Many-body Green's function theory of Heisenberg films

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.Comment: 124 pages, 32 figures, accepted by Physics Report

Parallel Susceptibility of Thin Ferromagnetic Films within Many-Body Green's Function Theory

“…For the terms stemming from the single-ion anisotropy we have chosen the Anderson-Callen decoupling procedure [7]. Using the eigenvector method (EVM) described, for example in [8], after Fourier transform to two-dimensional momentum space q (a wave vector in the planes parallel to the film surface), L coupled equations of motion for GFs G (l) νµ (q, ω) of layer labeled by µ can be written in the matrix form as…”

Heisenberg Model of a Ferromagnetic Monolayer Deposited on a Non-Magnetic Bulk Substrate

“…To obtain the magnetization S z of the spin S = 1 2 monolayer in the mean field theory (MFT) approximation, we use the many-body Green functions presented in [9]. Following a couple of calculations, we get the equation for the magnetization in the form…”

“…2. What is more, using the fact that the MFT approximation violates the Mermin-Wagner theorem [9,10], we can calculate the Curie temperature of the monolayer. We expand the left hand side of (16) for small S z and self-consistently evaluate the Curie temperature from T C = J eff (T C ) for different substrate's Debye temperatures Θ and lattice constants a 0 .…”

Behaviour of Thin Magnetic Films at Low Temperatures

“…In the last time interest for magnetic problems increases, [21][22][23][24][25][26][27][28][29][30] but nowhere the problem of broken symmetry structures is not in the first plan.…”

“…The inclusion of (58) into (44) Spectral intensity of this Green's function is given by the general formula (29), wherefrom it follows:…”