Quantum spin fluctuations and hydrogen bond network in the antiferromagnetic natural mineral henmilite

Henmilite {${\mathrm{Ca}}_{2}\mathrm{Cu}{(\mathrm{OH})}_{4}{[\mathrm{B}{(\mathrm{OH})}_{4}]}_{2}$} is a blue calcium copper borate mineral found only in the Fuka mine, Okayama Prefecture, Japan. Crystal structure refinement, magnetic and specific heat measurements, and density functional theory (DFT) calculations are performed to clarify its magnetic properties. Synchrotron x-ray diffraction experiments reveal that the hydrogen-bonded chains are arranged in an antiferroelectric manner, doubling the unit cell along the $a$ axis. An antiferromagnetic transition is observed at 0.2 K at zero magnetic field. Furthermore, a dome-shaped antiferromagnetic ordering region exists in the temperature--magnetic-field phase diagram, indicating the presence of quantum spin fluctuations. The obtained crystal structure in combination with DFT calculations suggests that the system has a coupled two-leg ladder magnetic lattice, explaining the very low ordering temperature.