Neutron spectroscopic determination of the crystalline electric field in ${\mathrm{HoBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

Inelastic neutron scattering has been employed to study the crystalline electric field (CEF) interaction in the high-$T_c$ superconductor ${\mathrm{HoBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. The CEF at the Ho site completely lifts the 17-fold degeneracy of the ground-state J multiplet. The observed energy spectra exhibit a large number of well-resolved CEF transitions between 0.5 and 73 meV, so that we have been able to assign the energies of ten excited CEF levels. On the basis of the observed intensities we have been able to unambiguously determine all nine CEF parameters required for orthorhombic symmetry. The CEF parameters turn out to be incompatible with any kind of point-charge calculation as expected. The results are used to predict the magnetization and the field-dependent Schottky anomaly of the heat capacity of ${\mathrm{HoBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ as well as to extrapolate the CEF interaction to ${\mathrm{ErBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, which yields good agreement with the experimental data.