Crystal-field spectrum in RBa₂Cu₃O_x (R = Er, Ho) high-T_c superconductors: Evidence for charge order in CuO₂ planes

A model of the crystal field generated by aperiodic array of charged tapes is developed to analyse the crystal-field interaction in RBa₂Cu_xO_x (R = Er, Ho) high-T_c copper oxides observed by the inelastic neutron scattering technique. The explicit calculation of the parameters of the Stevens Hamiltonian describing crystalline electric field effects in solids is performed for a specific charge density distribution uniformly extended in a certain direction of the crystal lattice. The model accounts for the x-dependence of the crystal-field parameters and allows us to determine the hole concentration in the CuO₂ planes as a function of oxygen stoichiometry. The model of the periodic array of charged tapes suggests a charge order induced in the CuO₂ planes by doping.