For about two decades, Tb2Ti2O7 has remained an enigma in condensed matter physics and frustrated magnetism.
For about two decades, Tb2Ti2O7 has remained an enigma in condensed matter physics and frustrated magnetism. This material evades long-range order down to temperature as low as 20 mK, and, as in spin ice, its ground state exhibits puzzling diffuse magnetic scattering. To shed light on this issue, we present spin dynamics measurements by inelastic neutron scattering, which we confront with random phase approximation calculations (RPA) to determine exchange couplings capable of reproducing the dispersion of the first excited crystal electric field level. These couplings suggest that Tb2Ti2O7 lives at the boundary between several phases, in particular the spin ice and planar antiferromagnetic ones.