  We report a thorough theoretical study of the low temperature phase diagram
of Cs_2CuCl_4, a spatially anisotropic spin S=1/2 triangular lattice
antiferromagnet, in a magnetic field. Our results, obtained in a
quasi-one-dimensional limit in which the system is regarded as a set of weakly
coupled Heisenberg chains, are in excellent agreement with experiment. The
analysis reveals some surprising physics. First, we find that, when the
magnetic field is oriented within the triangular layer, spins are actually most
strongly correlated within planes perpendicular to the triangular layers. This
is despite the fact that the inter-layer exchange coupling in Cs_2CuCl_4 is
about an order of magnitude smaller than the weakest (diagonal) exchange in the
triangular planes themselves. Second, the phase diagram in such orientations is
exquisitely sensitive to tiny interactions, heretofore neglected, of order a
few percent or less of the largest exchange couplings. These interactions,
which we describe in detail, induce entirely new phases, and a novel
commensurate-incommensurate transition, the signatures of which are identified
in NMR experiments. We discuss the differences between the behavior of
Cs_2CuCl_4 and an ideal two-dimensional triangular model, and in particular the
occurrence of magnetization plateaux in the latter. These and other related
results are presented here along with a thorough exposition of the theoretical
methods, and a discussion of broader experimental consequences to Cs_2CuCl_4
and other materials.
