  We obtain the steady-state phase diagram of a transverse field XY spin chain
coupled at its ends to magnetic reservoirs held at different magnetic
potentials. In the long-time limit, the magnetization bias across the system
generates a current-carrying non-equilibrium steady-state. We characterize the
different non-equilibrium phases as functions of the chain's parameters and
magnetic potentials, in terms of their correlation functions and entanglement
content. The mixed-order transition, recently observed for the particular case
of a transverse field Ising chain, is established to emerge as a generic
out-of-equilibrium feature and its critical exponents are determined
analytically. Results are also contrasted with those obtained in the limit of
Markovian reservoirs. Our findings should prove helpful in establishing the
properties of non-equilibrium phases and phase transitions of extended open
quantum systems.
