A low-energy theory for magnetic interactions between electrons in the multi-band Hubbard model in non-equilibrium conditions has been formulated. By introducing a time-dependent electric field it is possible to simulate laser-induced spin dynamics. Expressions for dynamical exchange parameters in terms of non-equilibrium Green's functions and self-energies are obtained via time-dependent dynamical mean-field theory. The analysis shows a new type of magnetic interaction, a so-called "twist exchange", which formally resembles Dzyaloshinskii-Moriya coupling, but is not due to spin-orbit interactions, but is due to an effective three-spin interaction.
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