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

Abstract

We have measured the insulating energy gap \ensuremath{\Delta} 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 \ensuremath{\delta} log\ensuremath{\Delta}/ \ensuremath{\delta} logd\ensuremath{\sim}-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 \ensuremath{\Delta} and J in the cuprates allow us to estimate that the hopping energy t scales with Cu-O distance as \ensuremath{\delta} logt/\ensuremath{\delta} logd\ensuremath{\sim}-4.