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

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

2004-07-07

arxiv.org/abs/cond-mat/0407171v2

Phys. Rev. B 70, 134424 (2004)

Physics

Condensed Matter

Statistical Mechanics

16 pages, 8 figures, missing figures added

Scientific paper

10.1103/PhysRevB.70.134424

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 <(S^x)^2>, <(S^y)^2> and <(S^z)^2> 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.

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