhomogeneous mode is increased, its amplitude tends to be distributed uniformly over the film thickness. In this case, eigenfrequencies (and fields) undergo a nonlinear shift, which is especially strong when the easy-plane type of anisotropy exists on the surface. As the excitation level increases, the eigenfrequencies (and eigenfields) cease to depend on the boundary conditions.
机译:对于厚度不均匀,从理论上研究了铁磁谐振器(放置在正常饱和磁场中的薄膜)中任意幅度的自旋本征振动。对于表面上自旋钉扎的任意特征和程度的情况,得出非线性边界条件。找到了用于磁化的非线性动力学方程的解,该解描述了角度变量(进动角-方位角)中的驻波。相平面上溶液的分析使得确定其模式组成并制定用于计算轮廓和光谱的简单算法成为可能。实验研究自旋波共振(SWR)时,必须在高激发水平上激发所考虑的非线性振荡。指出了具有有限激励阈值的一系列模式的存在(在硬激励的情况下)。当基本非均质模式的激发能级增加时,其幅度趋于在膜厚度上均匀地分布。在这种情况下,本征频率(和场)会发生非线性位移,当表面上存在易平面型各向异性时,该非线性尤其强烈。随着激发能级的增加,本征频率(和本征场)不再取决于边界条件。

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