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

Source: [Effect of Spin-Orbit Interaction in Spin-Triplet Superconductor: Structure of ${\\bf d}$-vector and Anomalous $^{17}$O-NQR Relaxation in Sr$\_2$RuO$\_4$](<https://www.sota2.com/research/paper/68fa2f341e209131ce869caf>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T17:23:44.915Z

Authors: K. Miyake

Published: 2010-01-18T10:11:38.000Z

## 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 $\\hbar{\\vec L}$ and the pair spin angular momentum ${\\rm i}{\\vec d}\\times{\\vec d}^{\*}$ 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$\_4$.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1001.2999>)

[PDF](<https://arxiv.org/pdf/1001.2999.pdf>)