  Recent experiments on the anisotropic spin-1/2 triangular antiferromagnet
Cs_2CuBr_4 have revealed a remarkably rich phase diagram in applied magnetic
fields, consisting of an unexpectedly large number of ordered phases. Motivated
by this finding, we study the role of spatial anisotropy, Dzyaloshinskii-Moriya
interactions, and quantum fluctuations on the magnetization process of a
triangular antiferromagnet, coming from the semiclassical limit. The richness
of the problem stems from two key facts: 1) the classical isotropic model
exhibits a large accidental ground state degeneracy, and 2) these three
ingredients compete with one another and split this degeneracy in opposing
ways. Using a variety of complementary approaches, including extensive Monte
Carlo numerics, spin-wave theory, and an analysis of Bose-Einstein condensation
of magnons at high fields, we find that their interplay gives rise to a complex
phase diagram consisting of numerous incommensurate and commensurate phases.
Our results shed light on the observed phase diagram for Cs_2CuBr_4 and suggest
a number of future theoretical and experimental directions that will be useful
for obtaining a complete understanding of this material's interesting
phenomenology.
