Crystal-field excitations in ${\mathrm{Nd}}_2$${\mathrm{CuO}}_4$, ${\mathrm{Pr}}_2$${\mathrm{CuO}}_4$, and related n-type superconductors

We report on a inelastic-neutron-scattering study of the crystal-field excitations in ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_4$ and ${\mathrm{Pr}}_2$ ${\mathrm{CuO}}_4$, and in the related electron-doped, high-temperature superconductors ${\mathrm{Nd}}_{1.85}$ ${\mathrm{Ce}}_{0.15}$ ${\mathrm{CuO}}_4$, ${\mathrm{Pr}}_{1.85}$ ${\mathrm{Ce}}_{0.15}$ ${\mathrm{CuO}}_4$, and ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_{3.7}$ ${\mathrm{F}}_{0.3}$. The crystal-field splittings of the ground-state multiplet were studied in each of the compounds and supplementary information on the crystal field was obtained from intermultiplet excitations measured in the energy range 250–300 meV. We present a detailed theoretical analysis of the crystal field in the nonsuperconducting compounds. The calculations employ a spherical-tensor technique which allows for the mixing of the intermediate-coupling ground state with all excited J multiplets up to an energy of 2 eV. We have also incorporated a molecular-field term into the model to account for exchange interactions. We propose consistent crystal-field parameters for ${\mathrm{Nd}}_2$ ${\mathrm{CuO}}_4$ and ${\mathrm{Pr}}_2$ ${\mathrm{CuO}}_4$, which achieve good agreement between the calculated and experimental transition energies, intensities, and magnetic susceptibilities. The excitation spectra of the superconducting compounds are found to exhibit some features in common, and we have deduced the presence of a molecular-field interaction with a magnitude of 0.10 meV in ${\mathrm{Nd}}_{1.85}$ ${\mathrm{Ce}}_{0.15}$ ${\mathrm{CuO}}_4$.