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Large quantum fluctuations in the strongly coupled spin-1/2 chains of green dioptase: a hidden message from birds and trees

The green mineral dioptase Cu6Si6O18(H2O)6 has been known since centuries and plays an important role in esoteric doctrines. In particular, the green dioptase is supposed to grant the skill to speak with trees and to understand the language of birds. Armed with natural samples of dioptase, we were able to unravel the magnetic nature of the mineral (presumably with hidden support from birds and trees) and show that strong quantum fluctuations can be realized in an essentially framework-type spin lattice of coupled chains, thus neither frustration nor low-dimensionality are prerequisites. We present a microscopic magnetic model for the green dioptase. Based on full-potential DFT calculations, we find two relevant couplings in this system: an antiferromagnetic coupling J_c, forming spiral chains along the hexagonal c axis, and an inter-chain ferromagnetic coupling J_d within structural Cu2O6 dimers. To refine the J_c and J_d values and to confirm the proposed spin model, we perform quantum Monte-Carlo simulations for the dioptase spin lattice. The derived magnetic susceptibility, the magnetic ground state, and the sublattice magnetization are in remarkably good agreement with the experimental data. The refined model parameters are J_c = 78 K and J_d = -37 K with J_d/J_c ~ -0.5. Despite the apparent three-dimensional features of the spin lattice and the lack of frustration, strong quantum fluctuations in the system are evidenced by a broad maximum in the magnetic susceptibility, a reduced value of the Neel temperature T_N ~ 15 K >> J_c, and a low value of the sublattice magnetization m = 0.55 Bohr magneton. All these features should be ascribed to the low coordination number of 3 that outbalances the three-dimensional nature of the spin lattice.