Spin susceptibility for orbital-singlet Cooper pair in three-dimensional Sr2RuO4 superconductor

Pairing symmetry in superconducting Sr2RuO4 (SRO) has been an unresolved issue in condensed matter physics. To determine the spin structure of the Cooper pair, temperature dependence of the spin susceptibility in the NMR experiments gives us the important information. Spin-triplet/chiral p-wave pairing with time-reversal symmetry breaking (TRS) [(px+ipy)-wave] was believed to the most promising one by the NMR experiments [1]. However, recent NMR experiments have reported the reduction of the spin susceptibility with the in-plane magnetic field [2] below the critical temperature Tc. These experiments seem to be inconsistent with spin-triplet/chiral p-wave where d-vector is aligned along the c-axis of SRO.
Since experimental signatures of a two-component superconducting order parameter in SRO were observed [3], several theoretical studies are focusing on the two-component order parameter with TRS breaking: the accidentally degenerated pairing [4] and the interorbital spin-triplet/orbital-singlet/s-wave Eg pairing [5]. In the latter case, we can introduce the interorbital pairing in the presence of t2g-orbtials and strong spin-orbit coupling in SRO. Thus, it is necessary to show the temperature dependence of the spin susceptibility for the interorbital Eg representation in SRO.
We study the temperature dependence of the spin susceptibility below Tc for the orbital-singlet pairing in three-dimensional SRO model by choosing the possible irreducible representations [6]. We focus on the spin-triplet/orbital-singlet/s-wave and spin-singlet/orbital-singlet/odd-parity pairing stemming from the multiorbital and strong spin-orbit coupling. In the former case, the pseudospin-singlet pairing is realized in the band basis, then the resulting spin susceptibility is reduced with the decrease of temperature irrespective of the direction of the magnetic field for all possible irreducible representations. In the latter case, since the pseudospin-triplet pairing is realized in the band basis, spin susceptibility does not change by the temperature when the applied magnetic field is along a perpendicular axis to the d-vector with the pseudospin-triplet pair potential. We conclude that the recently observed spin susceptibility of NMR experiments in SRO [2] can be explained by the interorbital spin-triplet/orbital-singlet/s-wave Eg representation.
*This work is supported by the JSPS KAKENHI (Grants No. JP15H05851, No. JP15H05853, No. JP15K21717, No. JP18H01176, No. JP18K03538, No. JP20H00131, and No. JP20H01857) from MEXT of Japan, Japan-RFBR Bilateral Joint Research Projects Seminars No. 19-52-50026, and the JSPS Core-to-Core program Oxide Superspin international network. We thank to Prof. Y. Maeno and P. Gentile.
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