期刊
ANNALS OF PHYSICS
卷 360, 期 -, 页码 61-97出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2015.05.002
关键词
Strongly correlated systems; Anisotropic exchange interaction; Dzyaloshinskii Moriya interaction; Green's functions; Orbital magnetism
资金
- European Union Seventh Framework Programme [281043]
- Deutsche Forschungsge-meinschaft [SFB-668]
We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin rotations in the two systems are equivalent up to second order in the rotation angles, when the electronic system is in a symmetry-broken phase. This allows to determine the parameters of relativistic and nonrelativistic magnetic interactions in the effective spin model in terms of equilibrium Green's functions of the electronic model. The Hamiltonian of the electronic system includes, in addition to the non-relativistic part, relativistic single-particle terms such as the Zeeman coupling to an external magnetic field, spin orbit coupling, and arbitrary magnetic anisotropies; the orbital degrees of freedom of the electrons are explicitly taken into account. We determine the complete relativistic exchange tensors, accounting for anisotropic exchange, Dzyaloshinskii-Moriya interactions, as well as additional non-diagonal symmetric terms (which may include-dipole dipole interaction). The expressions of all these magnetic interactions are determined in a unified framework, including previously disregarded features such as the vertices of two-particle Green's functions and non-local self-energies. We do not assume any smallness in spin-orbit coupling, so our treatment is in this sense exact. Finally, we show how to distinguish and address separately the spin, orbital and spin-orbital contributions to magnetism, providing expressions that can be computed within a tightbinding Dynamical Mean Field Theory. (C) 2015 Elsevier Inc. All rights reserved.
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