Crystal-field splittings and magnetic properties of ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Nd}}^{3+}$ in R${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

Neutron inelastic scattering spectra are reported for superconducting ${\mathrm{NdBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ and insulating ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. These spectra are analyzed in terms of standard crystal-field theory for 3+ rare-earth ions in a manner that is consistent with the level assignments made in a similar study of ${\mathrm{HoBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. Using the eigenfunctions and eigenvalues obtained from this analysis of the inelastic neutron scattering spectra, the corresponding magnetic susceptibilities as a function of temperature were calculated according to the van Vleck formalism. Good agreement with experimental susceptibilities is achieved for all three compounds over the range of 100 to 300 K. The observed magnetic scattering in ${\mathrm{NdBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ agrees very well with the crystal-field calculations. In spite of the observed large intrinsic widths of the experimental crystal-field peaks for ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, the measured intensity is consistent with the calculated crystal-field excitation spectrum for ${\mathrm{Pr}}^{3+}$ ions in this lattice. The standard crystal-field treatment of ${\mathrm{Pr}}^{3+}$ ions is shown to explain the magnetic properties of ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ with no need to consider either the static or dynamic coexistence of ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Pr}}^{4+}$.