On the spontaneous magnetization of two-dimensional ferromagnets.

Authors

  • Danilo Pescia Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland.
  • Alessandro Vindigni Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich, Switzerland.

DOI:

https://doi.org/10.4279/pip.160001

Keywords:

Two-dimensional magnetism, Magnetic domains

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 very 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.

The free energy F as a function of M . a: The graph for an infinite ferromagnetic body with sponta- neous magnetization has a flat portion between ±M s below the Curie temperature (see Ref.[1]). b: For a fi- nite ferromagnetic body, the free energy has minima at ±M s . c: A theorem by Griffiths [4] implies that the free energy has a minimum at M = 0 at any temperature.

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Published

2024-09-18

How to Cite

Pescia, D., & Vindigni, A. (2024). On the spontaneous magnetization of two-dimensional ferromagnets. Papers in Physics, 16, 160001. https://doi.org/10.4279/pip.160001

Issue

Section

Open Review Articles