In-plane dipole coupling anisotropy of a square ferromagnetic Heisenberg monolayer

TL;DR

This paper investigates how dipole interactions induce in-plane anisotropy in a square ferromagnetic monolayer, showing it increases with temperature and is analyzed using mean field and Green's function methods.

Contribution

It provides a detailed calculation of dipole-induced anisotropy in a ferromagnetic monolayer using advanced theoretical approaches, highlighting temperature dependence and quantum effects.

Findings

Anisotropy increases with temperature, peaking near Curie temperature.

At zero temperature, the system remains nearly isotropic.

Dipole-induced anisotropy is small compared to other effects.

Abstract

In this study we calculate the dipole-coupling-induced quartic in-plane anisotropy of a square ferromagnetic Heisenberg monolayer. This anisotropy increases with an increasing temperature, reaching its maximum value close to the Curie temperature of the system. At T=0 the system is isotropic, besides a small remaining anisotropy due to the zero-point motion of quantum mechanical spins. The reason for the dipole-coupling-induced anisotropy is the disturbance of the square spin lattice due to thermal fluctuations ('order-by-disorder' effect). For usual ferromagnets its strength is small as compared to other anisotropic contributions, and decreases by application of an external magnetic field. The results are obtained from a Heisenberg Hamiltonian by application of a mean field approach for a spin cluster, as well as from a many-body Green's function theory within the Tyablikov-decoupling (RPA).