Mechanical Bistability in Kerr-modified Cavity Magnomechanics

Bistable mechanical vibration is observed in a cavity magnomechanical system, which consists of a microwave cavity mode, a magnon mode, and a mechanical vibration mode of a ferrimagnetic yttrium-iron-garnet sphere. The bistability manifests itself in both the mechanical frequency and linewidth under a strong microwave drive field, which simultaneously activates three different kinds of nonlinearities, namely, magnetostriction, magnon self-Kerr, and magnon-phonon cross-Kerr nonlinearities. The magnon-phonon cross-Kerr nonlinearity is first predicted and measured in magnomechanics. The system enters a regime where Kerr-type nonlinearities strongly modify the conventional cavity magnomechanics that possesses only a radiation-pressure-like magnomechanical coupling. Three different kinds of nonlinearities are identified and distinguished in the experiment. Our Letter demonstrates a new mechanism for achieving mechanical bistability by combining magnetostriction and Kerr-type nonlinearities, and indicates that such Kerr-modified cavity magnomechanics provides a unique platform for studying many distinct nonlinearities in a single experiment.

Figure 1

Device schematic. Left panel: schematic of the CMM system. A 0.28 mm-diameter YIG sphere is placed (free to move) in a horizontal 0.9 mm-inner-diameter glass capillary and at the antinode of the magnetic field of the cavity mode ${\mathrm{TE}}_{101}$. The cavity has two ports: Port 1 is connected to a microwave source (MW) to load the drive field, and Port 2 is connected to a vector network analyzer (VNA) to measure the reflection of the probe field with the power of $-5\mathrm{dBm}$. We set the direction of the bias magnetic field $B_0$ as the $z$ direction, and the vertical direction as the $x$ direction. Right panel: schematic of the coupled three modes.

Figure 2

(a) Left panel: measured reflection spectra under a red-detuned drive. The frequency of the drive field ${\omega }_d/2\pi =7.645\mathrm{GHz}$ (black arrow). By increasing the drive power, the magnon frequency shift is negative: ${\omega }_m^L/2\pi =7.658\mathrm{GHz}$ (light green dashed line) at a lower power $P_d=4.7\mathrm{dBm}$ (upper panel) and ${\omega }_m^H/2\pi =7.640\mathrm{GHz}$ (dark green dashed line) at $P_d=29.7\mathrm{dBm}$ (lower panel). The green arrow indicates the direction in which the magnon frequency shifts by increasing the power. Right panel: enlargement of the red shaded areas in the left panel shows detailed spectra of the magnomechanically induced resonances, where ${\mathrm{\Delta }}_{\mathrm{pd}}={\omega }_p-{\omega }_d$. The black lines are the fitting curves. (b) Left panel: measured reflection spectra under a blue-detuned drive. The drive frequency ${\omega }_d/2\pi =7.660\mathrm{GHz}$. By adjusting the bias magnetic field, the magnon frequency is tuned close to the drive frequency ${\omega }_m^L/2\pi \simeq {\omega }_d$ at the power $P_d=4.7\mathrm{dBm}$. Increasing the power to 23.7 dBm, the magnon frequency ${\omega }_m^H/2\pi =7.645\mathrm{GHz}$. Right panel: enlargement of the blue shaded areas in the left panel shows detailed spectra of the magnomechanically induced resonances. We observe two adjacent mechanical modes with the frequencies ${\omega }_b/2\pi =11.0308\mathrm{MHz}$ and ${\omega }_b^{\prime }/2\pi =11.0377\mathrm{MHz}$. Because of their similar behaviors, we focus on the lower-frequency mode in the text.

Figure 3

Bistable mechanical frequency and linewidth under a red-detuned drive. (a) The mechanical frequency shift versus the drive power. The red (green) curve is the fitting of the frequency shift induced by the radiation-pressure-like coupling (cross-Kerr effect) using Eq. (6), and the black curve is the sum of the two contributions. (b) The mechanical linewidth variation versus the drive power. The black curve is the fitting of the linewidth change using Eq. (7). In both figures, the blue (orange) triangles are the experimental data obtained via forward (backward) sweep of the drive power.

Figure 4

Bistable mechanical frequency and linewidth under a blue-detuned drive. (a) The mechanical frequency shift and (b) the mechanical linewidth change versus the drive power. The curves and the triangles are shown in the same manner as in Fig. 3.