Doping states in a two-dimensional three-band Peierls-Hubbard model for the copper oxides are investigated with inhomogeneous Hartree-Fock (HF) and random-phase approximations. The doping states are sensitive to small changes of interaction parameters because they easily change local energy balance between different interactions around added holes. For the parameter values derived from constrained-density-functional methods for the copper oxides, added holes form isolated small ferromagnetic polar- ons. When the parameters are varied around these values, different types of doping states are obtained: For stronger on-site repulsion at Cu sites, larger ferromagnetic polarons are formed, which are qualitatively different from the small polarons; for stronger nearest-neighbor Cu-O repulsion, polarons are clumped or there occurs phase separation into Cu- and O-hole-rich regions; Intersite electron-lattice coupling rapidly changes the small polarons by quenching a Cu magnetic moment and locally distorting the lattice in an otherwise undistorted antiferromagnetic background. This is regarded as a rapid crossover from a Zhang-Rice singlet to a covalent molecular singlet, and occurs substantially below a critical strength for destruction of the stoichiometric antiferromagnetic state. However intrasite electron-lattice coupling, in contrast to the intersite coupling, does not dramatically affect the hole-doping states. Doping induces modes in magnetic, optical, and vibronic response functions. Local infrared-active phonon modes are induced in infrared absorption spectra for finite electron-lattice coupling. They are correlated with doping-induced particle-hole excitations observed in optical absorption spectra and in magnetic excitation spectra. These doping-induced particle-hole excitations are associated with the local HF eigenstates in the charge-transfer gap. Each doping state has distinctive excitation spectra in the magnetic, optical, and vibronic channels. In particular, the hole-doping states with small polarons have doping-induced, infrared absorption peaks on the low-frequency side of the stoichiometric peak, while the electron-doping states have them on the high-frequency side.

• Received 24 September 1992

DOI:https://doi.org/10.1103/PhysRevB.47.12059