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

## TL;DR

This study investigates the low-temperature specific heat and magnetic susceptibility of layered frustrated quantum antiferromagnets Cs$_2$CuCl$_{4-x}$Br$_x$, revealing a crossover from 1D to 2D magnetic behavior and unconventional magnetic excitations.

## Contribution

It provides experimental and theoretical evidence of a crossover from 1D to 2D magnetic excitations in Cs$_2$CuCl$_{4-x}$Br$_x$, highlighting the role of Fermi-like statistics in 2D frustrated antiferromagnets.

## Key findings

- Crossover from 1D to 2D magnetic behavior with changing $J'/J$ ratio.
- Observation of linear temperature dependence of specific heat in both 1D and 2D regimes.
- Contradiction of standard spin-wave theory predictions, indicating Fermi-like magnetic excitations.

## 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 $J'/J$ 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 $J'/J < 0.6$ to two-dimensional (2D) behavior for $J'/J \approx 0.78$ behavior. For $J'/J < 0.6$, realized for $x$ = 0, 1, and 4, we find a magnetic contribution to the low-temperature specific heat, $C_{\rm m} \propto T$, consistent with spinon excitations in 1D spin-1/2 Heisenberg antiferromagnets. Remarkably, for $x$ = 2, where $J'/J \approx 0.78$ implies a 2D magnatic character, we also observe $C_{\rm m} \propto T$. This finding, which contrasts the prediction of $C_{\rm m} \propto T^2$ 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.