We present a parametric study of the diffuse magnetic scattering at $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ positions in reciprocal space, ascribed to a frozen antiferromagnetic spin ice state in single-crystalline ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Our high-resolution neutron scattering measurements show that the elastic $(-0.02$ meV $<E<0.02$ meV) $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ scattering develops strongly below $\approx$275 mK, and correlates with the opening of a spin gap of $\approx 0.06$ to 0.08 meV over most of the Brillouin zone. 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 $\left[1\overline{1}0\right]$ direction destroys the $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ elastic scattering, revealing the fragility of this short-range ordered ground state. We construct a refined $H$-$T$ phase diagram for ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and $\left[1\overline{1}0\right]$ 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 $T_{\mathrm{c}}\approx$ 450 mK and no indication of a transition near $\approx$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 dipole correlations.

• Received 29 November 2013
• Revised 20 June 2014

DOI:https://doi.org/10.1103/PhysRevB.90.014429