Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb$_2$Ti$_2$O$_7$

The ground state of the candidate spin liquid pyrochlore magnet Tb$_2$Ti$_2$O$_7$ (TTO) has been long debated. Despite theoretical expectations of magnetic order below 1K based on classical Ising-like Tb spins, muSR and neutron scattering experiments show no long range order down to 50mK. Two theoretical scenarios have been put forward to account for this: the quantum spin ice scenario and a non-magnetic singlet ground state, but no clear consensus has been reached. We present neutron scattering measurements on TTO at 70mK that reveal elastic scattering intensity at (1/2,1/2,1/2) positions in reciprocal space[1]. The corresponding spin configuration can be modeled as a short-range antiferromagnetically ordered spin ice, in which spins obey a variant of the ice rules in each unit cell, and flip directions between adjacent cells. At low temperatures, this elastic scattering is separated from low-lying magnetic inelastic scattering by $\sim$0.05meV. The elastic signal disappears under the application of small magnetic fields and upon elevating temperature. Pinch-point-like elastic diffuse scattering is observed, which together with the elastic spin ice correlations strongly supports the quantum spin ice picture for TTO. [1] K. Fritsch et al., arXiv:1210.1242[cond-mat.str-el]