  We present calculations of the magnetic ground state of Cs_2CuCl_4 in an
applied magnetic field, with the aim of understanding the commensurately
ordered state that has been discovered in recent experiments. This layered
material is a realization of a Heisenberg antiferromagnet on an anisotropic
triangular lattice. Its behavior in a magnetic field depends on field
orientation, because of weak Dzyaloshinskii-Moriya interactions.We study the
system by mapping the spin-1/2 Heisenberg Hamiltonian onto a Bose gas with hard
core repulsion. This Bose gas is dilute, and calculations are controlled, close
to the saturation field. We find a zero-temperature transition between
incommensurate and commensurate phases as longitudinal field strength is
varied, but only incommensurate order in a transverse field. Results for both
field orientations are consistent with experiment.
