# Modelling long-range interactions in multiscale simulations of ferromagnetic materials

## TL;DR

This paper introduces a multiscale modelling approach for ferromagnetic materials that effectively incorporates long-range dipole-dipole interactions by modeling the demagnetising field at the continuum level and coupling it with atomistic and continuum models.

## Contribution

It presents a novel method to include long-range interactions in atomistic-continuum multiscale models of ferromagnets by modeling the demagnetising field at the continuum level.

## Key findings

- The atomistic magnetisation converges to the continuum magnetisation as interatomic spacing decreases.
- The proposed coupling method accurately captures long-range dipole interactions.
- The approach enhances 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 volume-averaged 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.