Determination of superexchange interactions for the CuO2 chains in LiCu2O2

Abstract

Starting from ab initio calculations, we derive a five-band Hubbard model to describe the ${\mathrm{CuO}}_{2}$ chains of ${\mathrm{LiCu}}_{2}{\mathrm{O}}_{2}$. This model is further simplified to a low-energy effective Heisenberg model with nearest-neighbor ${J}_{1}$ and next-nearest-neighbor ${J}_{2}$ interactions, combining perturbation theory, exact diagonalization calculations, and density matrix renormalization group results. For realistic parameters we find the corresponding values of these interactions. The obtained effective model is consistent with a spiral-magnetic ground state as experimentally observed. Using symmetry arguments, the spiral state is a sufficient condition for the ferroelectricity observed in the system.