Temperature and Magnetic Field Dependence of Spin Ice Correlations in the Pyrochlore Magnet Tb2Ti2O7

We present a parametric study of the diffuse magnetic scattering at (1/2,1/2,1/2) positions in reciprocal space, ascribed to a frozen antiferromagnetic spin ice state in single crystalline Tb2Ti2O7. Our high-resolution neutron scattering measurements show that the elastic (-0.02 meV < E < 0.02 meV) (1/2,1/2,1/2) scattering develops strongly below ~275 mK, and correlates with the opening of a spin gap of ~0.06-0.08 meV over most of the Brillouin zone. The concomitant low-lying magnetic spin excitations are weakly dispersive and appear to soften near the (1/2,1/2,1/2) wave vector at 80 mK. The nature of the transition at 275 mK has many characteristics of spin glass behavior, consistent with ac-susceptibility measurements. The application of a magnetic field of 0.075 T applied along the [1-10] direction destroys the (1/2,1/2,1/2) elastic scattering, revealing the fragility of this short-range ordered ground state. We construct a refined H-T phase diagram for Tb2Ti2O7 and [1-10] fields which incorporates this frozen spin ice regime and the antiferromagnetic long-range order previously known to be induced in relatively large fields. Specific heat measurements on the same crystal reveal a sharp anomaly at Tc~450 mK and no indication of a transition near ~275 mK. We conclude that the higher temperature specific heat peak is not related to the magnetic ordering but is likely a signal of other, nonmagnetic, correlations.