Neutron-spectroscopic studies of the crystal field in ${\mathrm{ErBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathit{x}}$ (6≤x≤7)

Inelastic neutron scattering has been employed to study in detail the full crystalline-electric-field (CEF) energy scheme in the ground-state J multiplet of ${\mathrm{Er}}^{3+}$ in ${\mathrm{ErBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathit{x}}$ as a function of the oxygen content x. We have been able to resolve the seven ground-state transitions for a series of samples covering the superconducting phase as well as the semiconducting one. J-mixing and intermediate-coupling effects as well as geometrical considerations are shown to be necessary to determine unambiguously the nine CEF parameters of the orthorhombic symmetry. The large energy shifts and intensity changes of the observed CEF spectra as a function of the oxygen content x are shown to be related predominantly to a charge-transfer process from the chains to the planes, the actual charge transfer being in excellent agreement with results derived from bond-valence-sum considerations of diffraction data. The CEF parameters are also used to calculate the magnetization and the field-dependent Schottky anomaly of the heat capacity, which yields remarkable agreement with the experimental data. A mean-field calculation allows us to estimate the x dependence of the saturated moment of the ${\mathrm{Er}}^{3+}$ ion in the ordered phase, which perfectly agrees with the results obtained by means of Mössbauer measurements, but considerably deviates from diffraction values.