Non-equilibrium magnetic interactions in strongly correlated systems

• We develop a theory for magnetism of strongly correlated systems out of equilibrium.
• Our theory is suitable for laser-induced ultrafast magnetization dynamics.
• We write time-dependent exchange parameters in terms of electronic Green functions.
• We find a new magnetic interaction, a “twist exchange”.
• We give general expressions for magnetic noise in itinerant-electron systems.

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii–Moriya coupling, but is not due to spin–orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.