Gapped and gapless short-range-ordered magnetic states with(12,12,12)wave vectors in the pyrochlore magnetTb2+xTi2−xO7+δ

Abstract

Recent low-temperature heat capacity $({C}_{P})$ measurements on polycrystalline samples of the pyrochlore antiferromagnet ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2\ensuremath{-}x}{\mathrm{O}}_{7+\ensuremath{\delta}}$ have shown a strong sensitivity to the precise Tb concentration $x$, with a large anomaly exhibited for $x\ensuremath{\sim}0.005$ at ${T}_{C}\ensuremath{\sim}0.5$ K and no such anomaly and corresponding phase transition for $x\ensuremath{\le}0$. We have grown single-crystal samples of ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2\ensuremath{-}x}{\mathrm{O}}_{7+\ensuremath{\delta}}$, with approximate composition $x=\ensuremath{-}0.001,+0.0042$, 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 $x=\ensuremath{-}0.001$ nor the $x=+0.0147$ single crystals display any such anomaly. We present new time-of-flight neutron scattering measurements on the $x=\ensuremath{-}0.001$ 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 $\ensuremath{\sim}0.1$ 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 $0\ensuremath{\le}x\ensuremath{\le}0.01$ for ${\mathrm{Tb}}_{2+x}{\mathrm{Ti}}_{2\ensuremath{-}x}{\mathrm{O}}_{7+\ensuremath{\delta}}$, and is not obviously connected with conventional order of magnetic dipole degrees of freedom.