Spin susceptibility for orbital-singlet Cooper pair in the three-dimensional Sr_{2}RuO_{4} superconductor

We study the spin susceptibility of the orbital-singlet pairings, including the spin-triplet/orbital-singlet/s-wave E_{g} representation proposed by Suh et al. [H. G. Suh et al., Phys. Rev. Research 2, 032023(R) (2020)2643-156410.1103/PhysRevResearch.2.032023], for a three-orbital model of superconducting Sr_{2}RuO_{4} in three dimensions. For the pseudospin-singlet states represented in the band basis, the spin susceptibility decreases when reducing the temperature, irrespective of the direction of the applied magnetic fields, even if they are spin-triplet/orbital-singlet pairings in the spin-orbital space. However, because the pseudospin-triplet d-vector in the band basis is not completely aligned in the xy-plane (along z-axis) owing to the strong atomic spin-orbit coupling, the spin susceptibility for spin-singlet/orbital-singlet/odd-parity pairings is reduced around 5–10 percent with the decrease of the temperature along the z (x) axis. We can determine the symmetry of the pseudospin structure of the Cooper pair by the temperature dependence of the spin susceptibility measured by nuclear magnetic resonance experiments. Our obtained results serve as a guide to determine the pairing symmetry of Sr_{2}RuO_{4}.