Gapped and gapless short range ordered magnetic states with (1/2,1/2,1/2) wavevectors in the pyrochlore magnet Tb₂₊ₓTi₂₋ₓO₇₊δ

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Recent low temperature heat capacity (Cₚ) measurements on polycrystalline samples of the pyrochlore antiferromagnet Tb₂₊ₓTi₂₋ₓO₇₊δ have shown a strong sensitivity to the precise Tb concentration x, with a large anomaly exhibited for x 0.005 at TC 0.5 K and no such anomaly and corresponding phase transition for x ≤ 0. We have grown single crystal samples of Tb₂₊ₓTi₂₋ₓO₇₊δ, with approximate composition x=-0.001, +0.0042, and +0.0147, where the x=0.0042 single crystal exhibits a large Cₚ anomaly at TC=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 (1/2,1/2,1/2) 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. These results show that the strong (1/2,1/2,1/2) quasi-Bragg peaks and gapped AFSI state at low temperatures under field cooled conditions are robust features of Tb₂Ti₂O₇, and are not correlated with the presence or absence of the Cₚ anomaly and phase transition at low temperatures. Further, these results show that the ordered state giving rise to the Cₚ anomaly is confined to 0 ≤ x ≤ 0.01 for Tb₂₊ₓTi₂₋ₓO₇₊δ, and is not obviously connected with conventional order of magnetic dipole degrees of freedom.