Spin and orbital exchange interactions from Dynamical Mean Field Theory

•We give formulas for the exchange interaction tensor in strongly correlated systems.•Interactions are written in terms of electronic Green's functions and self-energies.•The method is suitable for a Dynamical Mean Field Theory implementation.•No quenching of the orbital magnetic moments is assumed.•Spin and orbital contributions to magnetism can be computed separately.

We derive a set of equations expressing the parameters of the magnetic interactions characterizing a strongly correlated electronic system in terms of single-electron Green's functions and self-energies. This allows to establish a mapping between the initial electronic system and a spin model including up to quadratic interactions between the effective spins, with a general interaction (exchange) tensor that accounts for anisotropic exchange, Dzyaloshinskii–Moriya interaction and other symmetric terms such as dipole–dipole interaction. We present the formulas in a format that can be used for computations via Dynamical Mean Field Theory algorithms.