NMR compared to band structure calculations of the quaternary superconductor La${}_3$Ni${}_2$B${}_2$N${}_{3-x}$

We measured susceptibility and NMR spectra, spin-lattice, and spin-spin relaxation of ${}^{11}$B and ${}^{139}$La in the quaternary superconductor La${}_3$Ni${}_2$B${}_2$N${}_{3-x}$ and compare these experimental results to full potential density functional theory band structure calculations. The electric field gradients (EFGs) at B and La sites clearly show that the N vacancies are restricted to the N(2$b$) sublattice. Temperature-dependent susceptibility, Knight shift, and nuclear spin-lattice relaxation $T_1$ are successfully described within the Fermi-liquid model. The Hebel-Slichter peak is suppressed in the mixed state and in the presence of paramagnetic impurities.

Figure 1

Crystallographic structure of La${}_3$Ni${}_2$B${}_2$N${}_{3-x}$ with atom positions in the I4/mmm space group, multiplicities, and point symmetries.

Figure 2

NMR spin echo Fourier transform envelope powder spectra (symbols) of ${}^{11}$B and ${}^{139}$La in La${}_3$Ni${}_2$B${}_2$N${}_{3-x}$ at $T=17$ K. The lines are simulated spectra with parameters calculated by DFT (see text).

Figure 3

Density of states of La${}_3$Ni${}_2$B${}_2$N${}_{3-x}$, $x=0.0$, from DFT with total La, Ni, and (small) B contributions. The second panel shows the dependency of the total DOS near ${\varepsilon }_F=0$ on the N vacancy concentration in the virtual crystal approximation with quadratic fits (lines). The enhanced B-2$s$ and B-$p$ partial DOS for $x=0$ is also shown.

Figure 4

dc susceptibility of La${}_3$Ni${}_2$B${}_2$N${}_{3-x}$ in the normal state measured at 5.85 T in a SQUID magnetometer ($\Delta$: 4N-pure La and isotope pure ${}^{11}$B precursors, $\nabla$: NMR sample prepared from commercial precursors). Inset: dc susceptibility of a different sample measured up to 1000 K in a Quantum Design PPMS vibrating sample magnetometer (commercial precursors). The red lines are calculated from Eq. (1) with parameters from DFT (see text).

Figure 5

Knight shift of ${}^{11}$B ($B_0=1.3$ T, $T_c=13.4$ K) and ${}^{139}$La (scaled, see text, $B_0=3.0$ T, $T_c=10.5$ K) below 250 K compared to the susceptibility calculated from DFT shown in Fig. 4 according to Eq. (2) with (dotted) and without (line) impurity contribution. The vertical lines indicate the transition temperatures, the insets show that the B-central lines develop a double peak structure in the field cooled mixed state below $T_c$.

Figure 6

Nuclear spin lattice relaxation rate of ${}^{11}$B and ${}^{139}$La with fits (lines) to a Korringa law with a temperature-dependent Knight shift calculated from Eq. (2). The inset shows the low temperature regime for ${}^{11}$B with the Korringa law above $T_c=13.4$ K (line) and the exponential expected from BCS theory below (dotted).