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

Abstract

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.

Figures (3)

• Figure 1: (a) Crystal structure of clinoatacamite Malcherek2009 viewed along the $b$ axis [Cu(1): teal, Cu(2): light blue, Cu(3): dark blue, Cl: green, O: red, H: white]. (b) Motif of NN Cu-Cu exchange interactions $J_1$--$J_6$ and (c) their strength derived by means of DFT and GGA+$U$, plotted as function of the on-site Coulomb repulsion $U$. At $U = 7.19$ eV, the mean-field Curie-Weiss temperature agrees with the experimental value $\Theta_\mathrm{CW} = -165(1)$ K with $J_1 = -6.8$ K, $J_2 = -14.5$ K, $J_3= -30.3$ K, $J_4 = 120.1$ K, $J_5 = 211.6$ K and $J_6 = 367.7$ K (details in Ref. SI). In panels (a) and (b), the unit cells are indicated.
• Figure 2: (a) Magnetic specific heat $c_\mathrm{mag}$ and entropy $S_\mathrm{mag}$ in zero field and as function of temperature. The inset enlarges the region of the maxima at 6.2 K and 6.4 K. (b) Temperature dependence of the magnetization in weak dc magnetic fields (0.01 T, 0.1 T) for FC and ZFC samples ($\mathbf{H} \parallel b$ axis). The inset shows the subtle kink at $18.1$ K in 0.1 T. (c) Temperature dependence of the magnitude of the ac magnetic susceptibility $\left|\chi_\mathrm{ac}\right| = \sqrt{\chi^{\prime 2}_\mathrm{ac} + \chi^{\prime\prime 2}_\mathrm{ac}}$ with $\mu_0H_\mathrm{dc} = 0$ T and $\mu_0H_\mathrm{ac} = 0.5$ mT ($\mathbf{H} \parallel b$ axis) for various frequencies up to 9984 Hz. (d)--(e) In-phase and out-of-phase components of the ac susceptibility, $\chi^{\prime}_\mathrm{ac}$ and $\chi^{\prime\prime}_\mathrm{ac}$, in the region of the 6.2 K and 6.4 K anomalies.
• Figure 3: (a) Zero-field $\mu$SR asymmetry of single-crystalline clinoatacamite as function of time measured at 1.73 K, 5.3 K and 10.8 K. The data at 5.3 K and 10.8 K are shifted vertically. Solid lines are fits to the data; for details Ref. SI. (b) Rocking curves of the purely magnetic $(0\;0\;1)$ Bragg peak recorded at different temperatures on D10 ($\lambda = 2.36$ Å). Note: The peak has an asymmetric tail indicating a slight twinning of the crystal. (c) Integrated intensity of the magnetic $(0\;0\;1)$ reflection as function of temperature. (d)--(e) Magnetic structure at 1.7 K [$R_M = 0.0545$ (in $F$)] together with the dominant couplings $J_4$--$J_6$. Views are (d) on the $ac$ plane and (e) on a distorted kagome unit with Cu(2)/Cu(3) sites only.