High-Pressure Sequence of ${\mathrm{Ba}}_3{\mathrm{NiSb}}_2{\mathrm{O}}_9$ Structural Phases: New $S=1$ Quantum Spin Liquids Based on ${\mathrm{Ni}}^{2+}$

Two new gapless quantum spin-liquid candidates with $S=1$ (${\mathrm{Ni}}^{2+}$) moments: the $6H\mathrm{\text{−}}\mathrm{B}$ phase of ${\mathrm{Ba}}_3{\mathrm{NiSb}}_2{\mathrm{O}}_9$ with a ${\mathrm{Ni}}^{2+}$-triangular lattice and the 3C phase with a ${\mathrm{Ni}}_{2/3}{\mathrm{Sb}}_{1/3}$-three-dimensional edge-shared tetrahedral lattice were obtained under high pressure. Both compounds show no magnetic order down to 0.35 K despite Curie-Weiss temperatures ${\theta }_{\mathrm{CW}}$ of $-75.5$ ($6H\mathrm{\text{−}}\mathrm{B}$) and $-182.5\mathrm{K}$ (3C), respectively. Below $\sim 25\mathrm{K}$, the magnetic susceptibility of the $6H\mathrm{\text{−}}\mathrm{B}$ phase saturates to a constant value ${\chi }_0=0.013\mathrm{emu}/\mathrm{mol}$, which is followed below 7 K by a linear-temperature-dependent magnetic specific heat ($C_M$) displaying a giant coefficient $\gamma =168\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$. Both observations suggest the development of a Fermi-liquid-like ground state. For the 3C phase, the $C_M\propto T^2$ behavior indicates a unique $S=1$, 3D quantum spin-liquid ground state.

Figure 1

Powder XRD patterns (crosses) at 295 K for the ${\mathrm{Ba}}_3{\mathrm{NiSb}}_2{\mathrm{O}}_9$ polytypes: (a) $6H\mathrm{\text{−}}\mathrm{A}$, (b) $6H\mathrm{\text{−}}\mathrm{B}$, and (c) 3C. Solid curves are the best fits obtained from Rietveld refinements using FullProf. Schematic crystal structures for the ${\mathrm{Ba}}_3{\mathrm{NiSb}}_2{\mathrm{O}}_9$ polytypes: (d) $6H\mathrm{\text{−}}\mathrm{A}$, (e) $6H\mathrm{\text{−}}\mathrm{B}$, and (f) 3C; red octahedra represent Sb(M′) sites, and blue octahedra represent ${\mathrm{Ni}}_{2/3}{\mathrm{Sb}}_{1/3}(\mathrm{M})$ sites. Magnetic lattices composed of ${\mathrm{Ni}}^{2+}$ ions for the ${\mathrm{Ba}}_3{\mathrm{NiSb}}_2{\mathrm{O}}_9$ polytypes: (g) $6H\mathrm{\text{−}}\mathrm{A}$, (h) $6H\mathrm{\text{−}}\mathrm{B}$, and (i) 3C.

Figure 2

(a) Temperature dependencies of the dc magnetic susceptibility ($\chi$) for the ${\mathrm{Ba}}_3{\mathrm{NiSb}}_2{\mathrm{O}}_9$ polytypes. Inset: Temperature dependencies of $1/\chi$. The solid lines on $1/\chi$ data represent Curie-Weiss fits. For $6H\mathrm{\text{−}}\mathrm{B}$ phase, $\chi$ (open squares) is obtained by subtracting 1.7% ${\mathrm{Ni}}^{2+}$ orphan spin’s contribution (crosses) from the as-measured data (solid squares).

Figure 3

(a) Temperature dependencies for the magnetic specific heat ($C_M$) for all three ${\mathrm{Ba}}_3{\mathrm{NiSb}}_2{\mathrm{O}}_9$ polytypes. Solid lines are the fits as described in the main text. Inset: Variation in magnetic entropy $\Delta S$ below 30 K.