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Description:
In this work, we study the effects of spin-orbit and Coulomb anisotropy on the electronic and magnetic properties of the Mott insulator Ca$_{2}$ RuO$_{4}$. We use the local-density approximation + dynamical mean-field approach and spin-wave theory. We show that, contrary to a recent proposal, the Mott metal-insulator transition is not induced by the spin-orbit interaction. We confirm that, instead, it is mainly driven by the change in structure from long to short c-axis layered perovskite. We show that the magnetic ordering and the anisotropic Coulomb interactions play a small role in determining the the size of the gap. The spin-orbit interaction turns out to be essential for describing the magnetic properties. It not only results in a spin-wave gap, but it also enlarges significantly the magnon bandwidth.