Many-body Green's function theory for thin ferromagnetic anisotropic Heisenberg films: treatment of the exchange anisotropy

The many-body Green's function theory developed in our previous work for treating the reorientation of the magnetization of thin ferromagnetic films is extended to include the exchange anisotropy. This leads to additional momentum dependencies which require some non-trivial changes in the formalism. The theory is developed for arbitrary spin values S and for multilayers. The effects of the exchange anisotropy and the single-ion anisotropy, which was treated in our earlier work, on the magnetic properties of thin ferromagnetic films are compared.Comment: 24 pages, 7 figures, accepted for publication in Eur. Phys. J.

Anisotropic susceptibilities of thin ferromagnetic films within many-body Green's function theory

Transverse and parallel static susceptibilities of in-plane uniaxial anisotropic ferromagnetic films are calculated within many-body Green's function theory on the basis of an Heisenberg model. The importance of collective magnetic excitations in particular in the paramagnetic regime are stressed by comparing with mean field calculations. The paper generalizes the work of Jensen et al. [1] to the multilayer case and to spins with S>1/2.Comment: 10 pages, 8 figures, submitted to Phys. Rev.

Many-body Green's function theory of Heisenberg films

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

Many-body Green's function theory for thin ferromagnetic films: exact treatment of the single-ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many-body Green's funtion theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external field, a second- and fourth-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. The single-ion anisotropy terms can be treated exactly by introducing higher-order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest-order Green's functions. RPA-like approximations are used to decouple the exchange terms in both the low-order and higher-order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S=1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.Comment: 23 pages, 5 figure

Field-induced magnetic reorientation and effective anisotropy of a ferromagnetic monolayer within spin wave theory

The reorientation of the magnetization of a ferromagnetic monolayer is calculated with the help of many-body Green's function theory. This allows, in contrast to other spin wave theories, a satisfactory calculation of magnetic properties over the entire temperature range of interest since interactions between spin waves are taken into account. A Heisenberg Hamiltonian plus a second-order uniaxial single-ion anisotropy and an external magnetic field is treated by the Tyablikov (Random Phase Approximation: RPA) decoupling of the exchange interaction term and the Anderson-Callen decoupling of the anisotropy term. The orientation of the magnetization is determined by the spin components \la S^\alpha\ra ($\alpha=x,y,z$), which are calculated with the help of the spectral theorem. The knowledge of the orientation angle $\Theta_0$ allows a non-perturbative determination of the temperature dependence of the effective second-order anisotropy coefficient. Results for the Green's function theory are compared with those obtained with mean-field theory (MFT). We find significant differences between these approaches.Comment: to appear in Europ.J.Phys.B, 13 pages, 9 figure

Single-ion versus exchange anisotropy in calculating anisotropic susceptibilities of thin ferromagnetic Heisenberg films within many-body Green's function theory

We compare transverse and parallel static susceptibilities of in-plane uniaxial anisotropic ferromagnetic Heisenberg films calculated in the framework of many-body Green's function theory using single-ion anisotropies with the previously investigated case of exchange anisotropies. On the basis of the calculated observables (easy and hard axes magnetizations and susceptibilities) no significant differences are found, i. e. it is not possible to propose an experiment that might decide which kind of anisotropy is acting in an actual ferromagnetic film.Comment: 16 pages, 8 figure

Many-body Green's function theory of ferromagnetic Heisenberg systems with single-ion anisotropies in more than one direction

The behaviour of ferromagnetic systems with single-ion anisotropies in more than one direction is investigated with many-body Green's function theory generalizing earlier work with uniaxial anisotropies only. It turns out to be of advantage to construct Green's functions in terms of the spin operators S^x, S^y and S^z, instead of the commonly used S^+,S^- and S^z operators. The exchange energy terms are decoupled by RPA and the single-ion anisotropy terms by a generalization of the Anderson-Callen decoupling. We stress that in the derivation of the formalism none of the three spatial axes is special, so that one is always able to select a reference direction along which a magnetization component is not zero. Analytical expressions are obtained for all three components of the magnetization and the expectation values , and for any spin quantum number S. The formalism considers both in-plane and out-of-plane anisotropies. Numerical calculations illustrate the behaviour of the magnetization for 3-dimensional and 2-dimensional systems for various parameters. In the 2-dimensional case, the magnetic dipole-dipole coupling is included, and a comparison is made between in-plane and out-of-plane anisotropies.Comment: 16 pages, 8 figures, missing figures adde

The magnetic reorientation transition in thin ferromagnetic films treated by many-body Green's function theory

This contribution describes the reorientation of the magnetization of thin ferromagnetic Heisenberg films as function of the temperature and/or an external field. Working in a rotating frame allows an exact treatment of the single-ion anisotropy when going to higher-order Green's functions. Terms due to the exchange interaction are treated by a generalized Tyablikov (RPA) decoupling.Comment: 9 pages, 2 figure

Fragmentation Phase Transition in Atomic Clusters II - Coulomb Explosion of Metal Clusters -

We discuss the role and the treatment of polarization effects in many-body systems of charged conducting clusters and apply this to the statistical fragmentation of Na-clusters. We see a first order microcanonical phase transition in the fragmentation of $Na^{Z+}_{70}$ for Z=0 to 8. We can distinguish two fragmentation phases, namely evaporation of large particles from a large residue and a complete decay into small fragments only. Charging the cluster shifts the transition to lower excitation energies and forces the transition to disappear for charges higher than Z=8. At very high charges the fragmentation phase transition no longer occurs because the cluster Coulomb-explodes into small fragments even at excitation energy $\epsilon^* = 0$.Comment: 19 text pages +18 *.eps figures, my e-mail adress: [email protected] submitted to Z. Phys.

The spectral theorem of many-body Green's function theory when there are zero eigenvalues of the matrix governing the equations of motion

In using the spectral theorem of many-body Green's function theory in order to relate correlations to commutator Green's functions, it is necessary in the standard procedure to consider the anti-commutator Green's functions as well whenever the matrix governing the equations of motion for the commutator Green's functions has zero eigenvalues. We show that a singular-value decomposition of this matrix allows one to reformulate the problem in terms of a smaller set of Green's functions with an associated matrix having no zero eigenvalues, thus eliminating the need for the anti-commutator Green's functions. The procedure is quite general and easy to apply. It is illustrated for the field-induced reorientation of the magnetization of a ferromagnetic Heisenberg monolayer and it is expected to work for more complicated cases as well.Comment: 4 pages, 1 figure, accepted for publication in Physical Review B (16. May 2003