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

Henmilite {${\mathrm{Ca}}_2\mathrm{Cu}{\left(\mathrm{OH}\right)}_4{\left[\mathrm{B}{\left(\mathrm{OH}\right)}_4\right]}_2$} 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.

Figure 1

Image of a henmilite crystal.

Figure 2

Crystal structure of henmilite ${\mathrm{Ca}}_2\mathrm{Cu}{\left(\mathrm{OH}\right)}_4{\left[\mathrm{B}{\left(\mathrm{OH}\right)}_4\right]}_2$ in projection along [001] (left), [010] (center), and [100] (right). Hydrogen bonds highlighted with red lines show the antiferroelectric chains.

Figure 3

Diffraction spots of a henmilite single crystal. Odd $h$ index reflections correspond to superlattice reflections $\left(h/2kl\right)$ with the notation of the previously reported setting [15, 16]. The inset shows a magnified view of the $\left(-1104\right)$ reflection.

Figure 4

The Cu sublattice and the Cu-Cu bond lengths.

Figure 5

Temperature dependence of magnetic susceptibility $\chi$ of a henmilite powder sample (the zero-field process, solid blue circles), with Curie-Weiss fit $\chi =\frac{C}{T-{\mathrm{\Theta }}_{\mathrm{CW}}}+{\chi }_0$ (black curve), where $C$ is the Curie constant, ${\mathrm{\Theta }}_{\mathrm{CW}}$ is the Weiss temperature, and ${\chi }_0$ is a diamagnetic part. The fitting was performed between 30 and 300 K. Inset: Inverse of $\chi$ after substraction of ${\chi }_0$.

Figure 6

Temperature dependence of magnetic susceptibility of a henmilite single crystal in the $a^{*}$ (red), $b^{*}$ (blue), and $c^{*}$ (green) directions. Black curves represent the fitting result for the field cooling process. The applied magnetic field was 0.1 T.

Figure 7

Magnetic field dependence of magnetization ($M\text{−}H$ curve) of randomly oriented henmilite crystals (powder).

Figure 8

(a) Temperature dependence of specific heat in magnetic fields up to 15 T (${\mu }_{0}H\parallel b$*). All data are offset by 1 J/mol ${\mathrm{K}}^2$. (b) Entropy change estimated from the specific heat results. (c) Temperature dependence of specific heat (logarithmic) at 0 T and the fitting of $C=A{T}^{\alpha }$ between 0.4 and 1 K, where $A$ is a constant, $T$ is the temperature, and $\alpha$ is the exponent.

Figure 9

The magnetic phase diagram of henmilite (${\mu }_{0}H\parallel b$*) in the magnetic-field–temperature plane (zero-field cooling process). AFM and PM, antiferromagnetic and paramagnetic regions, respectively.

Figure 10

Band structure of ${\mathrm{Ca}}_2\mathrm{Cu}{\left(\mathrm{OH}\right)}_4{\left[\mathrm{B}{\left(\mathrm{OH}\right)}_4\right]}_2$ obtained from GGA calculations. Orbital weights for Cu $3d$ orbitals are highlighted.

Figure 11

(a) Exchange interactions of henmilite extracted by DFT energy mapping. Couplings are shown as a function of local Coulomb repulsion $U$ while Hund's rule coupling was fixed to $J_{\mathrm{H}}=1$ eV. $J_1$ and $J_2$ dominate, making henmilite a two-leg spin ladder compound, with an exchange network as shown in (b).