Time-resolved splitting of magnons into vortex gyration and Floquet spin waves

TL;DR

The study addresses real-time dynamics of spin-wave scattering in magnetic vortex disks, focusing on how driven azimuthal spin waves scatter into the vortex gyration mode and give rise to Floquet spin waves and a frequency comb. Time-resolved microwave electrical measurements are used with the disk embedded in a magnetic tunnel junction to monitor transient gyration and Floquet populations via I/Q demodulation of the MTJ voltage. The first scattering event is shown to be a three-wave splitting of a regular eigenmode with azimuthal index $m=-1$ into a gyration mode $g$ and a Floquet mode $SB^-$ with frequency $f_{rf}-f_g$, with minimal incubation delay when the drive resonates with $m=-1$. Time-domain data reveal synchronized growth of the gyration and the Floquet mode, indicating a common incubation delay that vanishes at the scattering threshold, with delays as short as about 3 ns. The results link steady-state Floquet interpretations to transient dynamics and suggest cascaded scattering pathways that populate additional Floquet states, with implications for frequency down-conversion and magnonics applications.

Abstract

Forced excitations at frequencies in the range of the first order azimuthal spin waves of a magnetic disk in the vortex state are known to scatter into the vortex gyration mode, thereby allowing the growth of Floquet spin waves forming a frequency comb. We study the temporal emergence of this dynamical state using time-resolved microwave electrical measurements. The most intense Floquet mode emerges synchronously with the gyration mode after a common incubation delay which diverges at the scattering threshold. This delay is minimal when the drive is resonant with one of the first order azimuthal spin waves. It can be as short as 3 ns for the maximum investigated power. We conclude that the first-to-occur scattering mechanism is the three-wave splitting of a regular azimuthal eigenmode into a coherent pair formed by a gyration magnon and a Floquet spin wave.

Figures (5)

• Figure 1: Set-up and effect of the dc and rf drives in the linear regime. (a) A wire fed with an rf current applies a field on a circular magnet in the vortex state. The magnet is part of a magnetic tunnel junction which delivers a voltage $V(t)$ to the measuring instruments. (b) Thermal spin waves (grey lines): Increase of the power spectral density of $V$ when changing the dc bias from 0 to 200 mV. The blue lines are the frequencies of the modes of azimuthal indices $m=\pm 1$ in the micromagentic simulations. (c) Spectrum with the signal of thermal spin waves, cross-talk signal and microwave mixing signal leading to the sidebands SB$^-$ and SB$^+$ when applying an rf drive at 4.13 GHz and 10.8 dBm. (d): Optical micrograph of a device.
• Figure 2: (c) Total power of the gyration mode (defined as $\int_{10~\textrm{MHz}}^{1~\textrm{GHz}} ||\tilde{V}(f)||^2 df$) versus stimulus power and drive frequency $f_\textrm{rf}$ for a bias of 200 mV on a device of diameter 400 nm, whose $m=-1$ regular mode is at 5.18 GHz (vertical blue line). The black color level corresponds to the power generated by the thermal fluctuations of the gyration.
• Figure 3: Scattering of the forced $\lvert \textrm{rf} \rangle$ mode into the gyration mode and resulting frequency comb for a 300 nm diameter device. Power spectral density when applying a pump at 5.04 GHz with a power of 10.8 dBm (a) in the presence of 200 mV of dc bias, and (b) in the absence of dc bias. The dashed yellow bar is the power threshold to be used later when analyzing the time-resolved amplitude of the first lower sideband SB$^-$.
• Figure 4: Time-resolved population of the gyration mode for a 300 nm device. (a, b) $V(t)$ (blue) and a low-pass-filtered version of it (red) for a drive at $f_\textrm{rf}=5.17$ GHz and 8.8 dBm with a dc bias of -200 mV. (c) Transients of the populations $n(t)$ of the gyration mode at $f_\textrm{g}=492$ MHz (red, $\times 8$ magnification), of the Floquet mode of the lower sideband SB$^-$ at $f_\textrm{rf}- f_\textrm{g}$ (green, $\times 60$ magnification) and of the signal at the forcing frequency $f_\textrm{rf}$ (black). The oscillations in the population of SB$^-$ originate from the experimental noise. (d) Dependence of the incubation delay of the gyration versus the pump frequency and the pump power. The vertical line is at the frequency of the regular eigenmode $\lvert m=-1 \rangle$.
• Figure 5: Correlation between the incubation delays of the gyration and of the appearance of the signal of the lower sideband. Each point is a single shot event for applied frequencies spanning from 5 to 5.44 GHz, a power of 10.8 dBm and dc biases of -200 and +200 mV.