We report an experimental and theoretical study of the low-temperature
specific heat C and magnetic susceptibility χ of the layered anisotropic
triangular-lattice spin-1/2 Heisenberg antiferromagnets
Cs2CuCl4−xBrx with x = 0, 1, 2, and 4. We find that the ratio
J′/J of the exchange couplings ranges from 0.32 to ≈0.78, implying a
change (crossover or quantum phase transition) in the materials' magnetic
properties from one-dimensional (1D) behavior for J′/J<0.6 to
two-dimensional (2D) behavior for J′/J≈0.78 behavior. For J′/J<0.6, realized for x = 0, 1, and 4, we find a magnetic contribution to the
low-temperature specific heat, Cm∝T, consistent with spinon
excitations in 1D spin-1/2 Heisenberg antiferromagnets. Remarkably, for x =
2, where J′/J≈0.78 implies a 2D magnatic character, we also observe
Cm∝T. This finding, which contrasts the prediction of Cm∝T2 made by standard spin-wave theories, shows that Fermi-like
statistics also plays a significant role for the magnetic excitations in
frustrated spin-1/2 2D antiferromagnets