Modelling long-range interactions in multiscale simulations of ferromagnetic materials

Doghonay Arjmand,Mikhail Poluektov,Gunilla Kreiss

doi:10.1007/s10444-020-09747-5

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.

Highlights

There are multiple ways of describing the physics of magnetic materials
This paper demonstrates a way of incorporating the long-range dipole-dipole interactions between the atomistic spin magnetic moments into the existing atomisticcontinuum 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 the continuum demagnetising field to the atomistic solution. This approximation relies on the atomistic expression for the magnetisation field converging to the continuum expression when the interatomic spacing approaches zero

Summary

Introduction

There are multiple ways of describing the physics of magnetic materials. The spin and orbital movements of electrons are modelled by electronic structure calculations. The rapid subatomic variations are Extended author information available on the last page of the article. Adv Comput Math (2020) 46: 2 averaged out and the interaction of spin magnetic moments of individual atoms is simulated, often by using parametrised interactions obtained from a smaller scale. The interaction of atomic spins is described by a system of coupled non-linear ordinary differential equations (ODEs). Non-linear partial differential equations (PDEs) are used to describe the evolution of volume-averaged quantities. The choice of a computational approach depends on the scale of application, and on the required computational efficiency. The atomistic models, relatively accurate, are prohibitively expensive to solve, whereas continuum models are computationally efficient but may lack certain accuracy

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