(color online) (a) Top view of the Cu₃Zn(OH)₆FBr crystal structure, where F (brown) is in the center between two hexagons of two kagome Cu planes. (b) Magnetic field dependence of the spin gap. The black short-dash line is fitted by Δ(B) = Δ(0) − gμ_BSB with spin quantum number S = 1/2, where g-factor obtained from bulk magnetic susceptibility is g = 2.4 and μ_B is the Bohr magneton. For comparison, Δ(B) for S = 1 is shown by the blue dash line constrained by the value at 0.914 T, which hardly describes the data. Inset shows the Arrhenius plot of ¹⁹ K − K_chem with the vertical axis in logarithmic scale, which demonstrates visually that the gap decreases with increasing magnetic field. The solid curve is the fitting function A exp(−Δ/T) for ¹⁹ K − K_chem.^[7]