  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.

Strongly Correlated Electrons;Disordered Systems and Neural Networks