$\mathbf{q}=0$ 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 $J_1$-$J_2$-$J_d$

Abstract

Crystal and magnetic structures of the mineral centennialite CaCu${}_3$(OH)${}_6$Cl${}_2\cdot 0.6$H${}_2$O are investigated by means of synchrotron x-ray diffraction and neutron diffraction measurements complemented by density functional theory (DFT) and pseudofermion functional renormalization group (PFFRG) calculations. CaCu${}_3$(OH)${}_6$Cl${}_2\cdot 0.6$H${}_2$O crystallizes in the $P\bar{3}m1$ space group and Cu${}^{2+}$ ions form a geometrically perfect kagome network with antiferromagnetic $J_1$. No intersite disorder between Cu${}^{2+}$ and Ca${}^{2+}$ ions is detected. CaCu${}_3$(OH)${}_6$Cl${}_2\cdot 0.6$H${}_2$O enters a magnetic long-range ordered state below $T_{\text{N}}=7.2$~K, and the $\mathbf{q}=0$ magnetic structure with negative vector spin chirality is obtained. The ordered moment at 0.3~K is suppressed to $0.58(2)\hat{I}{¼}_{\text{B}}$. Our DFT calculations indicate the presence of antiferromagnetic $J_2$ and ferromagnetic $J_d$ superexchange couplings of a strength which places the system at the crossroads of three magnetic orders (at the classical level) and a spin-$\frac{1}{2}$ PFFRG analysis shows a dominance of $\mathbf{q}=0$ type magnetic correlations, consistent with and indicating proximity to the observed $\mathbf{q}=0$ spin structure. The results suggest that this material is located close to a quantum critical point and is a good realization of a $J_1$-$J_2$-$J_d$ kagome antiferromagnet.

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