Bistability of Cavity Magnon Polaritons

We report the first observation of the magnon-polariton bistability in a cavity magnonics system consisting of cavity photons strongly interacting with the magnons in a small yttrium iron garnet (YIG) sphere. The bistable behaviors emerged as sharp frequency switchings of the cavity magnon polaritons (CMPs) and related to the transition between states with large and small numbers of polaritons. In our experiment, we align, respectively, the [100] and [110] crystallographic axes of the YIG sphere parallel to the static magnetic field and find very different bistable behaviors (e.g., clockwise and counter-clockwise hysteresis loops) in these two cases. The experimental results are well fitted and explained as being due to the Kerr nonlinearity with either a positive or negative coefficient. Moreover, when the magnetic field is tuned away from the anticrossing point of CMPs, we observe simultaneous bistability of both magnons and cavity photons by applying a drive field on the lower branch.

Figure 1

(a) Schematic diagram of the experimental setup. The 3D cavity, with a small YIG sphere embedded, is placed in the static magnetic field $B_0$ generated by an electromagnet. Ports 1 and 2 of the cavity, connected to a vector network analyzer (VNA), are used for transmission spectroscopy and port 3, connected to a microwave (MW) source, is for driving the YIG sphere. At the bottom, the magnetic-field distribution of the ${\mathrm{TE}}_{102}$ mode is magnified for clarity. The small YIG sphere is placed beside a circular-loop antenna and located at the magnetic-field antinode of the ${\mathrm{TE}}_{102}$ mode. (b) Transmission spectrum of the CMPs measured versus the magnet coil current (i.e., the static magnetic field) and the frequency of the probe field. Two vertical dashed lines indicate, respectively, the resonance and the very off-resonance points at which we show the CMP bistability.

Figure 2

(a) ${\mathrm{\Delta }}_{\mathrm{LP}}/2\pi$ versus $P_d$ when ${\delta }_{\mathrm{LP}}/2\pi =-14.1$, $-12.1$, and $-10.1\mathrm{MHz}$. (b) ${\mathrm{\Delta }}_{\mathrm{LP}}/2\pi$ versus ${\delta }_{\mathrm{LP}}/2\pi$ when $P_d=25$, 23, and 21 dBm. The black circle (blue triangle) dots are the forward (backward)-scanning results. The red dashed curves are theoretical results obtained using Eq. (2), with ${\gamma }_{\mathrm{LP}}/2\pi =({\gamma }_m+\kappa )/4\pi =10.65\mathrm{MHz}$. In (a), the characteristic constant $c/(2\pi {)}^3$ is fitted to be 3.15, 3.55, and $3.82{\mathrm{MHz}}^3/\mathrm{mW}$ for curves from top to bottom. In (b), $c/(2\pi {)}^3$ is fitted to be 1.85, 2.52, and $3.22{\mathrm{MHz}}^3/\mathrm{mW}$ for curves from top to bottom. The [100] crystallographic axis of the YIG sphere is aligned parallel to the static magnetic field $B_0$ and the magnons are in resonance with the cavity mode ${\mathrm{TE}}_{102}$.

Figure 3

(a) ${\mathrm{\Delta }}_{\mathrm{LP}}/2\pi$ versus $P_d$ when ${\delta }_{\mathrm{LP}}/2\pi =17.2$, 13.2, and 9.2 MHz. (b) ${\mathrm{\Delta }}_{\mathrm{LP}}/2\pi$ versus ${\delta }_{\mathrm{LP}}/2\pi$ when $P_d=25$, 23, and 21 dBm. The black circle (blue triangle) dots are the forward (backward)-scanning results. The red dashed curves are theoretical results obtained using Eq. (2), with ${\gamma }_{\mathrm{LP}}/2\pi =10.65\mathrm{MHz}$. In (a), $c/(2\pi {)}^3$ is fitted to be $-4$, $-3.5$, and $-3.1{\mathrm{MHz}}^3/\mathrm{mW}$ for curves from top to bottom. In (b), $c/(2\pi {)}^3$ is fitted to be $-3.01$, $-3.46$, and $-3.6{\mathrm{MHz}}^3/\mathrm{mW}$ for curves from top to bottom. The [110] crystallographic axis of the YIG sphere is aligned parallel to $B_0$ and the magnons are in resonance with ${\mathrm{TE}}_{102}$.

Figure 4

(a) ${\mathrm{\Delta }}_{\mathrm{LP}}/2\pi$ versus $P_d$ when ${\delta }_{\mathrm{LP}}/2\pi =-31.8$, $-27.8$, and $-23.8\mathrm{MHz}$. (b) ${\mathrm{\Delta }}_{\mathrm{LP}}/2\pi$ versus ${\delta }_{\mathrm{LP}}/2\pi$ when $P_d=25$, 23, and 21 dBm. The black circle (green triangle) dots are the forward (backward)-scanning results. The red dashed curves are theoretical results obtained using Eq. (2), with ${\gamma }_{\mathrm{LP}}/2\pi =16.8\mathrm{MHz}$. In (a), $c/(2\pi {)}^3$ is fitted to be 25.2, 25.0, and $25.3{\mathrm{MHz}}^3/\mathrm{mW}$ for curves from top to bottom. In (b), $c/(2\pi {)}^3$ is fitted to be 17.0, 19.0, and $22.7{\mathrm{MHz}}^3/\mathrm{mW}$ for curves from top to bottom. (c) and (d) ${\mathrm{\Delta }}_{\mathrm{UP}}/2\pi$ measured under the same conditions as in (a) and (b), respectively. The black circle (orange triangle) dots are the forward (backward)-scanning results. The blue dashed curves (except for the parts around small dips) are also obtained using Eq. (2), with the fitted ratio $\xi \equiv {\mathrm{\Delta }}_{\mathrm{UP}}/{\mathrm{\Delta }}_{\mathrm{LP}}$ for curves from top to bottom being 0.060, 0.062, and 0.061 in (c) and 0.062, 0.063, and 0.061 in (d). The [100] crystallographic axis of the YIG sphere is aligned parallel to $B_0$ and the magnons are far off resonance with ${\mathrm{TE}}_{102}$. In addition, the small dips in, e.g., (c) and (d) can be fitted by introducing a magnetostatic mode with the negative Kerr coefficient [35].