Minimum and maximum energy for crystals of magnetic dipoles

Josep Batle,Orion Ciftja

doi:10.1038/s41598-020-76029-x

Josep Batle, Orion Ciftja

Open Access

https://doi.org/10.1038/s41598-020-76029-x

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Abstract

Properties of many magnetic materials consisting of dipoles depend crucially on the nature of the dipole–dipole interaction. In the present work, we study systems of magnetic dipoles where the dipoles are arranged on various types of one-dimensional, two-dimensional and three-dimensional lattices. It is assumed that we are in the regime of strong dipole moments where a classical treatment is possible. We combine a new classical numerical approach in conjuncture with an ansatz for an energy decomposition method to study the energy stability of various magnetic configurations at zero temperature for systems of dipoles ranging from small to an infinite number of particles. A careful analysis of the data in the bulk limit allows us to identify very accurate minimum and maximum energy bounds as well as ground state configurations corresponding to various types of lattices. The results suggest stabilization of a particularly interesting ground state configuration consisting of three embedded spirals for the case of a two-dimensional hexagonal lattice.

Highlights

Properties of many magnetic materials consisting of dipoles depend crucially on the nature of the dipole–dipole interaction
Formation of a classical crystal of dipolar particles is expected at those temperatures where the thermal energy is weak relative to the dominant characteristic dipolar energy
The behavior of the system under these conditions is solely dominated by dipolar interactions

Summary

Introduction

Properties of many magnetic materials consisting of dipoles depend crucially on the nature of the dipole–dipole interaction. The dipole–dipole interaction potential energy between any two point dipoles, mu and mv localized, respectively, at two different sites ru and rv ( ru = rv) of a simple 2D square lattice can be written as: Eu,v μ0 4π m u · m v ru3v

Results

Conclusion