We present a first-principle study of spin-orbit coupling effects on the Fermi surface of Sr2RuO4 and Sr2RhO4. For nearly degenerate bands, spin-orbit coupling leads to a dramatic change of the Fermi surface with respect to non-relativistic calculati
ons; as evidenced by the comparison with experiments on Sr2RhO4, it cannot be disregarded. For Sr2RuO4, the Fermi surface modifications are more subtle but equally dramatic in the detail: spin-orbit coupling induces a strong momentum dependence, normal to the RuO2 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 Sr2RuO4.
