Direct imaging of long-range ferromagnetic and antiferromagnetic order in a dipolar metamaterial

Einar Digernes,Ambjørn D Bang,Anders Strømberg,Erik Folven,Jostein K Grepstad,Fredrik K Olsen,Elke Arenholz,Sam D Slöetjes,Rajesh V Chopdekar

doi:10.1103/physrevresearch.2.013222

Abstract

This paper demonstrates stabilization of long-range ferro- and antiferromagnetic order in a magnetic metamaterial. In arrays of dipolar-coupled ferromagnetic nanodisks, ferromagnetic order is observed when the disks are arranged in a hexagonal lattice, whereas antiferromagnetic order prevails for the square lattice.

Highlights

Luttinger and Tisza predicted that the magnetic order in a lattice of point dipoles is governed by the symmetry of the dipole lattice [1], suggesting a novel mechanism for ferromagnetic (FM) order not based on exchange interactions
The XMCD-PEEM images reveal FM ordering in the hexagonal lattice [Fig. 1(c)] and AF ordering in the square lattice [Fig. 1(d)]
The results demonstrate that magnetostatic coupling supports long-range order in these magnetic metamaterials

Summary

Introduction

Luttinger and Tisza predicted that the magnetic order in a lattice of point dipoles is governed by the symmetry of the dipole lattice [1], suggesting a novel mechanism for ferromagnetic (FM) order not based on exchange interactions. Magnetic elements below a critical size will be in a monodomain state, and the magnetization of each element can be described in terms of a single macrospin [9,10]. The ground-state ordering of these macrospins is determined by the geometric arrangement of the elements [11] as well as their shape. The total magnetization of a monodomain disk can be approximated as a point dipole. The predicted ground state is twofold-degenerate, with stripe-ordered antiferromagnetic

Methods

Results

Conclusion