Defect charging and resonant levels in half-Heusler Nb$_{1-x}$Ti$_x$FeSb

Abstract: We report $^{93}$Nb and $^{121}$Sb NMR and $^{57}$Fe M\"{o}ssbauer studies combined with DFT calculations of Nb$_{1-x}$Ti$_x$FeSb ($0\leqslant x \leqslant0.3$), one of the most promising thermoelectric systems for applications above 1000 K. These studies provide local information about defects and electronic configurations in these heavily $p$-type materials. The NMR spin-lattice relaxation rate provides a measure of states within the valence band. With increasing $x$, changes of relaxation rate vs carrier concentration for different substitution fractions indicate the importance of resonant levels which do not contribute to charge transport. The local paramagnetic susceptibility is significantly larger than expected based on DFT calculations, which we discuss in terms of an enhancement of the susceptibility due to a Coulomb enhancement mechanism. The M\"{o}ssbauer spectra of Ti-substituted samples show small departures from a binomial distribution of substituted atoms, while for unsubstituted $p$-type NbFeSb, the amplitude of a M\"{o}ssbauer satellite peak increases vs temperature, a measure of the $T$-dependent charging of a population of defects residing about 30 meV above the valence band edge, indicative of an impurity band at this location.