Valence bond state in the delafossite YCuO_2.5

We take advantage of the precise determination of the crystallographic structure of complex magnetic systems with localized moments to calculate their exchange interaction values using ab initio methods. The magnetic interactions are mapped onto a Heisenberg model whose exchange interaction terms are fitted to first-principles total energy calculations for different spin configurations. This method is well adapted to systems with well defined local moments, as is often the case in oxides. We discuss the delafossite YCuO_2.5, with triangular layers of magnetic ions without magnetic ordering, and for which the magnetic interactions are unknown. Using these ab initio parameters, we perform exact diagonalization, which yields a valence bond solid ground state and shows excellent agreement with experimental magnetic susceptibility, provided that the different interactions between Cu₁ and Cu₂ atoms in the same triangle are taken into account.