We present a study of the magnetic susceptibility $chi_{mol}$ under variable hydrostatic pressure on single crystals of Cs$_2$CuCl$_{4-x}$Br$_x$. This includes the border compounds textit{x} = 0 and 4, known as good realizations of the distorted triangular-lattice spin-1/2 Heisenberg antiferromagnet, as well as the isostructural stoichiometric systems Cs$_2$CuCl$_{3}$Br$_1$ and Cs$_2$CuCl$_{2}$Br$_2$. For the determination of the exchange coupling constants $J$ and $J^{prime}$, $chi_{mol}$ data were fitted by a $J-J^{prime}$ model cite{Schmidt2015}. Its application, validated for the border compounds, yields a degree of frustration $J^{prime}$/$J$ = 0.47 for Cs$_2$CuCl$_3$Br$_1$ and $J^{prime}$/$J$ $simeq$ 0.63 - 0.78 for Cs$_2$CuCl$_2$Br$_2$, making these systems particular interesting representatives of this family. From the evolution of the magnetic susceptibility under pressure up to about 0.4,GPa, the maximum pressure applied, two observations were made for all the compounds investigated here. First, we find that the overall energy scale, given by $J_c = (J^2$ + $J^{prime 2}$)$^{1/2}$, increases under pressure, whereas the ratio $J^{prime}$/$J$ remains unchanged in this pressure range. These experimental observations are in accordance with the results of DFT calculations performed for these materials. Secondly, for the magnetoelastic coupling constants, extraordinarily small values are obtained. We assign these observations to a structural peculiarity of this class of materials.
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