Possible Intermediate Quantum Spin Liquid Phase in $\alpha$-RuCl$_3$ under High Magnetic Fields up to 100 T

Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material $\alpha$-RuCl$_3$ has intrigued great research interest recently. A fascinating question is on the possible existence of field-induced QSL phase in this compound. Here we perform a high-field measurement of the magnetization process of $\alpha$-RuCl$_3$ up to 102 T employing the non-destructive and destructive pulsed magnets. Under the out-of-plane field along the c$^*$ axis (i.e., perpendicular to the honeycomb plane), two quantum phase transitions are uncovered at respectively 36 T and about 83 T, between which there lies an intermediate phase as the predicted QSL. By measuring the magnetization data with fields tilted from the c$^*$ axis up to $90^\circ$ (i.e., in-plane direction), we obtain the field-angle phase diagram that contains the zigzag, paramagnetic, and QSL phases. Based on the accurate $K$-$J$-$\Gamma$-$\Gamma^{\prime}$ model of $\alpha$-RuCl$_3$, we perform density matrix renormalization group simulations and reproduce the quantum phase diagram in excellent agreement with experiments.