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

Huai-Yu Wang·Zhen-Hong Dai·P. Fröbrich·P. J. Jensen·P. J. Kuntz
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Abstract

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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BibTeXRIS

Huai-Yu Wang, Zhen-Hong Dai, P. Fröbrich, P. J. Jensen, P. J. Kuntz. 2004-07-08. Many-body Green's function theory of ferromagnetic Heisenberg systems with single-ion anisotropies in more than one direction. https://doi.org/10.1103/physrevb.70.134424

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