First-principles determination of Heisenberg Hamiltonian parameters for the spin- 1 2 kagome antiferromagnet ZnCu3(OH)6Cl2

Abstract:

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 −0.035J1 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.

........... Therefore we undertake an effort to determine the parameters of the underlying Heisenberg Hamiltonian using all-electron density functional theory (DFT) methods. We will show in this paper that the exchange coupling constants from first principles corroborate that ZnCu3(OH)6Cl2 is a near-perfect realization of a kagome antiferromagnet with a dominant coupling of J1 = 182 K. However, there are small corrections to this picture. A next-nearest-neighbor coupling in the kagome layer of 0.019J1 and in particular, some interplanar couplings between −0.035J1 and 0.029J1 could actually be relevant for the nature and excitations of the spin liquid ground state in herbertsmithite. We perform density functional theory calculations with the full potential local orbital (FPLO) basis set17 using the generalized gradient approximation (GGA)18 and GGA + U functionals. The exchange couplings Ji are obtained from total energy calculations for different Cu spin configurations in supercells of various sizes.

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http://itp.uni-frankfurt.de/~jeschke/papers/PhysRevB88p075106.pdf