Many-body Green's function theory of Heisenberg films

TL;DR

This paper reviews the application of many-body Green's function theory to Heisenberg films, detailing the formalism, various decoupling schemes, and phenomena like magnetization reorientation, while discussing extensions and limitations of the approach.

Contribution

It provides a comprehensive derivation of Green's function equations for Heisenberg films and applies them to various magnetic configurations with detailed analysis of magnetization behavior.

Findings

Consistent description of ferromagnetic and antiferromagnetic films

Analysis of magnetization reorientation with temperature and thickness

Extension of theory beyond RPA and discussion of limitations

Abstract

The treatment of Heisenberg films with many-body Green's function theory (GFT) is reviewed. The basic equations of GFT are derived in sufficient detail so that the rest of the paper can be understood without having to consult further literature. The main part of the paper is concerned with applications of the formalism to ferromagnetic, antiferromagnetic and coupled ferromagnetic-antiferromagnetic Heisenberg films based on a generalized Tyablikov (RPA) decoupling of the exchange interaction and exchange anisotropy terms and an Anderson-Callen decoupling for a weak single-ion anisotropy. We not only give a consistent description of our own work but also refer extensively to related investigations. We discuss in particular the reorientation of the magnetization as a function of the temperature and film thickness. If the single-ion anisotropy is strong, it can be treated exactly by going to higher-order Green's functions. We also discuss the extension of the theory beyond RPA. Finally the limitations of GFT is pointed out.