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We present a parametric study of the diffuse magnetic scattering at(1/2,1/2,1/2) positions in reciprocal space, ascribed to a frozenantiferromagnetic spin ice state in single crystalline Tb2Ti2O7. Ourhigh-resolution neutron scattering measurements show that the elastic (-0.02meV < 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 ofthe Brillouin zone. The concomitant low-lying magnetic spin excitations areweakly dispersive and appear to soften near the (1/2,1/2,1/2) wave vector at 80mK. The nature of the transition at 275 mK has many characteristics of spinglass behavior, consistent with ac-susceptibility measurements. The applicationof 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-rangeordered ground state. We construct a refined H-T phase diagram for Tb2Ti2O7 and[1-10] fields which incorporates this frozen spin ice regime and theantiferromagnetic long-range order previously known to be induced in relativelylarge fields. Specific heat measurements on the same crystal reveal a sharpanomaly at Tc~450 mK and no indication of a transition near ~275 mK. Weconclude that the higher temperature specific heat peak is not related to themagnetic ordering but is likely a signal of other, nonmagnetic, correlations.

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