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Crystal and magnetic structures of the mineral centennialiteCaCu$_3$(OH)$_6$Cl$_2\cdot0.6$H$_2$O are investigated by means of synchrotronx-ray diffraction and neutron diffraction measurements complemented by densityfunctional theory (DFT) and pseudofermion functional renormalization group(PFFRG) calculations. CaCu$_3$(OH)$_6$Cl$_2\cdot0.6$H$_2$O crystallizes in the$P\bar{3}m1$ space group and Cu$^{2+}$ ions form a geometrically perfect kagomenetwork with antiferromagnetic $J_1$. No intersite disorder between Cu$^{2+}$and Ca$^{2+}$ ions is detected. CaCu$_3$(OH)$_6$Cl$_2\cdot0.6$H$_2$O enters amagnetic long-range ordered state below $T_\text{N}=7.2$~K, and the$\mathbf{q}=\mathbf{0}$ magnetic structure with negative vector spin chiralityis obtained. The ordered moment at 0.3~K is suppressed to$0.58(2)\mu_\text{B}$. Our DFT calculations indicate the presence ofantiferromagnetic $J_2$ and ferromagnetic $J_d$ superexchange couplings of astrength which places the system at the crossroads of three magnetic orders (atthe classical level) and a spin-$\frac{1}{2}$ PFFRG analysis shows a dominanceof $\mathbf{q}=\mathbf{0}$ type magnetic correlations, consistent with andindicating proximity to the observed $\mathbf{q}=\mathbf{0}$ spin structure.The results suggest that this material is located close to a quantum criticalpoint and is a good realization of a $J_1$-$J_2$-$J_d$ kagome antiferromagnet.

physical review. b./physical review. b

$\mathbf{q}=\mathbf{0}$ long-range magnetic order in centennialite  CaCu$_3$(OD)$_6$Cl$_2$$\cdot$0.6D$_2$O: A spin-1/2 perfect kagome  antiferromagnet with $J_1$-$J_2$-$J_d$