Tristability of cavity magnon polaritons

We carry out a theoretical study of the nonlinear behavior of cavity magnon polaritons (CMPs) under strong microwave driving, with two kinds of nonlinearity being involved: either (i) the photon Kerr effect (PKE) and the magnon saturation effect (MSE) or (ii) the magnon Kerr effect (MKE) and the MSE. The effects arising in these two cases are similar for the lower polariton mode of CMPs but opposite for the upper polariton mode. In case (i), the dominant nonlinearity for the upper polariton mode of CMPs changes from the MSE to the PKE as the driving intensity increases, which can lead to two hysteresis loops in opposite directions and hence to tristability. In case (ii), however, the upper polariton mode exhibits only the usual bistability rather than tristability since the MKE is dominated by the MSE. In particular, there is no bistable behavior in the upper polariton mode when the two nonlinearities balance each other. The results of this study provide a possible basis for the practical manipulation and control of information via the double nonlinearities in a cavity-magnon system.

Figure 1

(a) Schematic layout of the cavity-magnon system under study. The FMI sphere is positioned at the center of the microwave cavity, and two isotropic artificial Kerr-type media are placed symmetrically, one on each side of the sphere. “Input” and “Output” represent the incident and transmitted microwave driving fields, respectively. (b) Schematic representation of the interaction between the subsystems. The green arrow represents the PKE induced by the Kerr-type medium with photon Kerr coefficient $K_a$, while the blue arrow represents the coupling between the cavity photon with dissipation rate $\kappa$ and the magnon with dissipation rate $\gamma$. $g$ is the single-spin coupling strength.

Figure 2

(a) Frequency spectra of CMPs versus magnetic field. The vertical dashed red line indicates the resonance between the photon and magnon. (b) Intracavity amplitude ${\left|\alpha \right|}^2$ versus detuning ${\mathrm{\Delta }}_c/2\pi$ at $P_d=1.4\mathrm{mW}$ (without any nonlinearity). (c) and (d) ${\left|\alpha \right|}^2$ in the presence of only PKE (without MSE) at 390.7 and 596.2 mW, respectively. (e) and (f) ${\left|\alpha \right|}^2$ in the presence of only MSE (without PKE) at 194.7 and 250.1 mW, respectively. The green and red arrows indicate forward and backward sweeps, respectively.

Figure 3

(a)–(h) ${\left|\alpha \right|}^2$ versus ${\mathrm{\Delta }}_c/2\pi$ for various $P_d$. The left and right panels are for $K_A=3.5$ and 8 MHz, respectively. The green and red arrows indicate forward and backward sweeps, respectively.

Figure 4

(a) and (b) ${\left|\alpha \right|}^2$ versus $P_d$ for ${\mathrm{\Delta }}_c/2\pi =6.3$ and 9 MHz, respectively. The left and right panels are for $K_A=3.5$ and 8 MHz, respectively. The green and red arrows indicate forward and backward sweeps, respectively.

Figure 5

(a)–(c) ${\left|\alpha \right|}^2$ versus ${\mathrm{\Delta }}_c/2\pi$ for various values of $K_M$.