Determination of superexchange interactions for the CuO2 chains in LiCu2O2

Starting from ab initio calculations, we derive a five-band Hubbard model to describe the CuO2 chains of LiCu2O2. This model is further simplified to a low-energy effective Heisenberg model with nearest-neighbor J1 and next-nearest-neighbor J2 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.