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By using a high pressure, high temperature (HPHT) technique, theantiferromagnetically ordered ($T_N$ = 13.5 K) 6H-A phase ofBa$_3$NiSb$_2$O$_9$ was transformed into two new gapless quantum spinliquid(QSL) candidates with S=1 (Ni$^{2+}$) moments: the 6H-B phase with aNi$^{2+}$-triangular lattice and the 3C-phase with aNi$^{2+}$-three-dimensional (3D) edge-shared tetrahedral lattice. Bothcompounds show no magnetic order down to 0.35 K despite Curie-Weisstemperatures $\theta_{CW}$ of -75.5 K (6H-B) and -182.5 K (3C), respectively.Below $\sim 25$ K the magnetic susceptibility of the 6H-B phase saturates to aconstant value $\chi_0 = 0.013 $ emu/mol which is followed below 7 K, by alinear-temperature dependent magnetic specific heat ($C_M$) displaying a giantcoefficient $\gamma$ = 168 mJ/mol-K$^2$. Both observations suggest thedevelopment of a Fermi-liquid like ground state characterized by a Wilson ratioof 5.6 in this insulating material. For the 3C phase, the $C_M \propto T^2$behavior indicates a unique S=1, 3D QSL ground-state.

High pressure sequence of Ba_3NiSb_2O_9 structural phases: new $S = 1$ quantum spin-liquids based on Ni^{2+}