Anisotropic bulk and planar Heisenberg ferromagnets in uniform, arbitrarily oriented magnetic fields

TL;DR

This paper investigates the magnetic behavior of anisotropic Heisenberg ferromagnets in arbitrary magnetic fields across different dimensions, revealing how anisotropy and dimensionality influence properties like Curie temperature and magnetization.

Contribution

It provides a detailed theoretical analysis of anisotropic ferromagnets under arbitrary magnetic fields using Green's functions, highlighting the effects of anisotropy and dimensionality.

Findings

Spontaneous magnetization absent in 2D easy-plane systems

Magnetic reorientation transitions depend on anisotropy and field orientation

Curie temperature varies with anisotropy and external magnetic field

Abstract

Today, further downscaling of mobile electronic devices poses serious problems, such as energy consumption and local heat dissipation. In this context, spin wave majority gates made of very thin ferromagnetic films may offer a viable alternative. However, similar downscaling of magnetic thin films eventually enforces the latter to operate as quasi-two dimensional magnets, the magnetic properties of which are not yet fully understood, especially those related to anisotropies and external magnetic fields in arbitrary directions. To this end, we have investigated the behaviour of an easy-plane and easy-axis anisotropic ferromagnet -- both in two and three dimensions -- subjected to a uniform magnetic field, applied along an arbitrary direction. In this paper, a spin-1/2 Heisenberg Hamiltonian with anisotropic exchange interactions is solved using double-time temperature-dependent Green's functions and the Tyablikov decoupling approximation. We determine various magnetic properties such as the Curie temperature and the magnetization as a function of temperature and the applied magnetic field, discussing the impact of the system's dimensionality and the type of anisotropy. The magnetic reorientation transition taking place in anisotropic Heisenberg ferromagnets is studied in detail. Importantly, spontaneous magnetization is found to be absent for easy-plane two-dimensional spin systems with short range interactions.