Finite field regime for a quantum spin liquid in $\alpha$-RuCl$_3$

An external magnetic field can induce a transition in $\alpha$-RuCl$_3$ from an ordered zigzag state to a disordered state that is possibly related to the Kitaev quantum spin liquid. Here we present new field dependent inelastic neutron scattering and magnetocaloric effect measurements implying the existence of an additional transition out of the quantum spin liquid phase at an upper field limit $B_u$. The neutron scattering shows three distinct regimes of magnetic response. In the low field ordered state the response shows magnon peaks; the intermediate field regime shows only continuum scattering, and above $B_u$ the response shows sharp magnon peaks at the lower bound of a strong continuum. Measurable dispersion of magnon modes along the $(0,0,L)$ direction implies non-negligible inter-plane interactions. Combining the magnetocaloric effect measurements with other data a $T-B$ phase diagram is constructed. The results constrain the range where one might expect to observe quantum spin liquid behavior in $\alpha$-RuCl$_3$.