Inelastic-neutron-scattering study of the ${\mathrm{Er}}^{3+}$ energy levels in ${\mathrm{ErBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

Magnetic excitation spectra of ${\mathrm{ErBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ have been measured by use of inelastic neutron scattering. Optimal experimental conditions allow the resolution of the transitions between the ${\mathrm{Er}}^{3+}$ ground state and all seven excited states within the ${}_{}{}^4{}_{}{}^{}$ ${\mathit{I}}_{15/2}$ Russell-Saunders ground multiplet. The data are analyzed in terms of an intermediate-coupling crystal-field model, calculated using spherical-tensor techniques. Calculated spectra based on the results of this analysis are consistent with all experimental spectra, including those obtained at higher temperatures. The eigenfunctions and eigenvalues obtained from this analysis are used to calculate the magnetic properties expected of ${\mathrm{Er}}^{3+}$ in this crystal environment.