Time- and phase-resolved spectroscopy of three-magnon scattering

Abstract

In ferromagnets, scattering processes between magnon modes have been an active platform for the investigation of nonlinear wave interactions and chaotic dynamics for over six decades. Despite this rich history, questions remain regarding the nature of these interactions. In this regard, three-magnon scattering of the ferromagnetic resonance (FMR) mode is of particular appeal: the threshold FMR magnon population at which scattering occurs is distinctly low, enabling its investigation over a wide range of excitation powers. This particular scattering process requires the availability of magnon modes at half of the frequency of the FMR mode. This requirement is readily fulfilled in magnetic films of micrometer thickness, as the associated dipolar interactions lead to a dip in their magnon dispersion. Existing studies of three-magnon scattering have largely focused on its influence on the magnon populations and on the steady-state behavior. A comprehensive understanding of its transient behavior (i.e. how it evolves in time as it approaches steady state) is missing. Similarly, little is known about the influence of three-magnon scattering on the magnons' phases. This is largely the case for other magnon scattering processes as well. There is also a lack of a formal understanding of the relationship between the forward and backward three-magnon scattering processes, i.e. between splitting and confluence. These gaps are, in part, owing to the fact that there is a lack of a comprehensive time- and phase-resolved experimental investigation of the three-magnon scattering process. Magnon scattering processes are most commonly investigated through diode-based techniques, which are relatively insensitive and lack phase resolution. They are also most commonly investigated through Brillouin light scattering spectroscopy; this technique is typically employed for large excitation powers, and its phase-sensitive implementations have not been applied to three-magnon scattering. Motivated by the above, I have assembled a time- and phase-resolved homodyning spectrometer that is operable over six orders of magnitude in microwave power. This spectrometer demonstrates a time resolution of 2 ns, and its sensitivity enables measurement of the transient behavior down to an excitation power of 10 microwatts. Upon measuring the resonance peak of the FMR mode, I observed satellite peaks near that of the FMR resonance. Such satellite peaks are observed in the literature as well. I found that they originate from the excitation of magnon modes with finite in-plane wavevectors, due to the inhomogeneity of the microwave field throughout the sample. To address this inhomogeneity, I created a microstrip waveguide with a signal line width of approximately 3.4 mm, such that it is appreciably wider than the 2 mm-wide sample. This ensures a highly uniform microwave field and, therefore, the highly isolated excitation of the FMR mode. Isolating the excitation of the FMR mode in this manner enables a clear interpretation of the measured transient behavior, and contributes toward the strong agreement observed between my experiment and my semianalytical model. With the above developments, I have investigated the transient behavior of the FMR mode during this scattering process over five orders of magnitude in power. In addition to my observing the expected transient behavior, in which the scattering monotonically suppresses the FMR magnon population to its threshold value, I find a second nonlinear in which the FMR magnon population exhibits transient oscillations about its threshold value. I find that both these oscillations and the timescale of the initial transient peak are highly dependent on the excitation power. At high powers, I find a third nonlinear regime in which the scattering generates 180-degree phase shifts of the FMR magnons. Moreover, I find that both these phase shifts and the transient oscillations reappear upon removing the microwave excitation (i.e. after turn-off). To supplement the experiment, and to understand my findings, I have derived a simplified semianalytical model of this scattering process based on the Landau-Lifshitz-Gilbert equation. Upon linearizing my model, I found that the oscillatory regime corresponds to a transition of the nonlinear regime's fixed point from a stable node to a stable spiral. I also extracted the predicted scaling of the oscillation frequency with the microwave field amplitude. Upon extracting the associated scaling of the experimental data, I found it to be in quantitative agreement with the predicted scaling over several orders of magnitude in power. To investigate the 180-degree phase shifts observed in the experiment, I generalized my model to allow for phase dynamics by omitting the standard assumption of harmonic time dependence. Numerically solving this generalized model, I found that it predicts these 180-degree phase shifts. In order to derive the equations of motion of the magnon populations, one begins with the generalized model and assumes harmonic time dependence. Remarkably, when accounting for the 180-degree phase shift in this harmonic approximation, I found that the phase shifts correspond to reversals in the scattering direction: in the magnon populations' equations of motion, the phase shift switches the sign of the scattering terms such that the scattering is now driving the FMR mode instead of damping it. These reversals explain the observed transient oscillations after turn-off: even without the excitation field, the FMR population may still oscillate via reversals between the forward and backward scattering process. These experimental and theoretical developments further the state of the art of the investigation of magnon scattering processes. The findings of my investigation provide a more comprehensive understanding of the transient behavior of this scattering process, and reveal the nontrivial interplay between three-magnon scattering and the magnons' phases.