Atacamite Cu$_2$Cl(OH)$_3$: A model compound for the $S = 1/2$ sawtooth chain?

We present a combined experimental and theoretical study of the mineral atacamite Cu$_2$Cl(OH)$_3$. Based on {\it ab initio} band structure calculations, we derive a magnetic coupling scheme of essentially a $S = 1/2$ sawtooth chain. Experimentally, we fully characterize the long-range antiferromagnetically ordered state and field-induced behavior, here for $H \parallel b$ axis. Magnetic order is suppressed by magnetic fields of $\sim$ 20 T, while beginning at 31.5 T we observe a wide magnetization plateau at half of the saturation magnetization, $M_{\rm sat}/2$. Numerical calculations for the magnetization $M(H)$ of the quantum sawtooth chain reveal a plateau at $M_{\rm sat}/2$, raising the issue of the understanding of its microscopic nature.