Multimode cavity magnonics in mumax+: from coherent to dissipative coupling in ferromagnets and antiferromagnets

Abstract

Coherent coupling between microwave cavity photons and magnon excitations enables quantum transduction, magnon-mediated entanglement, and magnon number-resolved detection. Micromagnetic simulation of photon-magnon coupling typically requires either modifying the core solver or implementing a full electromagnetic solver. Here we present a two-tier cavity magnonics extension for mumax+, a GPU-accelerated open-source micromagnetic framework. The first tier consists of CUDA kernels that integrate N cavity-mode ODEs simultaneously with the LLG equation inside the GPU-based RK45 adaptive time-stepper, eliminating per-step GPU-CPU transfers; spatially resolved mode profiles enter both the coupling and the feedback, enabling selective addressing of non-uniform spin-wave modes. The second tier is a lightweight Python co-simulation class that reproduces the same uniform-mode physics through operator-split RK4 integration without recompilation. We validate the implementation with eight benchmark simulations: (i) magnon-polariton anticrossing spectra, (ii) vacuum Rabi oscillations, (iii) the cooperativity phase diagram spanning weak-to-strong coupling regimes, (iv) cavity mode-profile-dependent coupling selection rules, (v) multi-mode polariton hybridization with magnon-mediated cavity-cavity energy transfer, (vi) mode-selective coupling via spatial overlap engineering, (vii) antiferromagnetic magnon-cavity coupling with Neel-vector spectroscopy, and (viii) abnormal anticrossing from dissipative photon-magnon coupling, demonstrating the transition from level repulsion to level attraction.

Figures (12)

• Figure 1: (a) 3D microwave cavity with a ferrimagnetic YIG sphere at the center. A standing-wave RF field (sinusoidal curves) couples to the uniform magnon precession. A static external field $\mathbf{H}$ along $\hat{z}$ sets the magnon frequency $\omega_m = \gamma B_0$ ($B_0 = \mu_0 H$). Microwave signals enter and exit through coupling ports. (b) Energy-level diagram for the two-mode cavity--magnon system. Two cavity modes ($\omega_1$, $\omega_2$) couple to a single magnon mode ($\omega_m$) with strengths $g_1$, $g_2$; dashed arrows denote dissipation ($\kappa_1$, $\kappa_2$, $\gamma$). The hybridized eigenmodes consist of two bright polariton branches and one dark mode $|D\rangle \propto g_2|1\rangle - g_1|2\rangle$ that decouples from the magnon.
• Figure 2: Magnon-polariton anticrossing. (a) Combined spectral weight $|$FFT$(m^{-})|^2 + |$FFT$(a)|^2$ as a function of $B_0$ and frequency. White dashed lines: analytical polariton branches [Eq. \ref{['eq:polariton']}]; cyan dotted lines: uncoupled $\omega_c$ and $\omega_m(B_0)$. (b) Extracted peak frequencies (circles) compared with analytical theory (solid lines). Parameters: $\omega_c/(2\pi) = 5$ GHz, $Q = 5000$, $g/(2\pi) = 50$ MHz.
• Figure 3: Vacuum Rabi oscillations. (a) Photon ($|a|^2$) and magnon ($|m^{-}|^2$) populations versus time for $g/(2\pi) = 20$ MHz ($T_R = 25$ ns). Energy oscillates coherently between the cavity and magnon modes at the Rabi period $T_R = \pi/g$, with gradual decay from finite $\kappa$ and $\alpha$. (b) Rabi period versus coupling strength for $g/(2\pi) = 20$, 50, and 100 MHz. Circles: simulation; line: analytical prediction $T_R = \pi/g$.
• Figure 4: Cooperativity phase diagram. (a) Analytical cooperativity $C(g,\kappa)$ in the $(g,\kappa)$ plane; white dashed line: $C = 1$ boundary. Circles mark the three simulation points. (b) Spectral weight at resonance ($B_0 = B_\mathrm{res}$) for each regime. Strong coupling ($C = 1667$): two resolved polariton peaks separated by $2g/(2\pi) = 100$ MHz. Moderate ($C = 6.7$): two resolved peaks with splitting $21.3$ MHz (theory: $20.0$ MHz). Weak ($C \approx 0$): a single narrow peak with no visible splitting.
• Figure 5: Spatial profiles of three cavity modes on an $8\times 8$ grid. (a) Uniform ($n_x = 0$): spatially constant $u(\mathbf{r}) = 1$. (b) One node ($n_x = 1$): $u(\mathbf{r}) = \cos(\pi x/L_x)$. (c) Two nodes ($n_x = 2$): $u(\mathbf{r}) = \cos(2\pi x/L_x)$. The overlap integral $\langle u \rangle$ with the uniform Kittel magnon is 1.0 for (a) and vanishes for (b,c) due to cancellation of positive and negative lobes [Eq. \ref{['eq:overlap']}].