Conservation laws for interacting magnetic nanoparticles at finite temperature

We establish a general Langevin dynamics model of interacting, single-domain magnetic nanoparticles (MNPs) in liquid suspension at finite temperature. The model couples the Landau-Lifshitz-Gilbert equation for the moment dynamics with the mechanical rotation and translation of the particles. Within this model, we derive expressions for the instantaneous transfer of energy, linear, and angular momentum between the particles and with the environment. We demonstrate by numerical tests that all conserved quantities are fully accounted for, thus validating the model and the transfer expressions. The energy transfer expressions derived here are also useful analysis tools to decompose the instantaneous, nonequilibrium power loss at each MNP into different loss channels. To demonstrate the model capabilities, we analyze simulations of MNP collisions and high-frequency hysteresis in terms of power and energy contributions.