Static and Dynamic Electronic Properties of Weyl Semimetal NbP -- A Single Crystal ${}^{93}$Nb-NMR Study

Abstract

Nuclear magnetic resonance (NMR) techniques have been used to study the static and dynamic microscopic properties of the Weyl semimetal NbP. From a complete analysis of the angular dependence of the ${}^{93}$Nb-NMR spectra in a single crystal, the parameters for the electric quadrupole interactions and the magnetic hyperfine interactions were determined to be $\hat{I}{½}_{\mathrm{Q}}=0.61$\,MHz, $\hat{I}\cdot =0.20$, $(K_{XX},K_{YY},K_{ZZ})=(-0.06,0.11,-0.11)$\% at 4.5\,K. The temperature and field dependence of the ${}^{93}$Nb Knight shift revealed a characteristic feature of the shape of the density of states with nearly massless fermions. We clearly observed a quantum oscillation of the Knight shift associated with the band structure, whose frequency was in good agreement with the previous bulk measurements. The temperature dependence of the spin-lattice relaxation rate, $1/T_{1}T$, showed an almost constant behavior for $30<T<180$\,K, while a weak temperature dependence was observed below $\sim 30$\,K. This contrasts with the behavior observed in TaP and TaAs, where the $1/T_{1}T$ measured by the ${}^{181}$Ta nuclear quadrupole resonance (NQR) shows $1/T_{1}T\propto T^2$ and $T^4$ above approximately 30\,K. In TaP, the temperature dependent orbital hyperfine interaction plays a signficant role in nuclear relaxation, whereas this contribution is not observed in TaAs. Two-component spin echo oscillations were observed. The shorter-period oscillation is attributed to the origin of quadrupole coupling, while the longer-period oscillation indicates the presence of indirect nuclear spin-spin coupling, as discussed in other Weyl semimetal like TaP.