Theory of the changes of bond lengths along thecaxis inYBa2Cu3O7−x

Abstract

The three bond lengths Cu(1)-O(4), Cu(2)-O(4), and Cu(2)-Cu(2) along the c axis in the high-temperature superconductor ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ are calculated as a function of the oxygen deficiency x. We use a Hubbard Hamiltonian with on-site Coulomb repulsions at all oxygen and copper orbitals treated in the Hartree-Fock approximation. Thus, we determine the x dependence of the electronic charge distribution and the electronic energy of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$. The Madelung energy is obtained by using the self-consistently determined charges. Then we calculate the three bond lengths for a given x from a minimization of the total energy. Our results agree with experimental data [J. D. Jorgensen et al., Phys. Rev. B 41, 1863 (1990)] and show that the change of the c-axis bond lengths in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ due to variations of x results from electronic charge transfer from the Cu-O chains to the ${\mathrm{CuO}}_2$ planes. This may help to analyze the dependence of the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ on the oxygen content and the c-axis bond lengths.