On the spontaneous magnetization of two-dimensional ferromagnets

TL;DR

This paper investigates the conditions under which two-dimensional ferromagnetic materials can exhibit spontaneous magnetization, considering the effects of dipole interactions and finite size, and predicts a phase transition in thin films.

Contribution

It extends the understanding of ferromagnetism in two-dimensional systems by analyzing the influence of shape, size, and dipole interactions on spontaneous magnetization.

Findings

Perpendicular slabs do not exhibit spontaneous magnetization due to domain formation.

In-plane magnetized slabs can have spontaneous magnetization below a critical thickness.

A phase transition to a multi-domain state occurs at the critical thickness.

Abstract

Ferromagnetism is typically discussed in terms of the exchange interaction and magnetic anisotropies. Yet real samples are inevitably affected by the magnetostatic dipole-dipole interaction. Because of this interaction, a theorem (R.B. Griffiths, Free Energy of interacting magnetic dipoles, Phys. Rev. 176, 655 (1968)) forbids a spontaneous magnetization in, nota bene, three-dimensional bodies. Here we discuss perpendicularly and in-plane magnetized ferromagnetic bodies in the shape of a slab of finite thickness. In perpendicularly magnetized slabs, magnetic domains are energetically favored when the lateral size is sufficiently large, i.e. there is no spontaneous magnetization. For in-plane magnetization, instead, spontaneous magnetization is possible below a critical thickness which, in real thin films, could be as small as few monolayers. At this critical thickness, we predict a genuine phase transition to a multi-domain state. These results have implications for two-dimensional ferromagnetism.