  The novel magnetic phase diagram of the $Cs_2CuCl_{4-x}Br_x$ mixed system is
established by means of single crystal neutron diffraction in the lowest
temperature region and zero magnetic field. Two long-range ordered magnetic
phases exist in this mixed system depending on the Cl/Br concentration. In the
rich Cl concentration range, the ordered magnetic state occurs below the
ordering temperature $T_N = 0.51(1)K$ for $Cs_2CuCl_3Br_1$ and at
$Cs_2CuCl_{2.6}Br_{1.4}$ below $T_N = 0.24(2)K$. Magnetic order with a
temperature-independent position $(0, 0.573(1), 0)$ below the ordering
temperature $T_N = 0.63(1)K$ appears in the rich Br concentration for
$Cs_2CuCl_{0.6}Br_{3.4}$. Between the rich Cl and rich Br concentration ranges
(two magnetic phases), there is a range of x without magnetic order down to
$50mK$. A suggestion about the magnetic exchange paths in the $bc$-layer for
different regimes is presented, which can be controlled depending on the
preferred Br-occupation in the [CuX4] tetrahedra. The density functional theory
(DFT) calculations of the exchange coupling constants J, J^' for some ordered
compositions of the mixed system $Cs_2CuCl_{4-x}Br_x$ indicate that these are
not frustrated.
