A micromagnetic model with bidirectional magneto-thermal coupling
Most conventional micromagnetic frameworks in spin caloritronics rely on a unidirectional coupling approximation, wherein thermal fluctuations drive magnetization dynamics while the feedback of magnetic dissipation onto the thermal reservoir is neglected. Here, we establish a rigorously self-consistent bidirectional magneto-thermal coupling model by integrating the stochastic Landau-Lifshitz-Gilbert (sLLG) equation with a generalized heat transfer equation. In this closed-loop framework, the local temperature acts as a dynamical variable, and the damping-induced dissipation alongside stochastic work dynamically feeds back into the thermal bath as localized heat sources. Utilizing Ito stochastic calculus, we analytically prove that this coupled system strictly obeys the first law of thermodynamics and spontaneously recovers the correct Boltzmann statistics at equilibrium. Spatially resolved micromagnetic simulations further validate the energy exchange mechanism, capturing the finite-bath temperature reduction induced by spatial variation of magnetic moments and the modified density of states under exchange interactions. This bidirectional framework provides a robust microscopic foundation for investigating complex nonequilibrium magneto-thermal dynamics, such as the unidirectional spin-wave heat conveyer effect, paving the way for advanced spin-caloritronic applications.