We have measured the insulating energy gap Δ and the exchange interaction J in a series of cuprate crystals, including T’-phase ${\mathit{M}}_2$${\mathrm{CuO}}_4$ (M=Pr, Nd, Sm, Eu, and Gd), ${\mathit{T}}^{\mathrm{*}}$-phase La,Tb,${\mathrm{Sr}}_2$${\mathrm{CuO}}_4$, and T-phase ${\mathrm{La}}_2$${\mathrm{CuO}}_4$. We find that the energy gap scales predominantly with the in-plane Cu-O distance, scaling as δ logΔ/ δ logd∼-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 Δ and J in the cuprates allow us to estimate that the hopping energy t scales with Cu-O distance as δ logt/δ logd∼-4.

• Received 12 June 1990

DOI:https://doi.org/10.1103/PhysRevB.42.10785