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.