  Frustrated magnets with strong spin-orbit coupling promise to host
topological states of matter, with fractionalized excitations and emergent
gauge fields. Kitaev's proposal for a honeycomb-lattice Majorana spin liquid
has triggered an intense search for experimental realizations, with
bond-dependent Ising interaction being the essential building block. A prime
candidate is $\alpha$-RuCl$_3$ whose phase diagram in a magnetic field is,
however, not understood to date. Here we present conclusive experimental
evidence for a novel field-induced ordered phase in $\alpha$-RuCl$_3$,
sandwiched between the zigzag and quantum disordered phases at low and high
fields, respectively. We provide a detailed theoretical study of the relevant
effective spin model which we show to display a field-induced intermediate
phase as well. We fully characterize the intermediate phase within this model,
including its complex spin structure, and pinpoint the parameters relevant to
$\alpha$-RuCl$_3$ based on the experimentally observed critical fields. Most
importantly, our study connects the physics of $\alpha$-RuCl$_3$ to that of the
Kitaev-$\Gamma$ model, which displays a quantum spin liquid phase in zero
field, and hence reveals the spin liquid whose signatures have been detected in
a variety of dynamical probes of $\alpha$-RuCl$_3$.
