Modelling long-range interactions in multiscale simulations of ferromagnetic materials

Abstract

Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic approach handles the dynamics of spin magnetic moments of individual atoms, while the continuum approximations operate with volumeaveraged quantities, such as magnetisation. One of the challenges for multiscale models in relation to physics of ferromagnets is the existence of the long-range dipole-dipole interactions between spins. The aim of the present paper is to demonstrate a way of including these interactions into existing atomistic-continuum coupling methods based on the partitioned-domain and the upscaling strategies. This is achieved by modelling the demagnetising field exclusively at the continuum level and coupling it to both scales. Such an approach relies on the atomistic expression for the magnetisation field converging to the continuum expression when the interatomic spacing approaches zero, which is demonstrated in this paper.

A Finite Element Based Heterogeneous Multiscale Method for the Landau-Lifshitz Equation

“…This is due to the fact that the magnetization vectors in separate microscopic domains need to communicate with each other, which is computationally expensive and does not serve the idea of multiscale modeling. We also refer to [11] for a recent article on modeling the long-range in a different way, where the microscopic models are restricted by the macroscopic demagnetization field. In principle, both approaches use the macroscopic description of demagnetization field, but in our approach, the demagnetization field is explicitly expressed in the macro model, whereas in [11] it's effect is implicitly upscaled to the macro model.…”

“…We also refer to [11] for a recent article on modeling the long-range in a different way, where the microscopic models are restricted by the macroscopic demagnetization field. In principle, both approaches use the macroscopic description of demagnetization field, but in our approach, the demagnetization field is explicitly expressed in the macro model, whereas in [11] it's effect is implicitly upscaled to the macro model.…”