Harnessing magnetic anisotropy for nonlinear magnetization precession and spin waves

Abstract

The nonlinearity of magnetization precession and spin waves is a cornerstone of contemporary magnonics. We investigate nonlinear magnetization dynamics in a thin epitaxial iron film driven by femtosecond laser pulses in regimes of homogeneous precession and propagating magnetostatic spin wave packets. The magnetization precession anharmonicity, the generation of higher-order harmonics, and the dynamical rectification are experimentally demonstrated. The numerical solution of the non-linearized Landau-Lifshitz-Gilbert equation reveals that these effects stem from the asymmetry in the energy potential. This asymmetry is readily achievable when an external magnetic field with a strength comparable to the magnetic anisotropy field is applied close to the hard axis. This work establishes a connection between the geometry of the energy profile and nonlinear responses, paving the way for designing magnonic devices with controlled harmonic generation and nonlinear spin wave interaction.

Figures (3)

• Figure 1: Anharmonicity and higher harmonics generation. (a) Experimental pump-probe signals, proportional to the out-of-plane magnetization component (points). The measurements are performed in the field $\mu_0 H_{ext} = 40$ mT, directed at an angle $\phi_H=2.5\,^\circ$. The solid red and dashed black lines correspond to the numerical LLG solution and single frequency damped sine, respectively. Insert in (a) shows a sketch of the anisotropy axes in the plane of the film and the angles designations. Easy axes are shown by the double-headed arrows, hard axes -- by the dashed lines. (b) FFT of the experimental signals and the numeric LLG solution from (a). The observed harmonics are numbered (1 corresponds to the eigen frequency). (c) Field dependencies of the experimental eigen frequency (points), numeric (solid red line) and linearized (dashed black line) LLG solutions. Error bars shows the standard deviation of the experimental FFT peaks.
• Figure 2: Energy profile asymmetry as a source of anharmonicity. (a) Energy as a function magnetization direction in the film plane $\phi_M^{ip}$ before (blue line) and after (red line) excitation by a femtosecond laser pulse. The dashed black line is a sketch illustrating the in-plane deviation change during the damping process. (b) Trajectory of magnetization precession in coordinates deviation in-plane -- deviation out-of-plane of the film. Empty points show positions of the energy minima. Black points correspond to the mean magnetization direction ($\phi_{\langle M\rangle}$) over the precession period. (c) Dependence of rectification $R = \phi_{\langle M\rangle} - \phi^{min}_{M}$ on the external magnetic field at zero Gilbert damping. (d) Dependence of $R$ on the precession amplitude during the damping process for external magnetic field values of $\mu_0 H_{ext} = 30$ (red) and 40 mT (green).
• Figure 3: The second harmonic of a propagating magnetostatic wave. (a) Dependence of energy vs. magnetization direction in the film plane inside (red) and outside (blue) the excitation area at $\mu_0 H_{ext} = 35$ mT. (c) Map of pump-probe signal vs distance and delay time ($\Delta t$) between excitation and detection. The measurements performed in the field $\mu_0 H_{ext} = 35$ mT, directed at an angle $\phi_H$ of 2.5 $^\circ$ in the Damon-Eshbach geometry. (b,d) 2D FFT of the experimental data (d) and the data, obtained from the micromagnetic simulation at the same parameters (b). The dashed black lines show the second harmonic of the magnetization dynamics. The panels on the right show cross-sections of the corresponding maps at $k = 0.1$$\mu$m$^{-1}$ with a guide to the eyes (solid line). The cross-section are marked with a red dashed line on the maps. The arrows on the cross-sections indicate the peaks of the spectral amplitudes corresponding to the first and second harmonics of the FMR and SSW.