Fig. 6. Structure and quantum magnetism of Zn-substituted barlowite.

a Structures of Zn-substituted barlowite and herbertsmithite showing their interlayer metal coordination environments. The top–down view of Zn-substituted barlowite displays the coexistence of the centered (D_3h) Zn²⁺ site and the set of triplicated off-center (C_2v) Cu²⁺ interlayer sites, visualized in VESTA⁷⁴. The top–down view of herbertsmithite shows its distinct interlayer coordination: there is only one site for both Zn²⁺ and Cu²⁺, and the kagome layers above and below the interlayer site are rotated by 60°. In the top–down views, the atoms are displayed as thermal ellipsoids at 90% probability. F, Br, Cl, and H are not shown. b DC susceptibility (X) measured in an applied field μ₀H = 7 T of polycrystalline Zn_0.95, a collection of single crystals of Zn_0.56, and polycrystalline herbertsmithite. Also plotted is an estimate of the intrinsic susceptibility of the Zn-substituted barlowite kagome lattice. The amount of Cu²⁺ magnetic impurities in the herbertsmithite sample is estimated at 15%²⁷. The inset shows the inverse susceptibility of the interlayer Cu²⁺ magnetic impurities; the line is a Curie–Weiss fit from T = 10–50 K with no diamagnetic correction X₀. c Aligned magnetization as a function of applied field for a 1.4 mg single crystal of Zn_0.56. d Temperature dependence of C/T for Zn_0.95 and eZn_0.56 in applied fields of μ₀H = 0–9 T. Note: 1 emu (mol Oe)⁻¹ = 4π10⁻⁶ m³ mol⁻¹.