Gapped and gapless short range ordered magnetic states with $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ wavevectors in the pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+\delta }$

Abstract

Recent low temperature heat capacity (C${}_P$) measurements on polycrystalline samples of the pyrochlore antiferromagnet Tb${}_{2+x}$Ti${}_{2-x}$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 Tb${}_{2+x}$Ti${}_{2-x}$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. 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 Tb${}_2$Ti${}_2$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 Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+\delta }$, and is not obviously connected with conventional order of magnetic dipole degrees of freedom.

7 pages, 3 figures