  Cavity electromagnonic system, which simultaneously consists of cavities for
photons, magnons (quanta of spin waves), and acoustic phonons, provides an
exciting platform to achieve coherent energy transduction among different
physical systems down to single quantum level. Here we report a dynamical
phase-field model that allows simulating the coupled dynamics of the
electromagnetic waves, magnetization, and strain in 3D multiphase systems. As
examples of application, we computationally demonstrate the excitation of
hybrid magnon-photon modes (magnon polaritons), Floquet-induced magnonic
Aulter-Townes splitting, dynamical energy exchange (Rabi oscillation) and
relative phase control (Ramsey interference) between the two magnon polariton
modes. The simulation results are consistent with analytical calculations based
on Floquet Hamiltonian theory. Simulations are also performed to design a
cavity electro-magno-mechanical system that enables the triple
phonon-magnon-photon resonance, where the resonant excitation of a chiral,
fundamental (n=1) transverse acoustic phonon mode by magnon polaritons is
demonstrated. With the capability to predict coupling strength, dissipation
rates, and temporal evolution of photon/magnon/phonon mode profiles using
fundamental materials parameters as the inputs, the present dynamical
phase-field model represents a valuable computational tool to guide the
fabrication of the cavity electromagnonic system and the design of operating
conditions for applications in quantum sensing, transduction, and
communication.
