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Examples of materials where an "order by disorder" mechanism is at play toselect a particular ground state are scarce. It has recently been proposed,however, that the antiferromagnetic XY pyrochlore Er2Ti2O7, reveals a mostconvincing case of this mechanism. Observation of a spin gap at zone centershas recently been interpreted as a corroboration of this physics. In thispaper, we argue, however, that the anisotropy generated by theinteraction-induced admixing between the crystal-field ground and excitedlevels provides for an alternative mechanism. It especially predicts theopening of a spin gap of about 15 micro-eV, which is of the same order ofmagnitude as the one observed experimentally. We report new high resolutioninelastic neutron scattering data which can be well understood within thisscenario.

Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study