Valence of praseodymium in ${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$: Inelastic-neutron-scattering, specific-heat, and susceptibility study

We present results of inelastic-neutron-scattering, specific-heat, and susceptibility measurements of ${\mathrm{Pr}}_{\mathit{x}}$ ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, where a transition from superconductor to an antiferromagnetic insulator with increasing Pr concentration occurs. The inelastic-neutron-scattering spectra confirm the prediction of the crystal-field (CF) splitting of the J=4 Hund’s-rule ground state, based on the superposition model: a ‘‘quasitriplet’’ ground state and six further singlets at energies larger than 60 meV. The local susceptibility extracted directly from the magnetic neutron spectra is in good agreement with the bulk susceptibility for both ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ and ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_6$. Moreover we show that the experimental specific-heat and susceptibility data can be interpreted consistently in terms of the standard crystal-field theory of ${\mathrm{Pr}}^{3+}$ based on the CF parameters extracted from the neutron data via the superposition model.