Floquet engineering of Mott insulators with strong spin-orbit coupling

We propose a method for controlling the exchange interactions of Mott insulators with strong spin-orbit coupling. We consider a multiorbital system with strong spin-orbit coupling and a circularly polarized light field and derive its effective Hamiltonian in the strong-interaction limit. Applying this theory to a minimal model of alpha-RuCl3, we show that the magnitudes and signs of three exchange interactions, J, K, and Gamma, can be changed simultaneously. Then, considering another case in which one of the hopping integrals has a different value and the other parameters are the same as those for alpha-RuCl3, we show that the Heisenberg interaction J can be made much smaller than the anisotropic exchange interactions K and Gamma.