  We report on a systematic study of the magnetic properties on single crystals
of the solid solution Cs$_2$CuCl$_{4-x}$Br$_x$ (0 $\leq$ x $\leq$ 4), which
include the two known end-member compounds Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$,
classified as quasi-two-dimensional quantum antiferromagnets with different
degrees of magnetic frustration. By comparative measurements of the magnetic
susceptibility $\chi$($T$) on as many as eighteen different Br concentrations,
we found that the inplane and out-of-plane magnetic correlations, probed by the
position and height of a maximum in the magnetic susceptibility, respectively,
do not show a smooth variation with x. Instead three distinct concentration
regimes can be identified, which are separated by critical concentrations
x$_{c1}$ = 1 and x$_{c2}$ = 2. This unusual magnetic behavior can be explained
by considering the structural peculiarities of the materials, especially the
distorted Cu-halide tetrahedra, which support a site-selective replacement of
Cl- by Br- ions. Consequently, the critical concentrations x$_{c1}$ (x$_{c2}$)
mark particularly interesting systems, where one (two) halidesublattice
positions are fully occupied.
