Hybridization-driven gap in ${\text{U}}_3{\text{Bi}}_4{\text{Ni}}_3$: A ${}^{209}\text{B}\text{i}$ NMR/NQR study

We report ${}^{209}\text{B}\text{i}$ nuclear-magnetic-resonance and nuclear-quadrupole-resonance measurements on a single crystal of the Kondo insulator ${\text{U}}_3{\text{Bi}}_4{\text{Ni}}_3$. The ${}^{209}\text{B}\text{i}$ nuclear-spin-lattice relaxation rate $\left(T_1^{-1}\right)$ shows activated behavior and is well fit by a spin gap of 220 K. The ${}^{209}\text{B}\text{i}$ Knight shift $\left(\mathcal{K}\right)$ exhibits a strong temperature dependence arising from $5f$ electrons, in which $\mathcal{K}$ is negative at high temperatures and increases as the temperature is lowered. Below 50 K, $\mathcal{K}$ shows a broad maximum and decreases slightly upon further cooling. Our data provide insight into the evolution of the hyperfine fields in a fully gapped Kondo insulator based on $5f$ electron hybridization.

Figure 1

Magnetic susceptibility (○) ${}^{209}\text{B}\text{i}$ Knight shift $\mathcal{K}$ (●) as a function of temperature in a single crystal of ${\text{U}}_3{\text{Bi}}_4{\text{Ni}}_3$. The susceptibility was measured at 0.1 T. The sharp decrease of $\chi$ below 3.5 K is attributed to the small amount of superconducting BiNi on the surface. The solid curve is a Curie-Weiss fit, as discussed in the text. The inset shows $\mathcal{K}$ versus $\chi$. The solid line is a linear fit to the high-temperature data, yielding a hyperfine coupling constant $A_{\text{hf}}=94\left(5\right)\text{kOe}/{\mu }_B$ and temperature-independent shift ${\mathcal{K}}_0=-9\left(0.3\right)\%$. Below $T^{\ast }\approx 100\text{K}$, the linear relationship breaks down.

Figure 2

$K_{\text{cf}}$ versus $T$ in ${\text{U}}_3{\text{Bi}}_4{\text{Ni}}_3$ (●) and in ${\text{Ce}}_3{\text{Bi}}_4{\text{Pt}}_3$ (◇). The solid and dotted lines are fits as described in the text.

Figure 3

(Color online) ${}^{209}\text{B}\text{i}$ nuclear quadrupole frequency ${\nu }_Q$ as a function of temperature. Above 200 K, ${\nu }_Q$ increases with decreasing $T$, as expected from the phonon contribution $\propto T^{3/2}$ (dotted line). ${\nu }_Q$ bends over to a constant value below $\sim 170\text{K}$. Inset: the ${\text{U}}_3{\text{Bi}}_4{\text{Ni}}_3$ structure. The red (middle-size) atoms represent U, the green (large) atoms represent Bi, and the gray (small) atoms represent Ni.

Figure 4

$T_1^{-1}$ of ${}^{209}\text{B}\text{i}$ NQR in zero field measured at $4{\nu }_Q$ line. $T_1^{-1}$ versus $1/T$ plot reveals the activation behavior with the single activation energy $\Delta =220\text{K}$. Inset shows that $T_1^{-1}$ decreases exponentially with decreasing temperature.