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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

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Articles you may be interested inDynamics of the C ( D 1 ) + D 2 reaction: A comparison of crossed molecular-beam experiments with quasiclassical trajectory and accurate statistical calculationsThe O ( 1 D)+ H 2 reaction at 56 meV collision energy: A comparison between quantum mechanical, quasiclassical trajectory, and crossed beam results Probing the effect of the H 2 rotational state in O ( 1 D)+ H 2 →OH+H : Theoretical dynamics including nonadiabatic effects and a crossed molecular beam studyThe dynamics of the reactions O( 1 D)ϩH 2 →OHϩH and O( 1 D)ϩD 2 →ODϩD have been investigated in crossed molecular beam experiments with mass spectrometric detection at the collision energies of 1.9 and 3.0 kcal/mol, and 5.3 kcal/mol, respectively. From OH͑OD͒ product laboratory angular and velocity distribution measurements, center-of-mass product translational energy and angular distributions were derived. The angular distributions are nearly backwardforward symmetric with a favored backward peaking which increases with collision energy. About 30% of the total available energy is found to be channeled into product translational energy. The results are compared with quasiclassical trajectory calculations on a DIM ͑diatomic-in-molecules͒ potential energy surface. Related experimental and theoretical works are noted. Insertion via the 1 1 AЈ ground state potential energy surface is the predominant mechanism, but the role of a second competitive abstraction micromechanism which should evolve on one of ͑or both͒ the first two excited surfaces 1 AЉ and 2 1 AЈ is called into play at all the investigated energies to account for the discrepancy between theoretical predictions and experimental results.

The stochastic series expansion quantum Monte Carlo method is used to study thin ferromagnetic films, described by a Heisenberg model including local anisotropies. The magnetization curve is calculated, and the results compared to Schwinger boson and many-body Green's function calculations. A transverse field is introduced in order to study the reorientation effect, in which the magnetization changes from out-of-plane to in-plane. Since the approximate theoretical approaches above differ significantly from each other, and the Monte Carlo method is free of systematic errors, the calculation provides an unbiased check of the approximate treatments. By studying quantum spin models with local anisotropies, varying spin size, and a transverse field, we also demonstrate the general applicability of the recent cluster-loop formulation of the stochastic series expansion quantum Monte Carlo method.Comment: 9 pages, 12 figure