Effects of magnonic Kerr nonlinearity on magnon-polaritons with a soft-mode

TL;DR

This work addresses how magnonic Kerr nonlinearity affects magnon-polaritons with a soft-mode in easy-axis ferromagnets coupled to a microwave cavity. Using an effective circuit model that remains valid into the nonperturbative strong-coupling (NSC) regime, it analyzes MP dynamics at original mode-crossing points and at the soft-mode critical field. Key findings show that in the typical strong-coupling (SC) regime with $g/\omega_c\approx 0.01$, Kerr nonlinearity drives chaotic and frequency-comb-like behavior at mode crossings, and opens a finite gap in the soft-mode near $H_0 = M_s/2$; however, in NSC with $g/\omega_c \approx 1$, nonlinear effects are largely suppressed, preserving linear spin-wave behavior and enabling robust coupling to soft magnons. The results highlight regime-dependent nonlinear dynamics in cavity magnonics and support the viability of achieving quantum squeezing using soft zero-mode magnons under NSC conditions.

Abstract

We theoretically study the effects of magnonic Kerr nonlinearity on magnon-polaritons (MPs) with a soft-mode in easy-axis ferromagnets coupled to a microwave cavity. Using an effective circuit model capable of describing MPs up to the nonperturbative strong-coupling regime, we show that chaotic and frequency-comb-like behaviors of MPs emerge at the original modes crossing point. Furthermore, we demonstrate that the Kerr nonlinearity induces a finite excitation gap in the soft-mode, particularly in the strong-coupling regime.

Figures (4)

• Figure 1: (a) Effective circuit model of a cavity magnonics system, where ${\bf M}(t)$ represents the uniform magnetization dynamics (magnons) in an easy-axis ferromagnet (FM) and ${\bf H}(t)$ denotes the microwave magnetic field (photons) in the inductor. The equilibrium magnetization is characterized by the angle $\theta_{\infty}$ measured from the $z$ axis. (b) Total magnetic energy $U_{\rm m}$ as a function of the polar angle $\theta$ at $\varphi = 0$ for different values of $H_0/M_{\rm s}$. (c) Eigenfrequencies ($\omega_\pm$) of MPs as a function of the external magnetic field ($\mu_0H_0$) for different ratios of $d_{\rm M}/d$: SC for $d_{\rm M}/d = 0.02$ and NSC for $d_{\rm M}/d = 1$. The critical field $H_{0c} = M_{\rm s}/2$ marks the transition of the equilibrium magnetization position. (d),(e) Phase portraits for (b), where the red line, filled circles, and open circle denote the homoclinic orbit, centers, and saddle point, respectively: (d) $H_0 < H_{0c}$ and (e) $H_0 > H_{0c}$.
• Figure 2: Fourier spectra of (a) magnon and (b) photon dynamics at $H_0 = H_{01}$ for the SC case with $d/d_{\rm M} = 0.02$. (c),(d) Fourier spectra for the NSC case with $d/d_{\rm M} = 1$. Insets show the corresponding phase-space trajectories of the magnon and photon dynamics. Calculations are performed with the initial conditions $h_x(0) = 0.02$ and $m_x(0) = 0$ under ${\bf H}_V(t>0) = {\bf 0}$. The Fourier spectra are obtained from the dynamics in the time window $t = 440$--500 ns.
• Figure 3: Fourier spectra of (a) magnon and (b) photon dynamics at $H_0 = H_{02}$ for the SC case with $d/d_{\rm M} = 0.02$. The Fourier spectrum of $m_z$ is shown in magenta. (c),(d) Fourier spectra for the NSC case with $d/d_{\rm M} = 1$. Insets show the corresponding phase-space trajectories of the magnon and photon dynamics. Calculations are performed under the same conditions as in Fig. \ref{['Fig:H01']}.
• Figure 4: Fourier spectra of (a) magnon and (b) photon dynamics at $H_0 = H_{0c}$ for the SC case with $d/d_{\rm M} = 0.02$. (c),(d) Fourier spectra for the NSC case with $d/d_{\rm M} = 1$. Insets show the corresponding phase-space trajectories of the magnon and photon dynamics. Calculations are performed under the same conditions as in Fig. \ref{['Fig:H01']}.