DFT investigation of the effect of spin-orbit coupling on the NMR shifts in paramagnetic solids

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for studying the structural and electronic properties of paramagnetic solids. However, the interpretation of paramagnetic NMR spectra is often challenging as a result of the interactions of unpaired electrons with the nuclear spins of interest. In this work, we extend the formalism of the paramagnetic NMR shielding in the presence of spin-orbit coupling towards solid systems with multiple paramagnetic centers. We demonstrate how the single-ion electron paramagnetic resonance g tensor is defined and calculated in periodic paramagnetic solids. We then calculate the hyperfine tensor and the g tensor with density functional theory to show the validity of the presented model and we further demonstrate how these interactions can be combined to give the overall paramagnetic shielding tensor, σs. The method is applied to a series of olivine-type LiTMPO4 materials (with TM=Mn, Fe, Co, and Ni) and the corresponding Li7 and P31 NMR spectra are simulated. We analyze the effects of spin-orbit coupling and of the electron-nuclear magnetic interactions on the calculated NMR parameters. A detailed comparison is presented between contact and dipolar interactions across the LiTMPO4 series, in which the magnitudes and signs of the nonrelativistic and relativistic components of the overall isotropic shift and shift anisotropy are computed and rationalized.