Competing Ordering Modes in the Distorted Quantum Kagome Material Clinoatacamite Cu$_2$Cl(OH)$_3$

We have studied the magnetic properties of clinoatacamite Cu$_2$Cl(OH)$_3$, the parent compound of the quantum spin liquid candidate herbertsmithite and a longstanding puzzle among frustrated quantum magnets. As we reveal using density-functional theory, clinoatacamite belongs to the class of distorted kagome antiferromagnets with the kagome plane being embedded into a low-symmetry crystal structure. By means of thermodynamic measurements, muon spin rotation/relaxation as well as neutron diffraction on single crystals, we find a complex sequence of phases/regions below 18.1 K in zero magnetic field. We propose this complexity in multicritical clinoatacamite to arise from the competition of antiferromagnetic ordering modes from the underconstrained manifold of modes, which can lead to a metamagnetic texture in zero magnetic field.

💡 Research Summary

In this work the authors investigate the magnetic behavior of clinoatacamite Cu₂Cl(OH)₃, the parent compound of the quantum‑spin‑liquid candidate herbertsmithite. Using single‑crystal neutron diffraction they first determine the precise atomic positions and confirm that the material crystallizes in the monoclinic space group P2₁/n with three inequivalent Cu sites. Density‑functional theory (GGA + U, U≈7.2 eV) is then employed to calculate the six nearest‑neighbour exchange constants J₁–J₆. The three largest couplings (J₄≈120 K, J₅≈212 K, J₆≈368 K) are antiferromagnetic and define a strongly frustrated, non‑uniform kagome layer formed by Cu(2) and Cu(3). The remaining three couplings (J₁≈‑7 K, J₂≈‑15 K, J₃≈‑30 K) are weakly ferromagnetic and connect the kagome planes to interlayer Cu(1) sites. Next‑nearest‑neighbour interactions are all smaller than 10 K, confirming that the magnetic physics is dominated by the six dominant exchanges.

Thermodynamic measurements on natural single crystals reveal a primary anomaly at 18.1 K in the magnetic specific heat, signalling the onset of long‑range order. Additional, sharper features appear at 6.4 K, 6.2 K and a weak kink at 4.6 K. The magnetic entropy recovered at 18.1 K is only about one third of the full S = ½ value, indicating that a large portion of the spin degrees of freedom remain fluctuating or are frozen into a complex state. AC susceptibility shows a pronounced frequency dependence at 6.4 K, but no signature at 18.1 K, ruling out a conventional spin‑glass scenario.

Zero‑field (ZF) and weak transverse‑field (wTF) muon‑spin rotation (μSR) experiments demonstrate that the whole sample becomes magnetically ordered below 18.1 K, as the wTF asymmetry disappears. ZF spectra taken at 10.8 K, 5.3 K and 1.73 K display three distinct regimes: (i) above 6.4 K a set of three well‑defined precession frequencies corresponding to static internal fields, (ii) between 6.2 K and 6.4 K a highly damped signal indicating enhanced spin dynamics, and (iii) below 4.6 K a return to three clear frequencies, now reflecting a different ordered state.

Single‑crystal neutron diffraction identifies magnetic Bragg peaks below 6.4 K with propagation vector qₘ = (0,0,0). The intensity of the (001) magnetic reflection vanishes between 6.0 K and 6.4 K, confirming the disappearance of this phase. Earlier powder work had reported weak half‑integer peaks indexed by qₘ = (‑0.5,0,0.5) around 7 K; the present study reproduces these reflections in single crystals, suggesting a second, incommensurate magnetic phase at higher temperature.

A full magnetic‑structure refinement using representation analysis yields a mixed symmetry state. Cu(1) and Cu(2) moments lie in the ac‑plane, are collinear, and point almost perpendicular to the kagome plane, representing an even‑parity (inversion‑symmetric) ordering mode. Cu(3) moments lie in the ab‑plane, are non‑collinear, and belong to an odd‑parity (inversion‑broken) mode. Both sublattices carry essentially the same ordered moment (~0.38 μ_B). The coexistence of even‑ and odd‑parity modes indicates that clinoatacamite is situated near a multicritical point where several ordering channels are nearly degenerate.

The authors argue that the low‑symmetry crystal structure distorts the ideal kagome lattice, preserving an under‑constrained manifold of magnetic modes. The competition between the two symmetry‑distinct antiferromagnetic ordering patterns generates a metamagnetic texture even in zero field, i.e., a spatially modulated pattern of spin canting and domain‑like structures without external magnetic bias. This explains the multiple thermodynamic anomalies, the intermediate‑temperature dynamical regime observed by μSR, and the frequency‑dependent AC susceptibility.

Overall, the paper provides a comprehensive picture of clinoatacamite as a distorted quantum kagome antiferromagnet where non‑uniform exchange interactions and structural low symmetry give rise to a rich hierarchy of magnetic phases. The work highlights the importance of considering multiple competing ordering modes and multicriticality in frustrated quantum magnets, and positions clinoatacamite as a valuable platform for exploring exotic magnetic textures such as metamagnetic domains, quantum spin‑liquid proximate states, and field‑induced phenomena in non‑uniform kagome systems.