We report an experimental and theoretical study of the low-temperature specific heat $C$ and magnetic susceptibility $\chi$ of the layered anisotropic triangular-lattice spin-$1/2$ Heisenberg antiferromagnets ${\mathrm{Cs}}_2{\mathrm{CuCl}}_{4-x}{\mathrm{Br}}_x$ with $x=0$, 1, 2, and 4. We find that the ratio $J^{\prime }/J$ of the exchange couplings ranges from 0.32 to $\approx 0.78$, implying a change (crossover or quantum phase transition) in the materials’ magnetic properties from one-dimensional (1D) behavior for $J^{\prime }/J<0.6$ to two-dimensional (2D) behavior for $J^{\prime }/J\approx 0.78$. For $J^{\prime }/J<0.6$, realized for $x=0$, 1, and 4, we find a magnetic contribution to the low-temperature specific heat, $C_m\propto T$, consistent with spinon excitations in 1D spin-$1/2$ Heisenberg antiferromagnets. Remarkably, for $x=2$, where $J^{\prime }/J\approx 0.78$ implies a 2D magnetic character, we also observe $C_m\propto T$. This finding, which contrasts the prediction of $C_m\propto T^2$ made by standard spin-wave theories, shows that Fermi-like statistics also plays a significant role for the magnetic excitations in spin-$1/2$ frustrated 2D antiferromagnets.

• Received 22 January 2019
• Revised 30 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.147202