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.
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