High-pressure magnetization and NMR studies on $\alpha$-RuCl$_3$.

We report high-pressure magnetization and $^{35}$Cl NMR studies on $\alpha$-RuCl$_3$ with pressure up to 1.5~GPa. At low pressures, the magnetic ordering is identified by both the magnetization data and the NMR data, where the $T_N$ shows a concave shape dependence with pressure. These data suggest stacking rearrangement along the $c$-axis. With increasing pressure, phase separation appears prominently at $P\ge$~0.45~GPa, and the magnetic volume fraction is completely suppressed at $P\ge$~1.05~GPa. Meanwhile, a phase-transition-like behavior emerges at high pressures in the remaining volume by a sharp drop of magnetization $M(T)$ upon cooling, with the transition temperature $T_x$ increased to ~250~K at 1~GPa. The $1/^{35}T_1$ is reduced by over three orders of magnitude when cooled below 100~K. This characterizes a high-pressure, low-temperature phase with nearly absent static susceptibility and low-energy spin fluctuations. The nature of the high-pressure ground state is discussed, where a magnetically disordered state is proposed as a candidate state.