Long-range order and spin-liquid states of polycrystalline Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$

Low-temperature states of polycrystalline samples of a frustrated pyrochlore oxide Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ have been investigated by specific heat, magnetic susceptibility, and neutron scattering experiments. We have found that this system can be tuned by a minute change of $x$ from a spin-liquid state ($x < x_{\text{c}}$) to a partly ordered state with a small antiferromagnetic ordering of the order of $0.1 \mu_{\text{B}}$. Specific heat shows a sharp peak at a phase transition at $T_{\text{c}}= 0.5$ K for $x=0.005$. Magnetic excitation spectra for this sample change from a quasielastic to a gapped type through $T_{\text{c}}$. The possibility of a Jahn-Teller transition is discussed.