NMR Evidence for the Topologically Nontrivial Nature in a Family of Half-Heusler Compounds

Spin-orbit coupling (SOC) is expected to partly determine the topologically nontrivial electronic structure of heavy half-Heusler ternary compounds. However, to date, attempts to experimentally observe either the strength of SOC or how it modifies the bulk band structure have been unsuccessful. By using bulk-sensitive nuclear magnetic resonance (NMR) spectroscopy combined with first-principles calculations, we reveal that Bi-209 NMR isotropic shifts scale with relativity in terms of the strength of SOC and average atomic numbers, indicating strong relativistic effects on NMR parameters. According to first-principles calculations, we further claim that nuclear magnetic shieldings from relativistic p(1/2) states and paramagnetic contributions from low-lying unoccupied p(3/2) states are both sensitive to the details of band structures tuned by relativity, which explains why the hidden relativistic effects on band structure can be revealed by Bi-209 NMR isotropic shifts in topologically nontrivial half-Heusler compounds. Used in complement to surface-sensitive methods, such as angle resolved photon electron spectroscopy and scanning tunneling spectroscopy, NMR can provide valuable information on bulk electronic states.