High-field spin-flop state in green dioptase

The high-field magnetic properties and order of the gem mineral green dioptase Cu$_6[$Si$_6$O$_{18}]\cdot 6$H$_2$O have been studied by means single-crystal neutron diffraction in fields up to $21~$T magnetization measurements $30~$T. In zero field, Cu$^{2+}$-moments antiferromagnetic chains are oriented along $c$-axis with a small off-axis tilt. For field applied parallel $c$-axis, shows spin-flop-like transition at $B^*=12.2~$T $1.5~$K. Neutron experiments show smooth behavior intensities reflections without any change periodicity structure. Bulk microscopic observations well described model ferromagnetically coupled $XXZ$ spin-$\frac{1}{2}$ chains, taking into account local easy-axis direction. We demonstrate that structure evolves smoothly from deformed N\'eel state low spin-flop high via strong crossover around $B^*$. results generalized for different values interchain coupling spin anisotropy.