Phase diagram of the 2D frustrated quantum magnet Cs$_2$CuCl$_4$ in applied field

We use neutron scattering, magnetization and specific heat to probe how the ground state of the 2D spin-1/2 anisotropic triangular lattice antiferromagnet Cs$_2$CuCl$_4$ evolves as a function of applied magnetic field. We observe that the zero- field incommensurate spin spiral is suppressed by relatively small in-plane fields giving way to a commensurate 2D antiferromagnetic pattern stable over most of the intermediate field region, with incommensurate order appearing again for a narrow field range just below ferromagnetic saturation. The commensurate phase is not captured by a classical mean-field approach, suggesting that quantum fluctuations may be important in stabilizing this type of order.