Strong Spin-Orbit Coupling Effects on the Fermi Surface of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$

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 ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

Figure 1

(a),(b) LDA Fermi surface of ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$ and (c),(d) ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$; (e)–(h) $k_z$ electronic dispersion for the ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ cuts highlighted in (c),(d) by solid green bars. Calculations were performed without SOC (top panels) and with SOC (bottom panels). The gray-scale ARPES $E_F$-intensity maps are here reproduced from (a),(b) Kim et al. [11] and (c),(d) Damascelli et al. [5].

Figure 2

LDA (top) and $\mathrm{LDA}+\mathrm{SOC}$ (bottom) band dispersion of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ (left) and ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$ (right). (e),(f) Enlarged view of the marked $E_F$ regions in (c),(d).