Effect of Spin-Orbit Interaction in Spin-Triplet Superconductor: Structure of $\mathbf{d}$-vector and Anomalous ${}^{17}$O-NQR Relaxation in Sr${}_2$RuO${}_4$

Abstract

Supposing the spin-triplet superconducting state of Sr${}_2$RuO${}_4$, the spin-orbit (SO) coupling associated with relative motion in Cooper pairs is calculated by extending the method for the dipole-dipole coupling given by Leggett in the superfluid ${}^3$He. It is shown that the SO coupling works only in the equal-spin pairing (ESP) state to make the pair angular momentum $\hslash \vec{L}$ and the pair spin angular momentum $\mathrm{i}\vec{d}\times {\vec{d}}^{\ast }$ parallel with each other. The SO coupling gives rise to the internal Josephson effect in a chiral ESP state as in superfluid A-phase of ${}^3$He with a help of an additional anisotropy arising from SO coupling of atomic origin which works to direct the {\bf d}-vector into $ab$-plane. This resolves the problem of the anomalous relaxation of ${}^{17}$O-NQR and the structure of {\bf d}-vector in Sr${}_2$RuO${}_4$.

Accepted for publication in J. Phys. Soc. Jpn. vol.79 (2010), No.2 (February issue); 18 pages, 2 figures