First-principles study of spin-orbit effects and NMR in Sr2RuO4

We present a first principles study of nuclear magnetic resonance (NMR) and spin orbit effects in the unconventional superconductor ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$. We have calculated the uniform magnetic susceptibility, which agrees rather well with the experiment in amplitude, but, as in an earlier model result we found the calculated hard axis to be $z$, opposite to the experiment. We have also calculated the Knight shifts and the NMR relaxation rates for all atoms, and again found an overall good agreement, but with important deviations from the experiment in the same particular characteristics, such as the Knight shift anisotropy. Our results suggest that correlations in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ lead to underestimations of the orbital effects in density-functional-based calculations. We also argue that the accepted ``experimental'' value for the relative contribution of orbital polarization in susceptibility, 10\char21{}15 %, is also an underestimation. We discuss the puzzling invariance of the O and Ru Knight shifts across the superconducting transition for all directions of the applied field. We show that this fact cannot be explained by accidental cancellations or spin-flip scattering, as it happens in some elemental superconductors. We also point out that a large contribution of the dipole and orbital hyperfine field into the Knight shifts in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$, combined with the possibility of an orbital-dependent superconductivity, calls for a revision of the standard theory of the Knight shift in the superconducting state.