Magnonic spontaneous oscillation induced by parametric pumping

Abstract

Spontaneous dynamic systems have attracted significant attention for their rich underlying physics such as phase-locking and synchronization. In this work, we report a new mechanism of generating magnetic spontaneous oscillation via parametric pumping. By applying a pump tone to excite propagating spin waves in a yttrium iron garnet delay line, four-wave mixing converts the pump mode into two phase-autonomous propagating magnon modes, i.e. a spontaneous mode with nearly twice the wavenumber of the pump mode and an idler mode with nearly zero wavenumber. This allows us to reliably generate ultrasharp spin wave dynamics with broad frequency tunability from the pump and magnetic field. We show that the spontaneous mode can be phase-locked to a probe tone, similar to an auto-oscillator. Furthermore, the spontaneous dynamics can be used to implement a high-gain magnonic parametric amplifier with a gain up to 40 dB. Our results open a new avenue for studying nonlinear magnonics and synchronization physics in propagating magnon geometry and for developing new magnonic devices.

Figures (5)

• Figure 1: (a) Schematic of spontaneous mode measurements of a YIG delay line using a spectrum analyzer. The magnetic field is set at $\mu_0H_B=0.11$ T. (b) Illustration of 4-wave mixing using Damon-Eshbach magnetostatic modes, where two $f_\text{pump}$ magnons is converted to one $f_\text{spon}$ magnon and one $f_\text{idler}$ magnon. The antenna efficiency function is also plotted with a blue curve showing the first and third harmonics. (c) Comparison of VNA measurements with pump on and off at $f_\text{pump}=5.53$ GHz and $P_{pump}=-9$ dBm. The red arrow indicates the spontaneous mode. (d) SA measurement of spontaneous mode at $f_\text{pump}=5.53$ GHz and $P_{pump}=-9$ dBm, with a resolution bandwidth (RBW) of 20 kHz. (e-f) Zoom-in measurements of (e) the pump signal $f_\text{pump}$ and (f) the spontaneous mode signal $f_\text{spon}$ with a RBW of 200 Hz. (g) Evolution of the spontaneous mode peak at different $P_{pump}$. The red trace corresponds to the data shown in (f).
• Figure 2: (a) Evolution of the spontaneous mode peaks (solid curves) at different $f_\text{pump}$ (dashed lines, from 5.5 GHz to 5.58 GHz), with the peak amplitudes following the VNA-measured magnon transmission band (gray curve). (b) VNA pump-probe measurements as a function of $f_\text{pump}$ at $P_\text{pump}=-9$ dBm. Red circles label SA-measured $f_\text{spon}$ as a function of $f_\text{pump}$. The black dashed line denotes $f_\text{pump}$. The blue dashed line denotes $f_\text{K}$. The red dashed line denotes $2f_\text{pump}-f_\text{K}$.
• Figure 3: (a) Schematic of phase-locking measurement with pump and probe tones mixed as the input. The magnetic field is set at $\mu_0H_B=0.21$ T and the pump frequency is set to $f_\text{pump}=8.51$ GHz. (b) Illustration of the frequency relationship among $f_\text{pump}$, $f_\text{probe}$ and $f_\text{spon}$. (c) Phase locking of the spontaneous mode as a function of $f_\text{probe}$, with $P_\text{pump}=-11.0$ dBm and $P_\text{probe}=-30$ dBm. (d) Fitting curves plotted on top of the extracted peak positions for the main mode (cyan) and the first harmonic mode (red). (e) Phase locking spectra measured at $P_{probe}=-34$, -32, -30, -28 and -26 dBm, with $P_{pump}=-11.0$ dBm. (f) Extracted phase-locking bandwidth $\Delta$ as a function of $\sqrt{P_\text{probe}}$. (g) Phase locking spectra measured at $P_{pump}=-12.2$, -11.6 and -10.8 dBm, with $P_{probe}=-30$ dBm. (h) Extracted phase-locking bandwidth as a function of square root of spontaneous mode power.
• Figure 4: (a) Illustration of the frequency relationship to search for the idler mode ($f_{idler}$) with a probe tone ($f_{probe}$). (b) Measurements of the spontaneous and idler modes for $\mu_0H_B=0.21$ T at different $f_{pump}$, with $f_{pump}=8.46$ GHz showing the idler mode. (c-d) Comparison of (c) the idler mode and (d) the main spontenous mode at $f_{pump}=8.46$ GHz. (e-f) Phase locking of (e) the idler mode and (f) the main spontenous mode by applying $f_{probe}$ around $f_{idler}$ at $P_{probe}=-22$ dBm. The yellow diagonal dashed line shows the probe signal $f_{probe}$ in (e) and the mixing signal $2f_{pump}-f_{probe}$ in (f). The vertical white dashed lines show the phase-locking bandwidth.
• Figure 5: (a) Gain map of magnonic parametric amplification at $\mu_0H_B=0.21$ T, $f_{pump}=8.51$ GHz and $P_{pump}=-10.7$ dBm. (b-d) Spectral evolution of the mode interaction in the phase-locking regime at $P_{probe}=-40$ dBm. (e-g) Spectral evolution of the probe signal in the constant gain regime at $P_{probe}=-60$ dBm. (h) Comparison of probe tone lineshape with pump on and off at $P_{probe}=-60$ dBm. (i) Comparison of gain (solid curve and circles) and spontaneous mode lineshape (dashed curve) at different $P_{pump}$, measured at $P_{probe}=-60$ dBm.