Parametric frequency mixing in a magnetoelastically driven linear ferromagnetic-resonance oscillator

Abstract

We demonstrate the nonlinear frequency conversion of ferromagnetic resonance (FMR) frequency by optically excited elastic waves in a thin metallic film on dielectric substrates. Time-resolved probing of the magnetization directly witnesses magneto-elastically driven second harmonic generation, sum-and difference frequency mixing from two distinct frequencies, as well as parametric downconversion of each individual drive frequency. Starting from the Landau-Lifshitz-Gilbert equations, we derive an analytical equation of an elastically driven nonlinear parametric oscillator and show that frequency mixing is dominated by the parametric modulation of FMR frequency. PACS numbers:Parametric behaviour emerges in a wide range of periodically driven systems when their parameters are also periodically modulated [1].Examples can be found in nano-optomechanical [2-4] and microelectromechanical systems [5], (spin) wave dynamics [6], quantum circuitry [7], energy harvesting applications [8], and in line with our current report, magneto-mechanical systems [9] including spin pumping capabilities [10]. The utility of parametric behaviour has been shown for quantum limited detection, noise floor reduction or low noise amplification of small signals [2,7].Parametric phenomena in magnetization dynamics have also been extensively studied in the framework of spintronic and magnonic applications [11], where the downconversion of a microwave-driven uniform precession can generate two counter-propagating spin waves of varying frequency and wavevector. The onset of parametric behaviour in these cases is monitored via the enhanced damping and linewidth changes of the ferromagnetic resonance (FMR) precessional motion. Furthermore, time domain probing of FMR precession modulated with multiple microwave electromagnetic fields leads to seeded parametric downconversion [12]. Additional studies along these lines have resulted in the generation and detection of a range of frequency mixing processes of both uniform precessional modes as well as higher energy spin waves [13][14][15], including frequency upand down-conversion.Looking beyond microwave excitation, the overlapping frequency range of (surface) acoustic waves and magnetization precession provides for a unique opportunity to study their interactions and to explore physical processes where coherent elastic deformations could provide the necessary parametric modulation to drive complex magnetization dynamics. In recent years, magnetoelastic interactions have seen a resurgence of interest, and linear coupling between these degrees of freedom have been demonstrated [16][17][18][19][20][21]. To our knowledge, only a single report has discussed the potential for nonlinearities in the magnetoelastic interactions [22].In this report we present experimental evidence for the nonlinear (in the sense of frequency mixing) interaction between multiple coherent elastic deformations and the magnetization precession in a thin ferromagnetic film. To explain our results we perform analytical calculations of...

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