Specific Heat Study of 1D and 2D Excitations in the Layered Frustrated Quantum Antiferromagnets Cs${}_2$CuCl${}_{4-x}$Br${}_x$

Abstract

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 Cs${}_2$CuCl${}_{4-x}$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 $J^{\prime }/J\approx 0.78$ behavior. For $J^{\prime }/J<0.6$, realized for $x$ = 0, 1, and 4, we find a magnetic contribution to the low-temperature specific heat, $C_{\mathrm{m}}\propto T$, 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 magnatic character, we also observe $C_{\mathrm{m}}\propto T$. This finding, which contrasts the prediction of $C_{\mathrm{m}}\propto T^2$ made by standard spin-wave theories, shows that Fermi-like statistics also plays a significant role for the magnetic excitations in frustrated spin-1/2 2D antiferromagnets.