High-Field Heat Capacity of Atacamite Cu$_2$Cl(OH)$_3$ for $\mathbf{H} \parallel b$ axis: From Antiferromagnetic Order to Correlated Disorder

We present the heat capacity of the frustrated sawtooth-chain compound atacamite Cu$_2$Cl(OH)$_3$ in high magnetic fields up to 35 T for $\mathbf{H} \parallel b$ axis. We clearly observe the change from antiferromagnetic long-range order, indicated by a sharp transition anomaly shifted to lower temperatures when increasing field, to a field-induced spin-liquid-like state with the absence of any transition anomaly. Here, in highest magnetic fields above 32 T a broad anomaly is present which is shifted to higher temperatures as the field is increased. The low-temperature heat capacity in the high-field region can be described well by an exponential behavior indicating a thermal activation over a spin gap. The findings are consistent with our scenario for the high-field state in atacamite for $\mathbf{H} \parallel c$ axis, where we proposed the sawtooth chains to decouple into two spin subsystems, basal and apical spin sites, leading to a partially polarized state with $M \sim M_\mathrm{sat}/2$.