In this master project, we investigate a non-equilibrium Dynamical Mean Field Theory (DMFT) model of t2g orbitals with variable spin-orbit coupling.
DMFT is a well-known method used to account for the interplay of spin, charge and orbital momen- tum in materials with an open d or f sub-shell. The terahertz dynamics of such material is currently an important area of research.

In their 2025 paper, Salikhov et al. [15] identified a third harmonic generation (THG) in transition metal films, as well as a filling-dependent phase shift in that THG. Furthermore, they suggest that the phase shift might have a spintronic origin, since the THG is correlated to the Spin Hall Conductivity. In this work, we try to simulate the results of Salikhov et al. using non-equilibrium DMFT.

We first introduce the key concepts and equations behind DMFT, and discuss the spin-orbit coupling approach implemented in the numerical model. We do not discuss the non-equilibrium DMFT tech- niques used in the model, which would be beyond the scope of the master project.
Finally, we present our results and compare them with those from Salikhov et al.

Our simulations give rise to a THG and an odd-harmonics behavior of the current frequency spectrum, which depends on the spin-orbit coupling strength, and seems to be correlated with the emergence of a gap in the density of state (DOS). A continuous π/2 phase shift as a function of spin-orbit coupling was also found. However, no discontinuous π phase-shift as a function of the filling d could be obtained.

The emergence of the THG is encouraging, but further work on the model is necessary to draw any hard conclusions.