Recent low-temperature heat capacity $\left(C_P\right)$ measurements on polycrystalline samples of the pyrochlore antiferromagnet ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+\delta }$ have shown a strong sensitivity to the precise Tb concentration $x$, with a large anomaly exhibited for $x\sim 0.005$ at $T_C\sim 0.5$ K and no such anomaly and corresponding phase transition for $x\le 0$. We have grown single-crystal samples of ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+\delta }$, with approximate composition $x=-0.001,+0.0042$, and $+0.0147$, where the $x=0.0042$ single crystal exhibits a large $C_P$ anomaly at $T_C=0.45$ K, but neither the $x=-0.001$ nor the $x=+0.0147$ single crystals display any such anomaly. We present new time-of-flight neutron scattering measurements on the $x=-0.001$ and the $x=+0.0147$ samples which show strong $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ quasi-Bragg peaks at low temperatures characteristic of short-range antiferromagnetic spin ice (AFSI) order at zero magnetic field but only under field-cooled conditions, as was previously observed in our $x=0.0042$ single crystal. Furthermore, the frozen AFSI state displays a gapped spin excitation spectrum around $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$, with a gap of $\sim 0.1$ meV, again similar to previous observations on the $x=0.0042$ single crystal. These results show that the strong $\left(\frac{1}{2},\frac{1}{2},\frac{1}{2}\right)$ quasi-Bragg peaks and gapped AFSI state at low temperatures under field-cooled conditions are robust features of ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, and are not correlated with the presence or absence of the $C_P$ anomaly and phase transition at low temperatures. Further, these results show that the ordered state giving rise to the $C_P$ anomaly is confined to $0\le x\le 0.01$ for ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+\delta }$, and is not obviously connected with conventional order of magnetic dipole degrees of freedom.

• Received 23 October 2015

DOI:https://doi.org/10.1103/PhysRevB.92.245114