Strong Spin-Orbit Coupling Effects on the Fermi Surface ofSr2RuO4andSr2RhO4

We present a first-principles study of spin-orbit coupling effects on the Fermi surface of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$. For nearly degenerate bands, spin-orbit coupling leads to a dramatic change of the Fermi surface with respect to nonrelativistic calculations; as evidenced by the comparison with experiments on ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$, it cannot be disregarded. For ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, the Fermi surface modifications are more subtle but equally dramatic in the detail: Spin-orbit coupling induces a strong momentum dependence, normal to the ${\mathrm{RuO}}_2$ planes, for both orbital and spin character of the low-energy electronic states. These findings have profound implications for the understanding of unconventional superconductivity in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.