Crystal-field interaction in the pyrochlore magnet $Ho_2Ti_2O_7$

Neutron time-of-flight spectroscopy has been employed to study the crystal-field interaction in the pyrochlore titanate $Ho_2Ti_2O_7$. The crystal-field parameters and corresponding energy-level scheme have been determined from a profile fit to the observed neutron spectra. The ground state is a well separated $E_g$ doublet with a strong Ising-like anisotropy, which can give rise to frustration in the pyrochlore lattice. Using the crystal-field parameters determined for the Ho compound as an estimate of the crystal-field potential in other pyrochlore magnets, we also find the Ising type behavior for Dy. In contrast, the almost planar anisotropy found for Er and Yb prevents frustration, because of the continuous range of possible spin orientations in this case