Optical studies of gap, exchange, and hopping energies in the insulating cuprates

We have measured the insulating energy gap and the exchange interaction J in a series of cuprate crystals, including T-phase M2CuO4 (M=Pr, Nd, Sm, Eu, and Gd), T*-phase La,Tb,Sr2CuO4, and T-phase La2CuO4. We find that the energy gap scales predominantly with the in-plane Cu-O distance, scaling as loglogd-6. Furthermore, contrary to simple expectations, the energy gap increases with decreasing Cu-O distance, suggesting that Coulomb and other repulsive energies dominate the effects of band hybridization. Using a three-band Hubbard-model expression, our studies of and J in the cuprates allow us to estimate that the hopping energy t scales with Cu-O distance as logt/ logd-4.