First-principles determination of Heisenberg Hamiltonian parameters for the spin-12 kagome antiferromagnet ZnCu³(OH)⁶Cl²

Herbertsmithite [ZnCu³(OH)⁶Cl²] is often discussed as the best realization of the highly frustrated antiferromagnetic kagome lattice known so far. We employ density functional theory (DFT) calculations to determine eight exchange coupling constants of the underlying Heisenberg Hamiltonian. We find the nearest-neighbor coupling J₁ to exceed all other couplings by far. However, next-nearest-neighbor kagome layer couplings of 0.019J₁ and interlayer couplings of up to -0.035J ₁ slightly modify the perfect antiferromagnetic kagome Hamiltonian. Interestingly, the largest interlayer coupling is ferromagnetic, even without Cu impurities in the Zn layer. In addition, we validate our DFT approach by applying it to kapellasite, a polymorph of herbertsmithite, which is known experimentally to exhibit competing exchange interactions.