CsCuCl3 is a ferromagnetically stacked triangular spin-1/2 antiferromagnet.
We discuss models for its zero-temperature magnetization process. The mode
ls range from three antiferromagnetically coupled ferromagnetic chains to t
he full three-dimensional situation. The situation with spin-1/2 is treated
by expansions around the Ising limit and exact diagonalization. Further, w
eak-coupling perturbation theory is used mainly for three coupled chains wh
ich are also investigated numerically using the density-matrix renormalizat
ion group technique. We find that already the three-chain model gives rise
to the plateau-like feature at one third of the saturation magnetization wh
ich is observed in magnetization experiments on CsCuCl3 for a magnetic fiel
d perpendicular to the crystal axis. For a magnetic field parallel to the c
rystal axis, a jump is observed in the experimental magnetization curve in
the region of again about one third of the saturation magnetization. In con
trast to earlier spinwave computations, we do not find any evidence for suc
h a jump with the model in the appropriate parameter region.