Coherent control of Floquet-engineered magnon frequency combs

Abstract

Frequency combs represent a hallmark of coherence emerging from nonlinear dynamics, where periodic driving organizes energy into a precisely spaced spectral structure. Extending this concept to collective excitations in solids such as magnons, the quanta of spin waves in magnetically ordered materials, offers a powerful route to control energy flow, coherence, and information processing in condensed matter systems. Here, we demonstrate deterministic control of Floquet-engineered magnon frequency combs in magnetic vortices using nanosecond voltage pulses. By tuning the pulse duration and timing, we control the nonlinear energy transfer between magnons and the vortex core, enabling the Floquet-engineered initiation or suppression of magnon frequency combs far below their spontaneous instability threshold. This pulse-programmable interaction allows the vortex to sustain magnon-driven auto-oscillation with high phase stability, or to revert to its static ground state on demand. Our results establish vortex-based magnetic systems as a robust solid-state platform for Floquet engineering, bridging nonlinear spin dynamics with frequency conversion and coherent spin-based quantum devices.

Figures (4)

• Figure 1: From the regular magnon dispersion to Floquet-engineered frequency combs in a magnetic vortex.a, Simulated regular magnon dispersion of a 2µm-diameter, 50nm-thick Ni$_{81}$Fe$_{19}$ disk in the vortex ground state, with the static magnetization configuration shown in the inset. High-frequency magnon modes characterized by their radial and azimuthal indices $(n, m)$ are marked by circles, while the low-frequency excitations corresponding to the thermally populated vortex-core gyration are indicated by squares. b, Floquet magnon dispersion under driven vortex-core gyration, as sketched in the inset. The circles overlay the regular magnon modes of the static vortex, highlighting the formation of additional Floquet sidebands and avoided crossings induced by the periodic drive. c, Scanning electron microscopy image of Ni$_{81}$Fe$_{19}$ disks patterned on a gold coplanar waveguide (CPW). The excitation signal is provided through a diplexer combining the high-frequency microwave input ($f_{nm}$) with the nanosecond voltage pulses ($V_\text{pulse}$) applied via ground-signal-ground (GSG) probes. d, Brillouin light scattering (BLS) microscopy spectra measured under single-tone excitation at $f_{nm} = 4.8GHz$, corresponding to the azimuthal mode $m = -1$, for varying excitation power. At sufficiently high powers, distinct magnon frequency combs emerge, marking the onset of nonlinear scattering processes and self-induced Floquet magnon states. The upper (lower) panel shows data obtained during power increase (decrease), revealing a clear hysteresis between the two sweep directions that reflects the threshold behaviour of the nonlinear magnon-magnon interaction.
• Figure 2: Nanosecond-pulse control of Floquet-engineered magnon frequency combs in a magnetic vortex.a, Vortex-core trajectories derived from micromagnetic simulations for different pulse durations $\tau$. Red (gray) traces denote the core motion during (after) the field pulse, and the red (black) circles mark the equilibrium positions during (after) excitation. A pulse with duration $\tau = 0.5T_\text{gy}$ displaces the core, triggering sustained gyration. In contrast, a pulse with $\tau = T_\text{gy}$ returns the core to the disk center at its falling edge, suppressing the gyration. b, Time-integrated BLS spectra recorded as a function of pulse duration $\tau$. The Floquet states vanish whenever $\tau$ matches integer multiples of the vortex-core gyration period ($\tau = \ell T_\mathrm{gy}$, with $\ell = 1, 2, 3, …$), demonstrating that comb generation and suppression are governed by the phase relation between the external voltage pulses and the vortex-core motion. c,d, Time-resolved BLS spectra measured on a Ni$_{81}$Fe$_{19}$ disk while exciting the $m = -1$ azimuthal mode at $f_{nm} = 4.8GHz$ with a 400ns microwave pulse below the threshold for spontaneous nonlinear coupling to the vortex-core gyration and self-induced Floquet states. At $t=120ns$, single voltage pulses of different duration are applied, as illustrated schematically above the spectra. A short pulse of $\tau = 2.5ns$, close to half the gyration period, induces a clear magnon frequency comb, while a slightly longer pulse of $\tau = 5.25ns$, approximately one gyration period, leaves the system in a single-tone state, suppressing the comb.
• Figure 3: Coherent control of magnon frequency-comb generation and suppression across all relevant timescales.a, Time-integrated BLS spectra recorded as a function of pulse duration $\tau$. MFCs vanish whenever $\tau$ equals an integer multiple of the vortex-core gyration period ($\tau = \ell T_\text{gy}$, with $\ell = 1, 2, 3, …$), indicating that comb generation depends sensitively on the timing of the pulse within the gyration cycle. b, BLS intensity integrated over the spectral ranges corresponding to the direct excitation ($I_{nm}$) and the lower-frequency comb modes ($I_\text{MFC}$), as sketched in panel (a). Peaks in $I_{nm}$ coincide with suppressed comb generation, reflecting that no energy is transferred into the sidebands when the pulse ends with the vortex core at the disk center. c,d, Extended time-resolved BLS spectra for long pulses covering hundreds of gyration periods. In c, a 526.7ns pulse ($\approx 100T_\text{gy}$) terminates when the vortex core is near the disk center, restoring the static configuration and suppressing the comb. In d, increasing the pulse length by only 1.4ns leaves the core displaced at the falling edge, sustaining the gyration and preserving the frequency comb after the drive ends. e,f, Temporal evolution of the integrated intensities for the direct excitation ($I_{nm}$) and lower-frequency comb sidebands ($I_\text{MFC}$). During the pulse, the direct excitation diminishes as energy is redistributed into the comb modes. When the pulse ends at the gyration period (d), the excitation recovers; when the pulse ends out of phase (f), the gyration remains, maintaining the comb.
• Figure 4: Phase-controlled switching of magnon frequency combs using double-pulse excitation.a, Modified excitation scheme with two voltage pulses of equal duration, $\tau_1=\tau_2=2.6ns$, separated by a delay $\Delta t$. b, Schematic vortex-core trajectories for two representative delays. In both cases, the first pulse ($\tau_1$) shifts the equilibrium position from the black dot to the red dot, initiating the gyration over half a period (red trace). For $\Delta t =2.6ns$, the core completes half a precession around the disk center (blue trace) before the second pulse ($\tau_2$) arrives, expanding the orbit further (yellow trace). For $\Delta t =5.2ns$, corresponding to a full gyration period, the second pulse drives the core back to the disk center, quenching the gyration. c, Time-integrated BLS spectra as a function of pulse delay $\Delta t$. Whenever the delay equals in integer multiple of the gyration period, $\Delta t = \ell T_\text{gy}$, with $\ell =1,2,3...$, the comb sidebands and Floquet features are suppressed. d, e, Time-resolved BLS spectra for delays $\Delta t=8.4ns$ and 10.8ns, corresponding to $1.6 T_\text{gy}$ and $2 T_\text{gy}$ respectively. For the shorter delay, the gyration is sustained and a MFC forms; for the longer delay, the motion is suppressed and only single-frequency excitation remains.