Low-Temperature Low-Field Phases of the Pyrochlore Quantum Magnet Tb$_2$Ti$_2$O$_7$

By means of ac magnetic-susceptibility measurements, we have found evidence for a new magnetic phase of Tb$_2$Ti$_2$O$_7$ below about 140~mK in zero magnetic field. In magnetic fields parallel to [111], this phase---exhibiting frequency- and amplitude-dependent susceptibility and an extremely slow spin dynamics---extends to about 70~mT, at which it gives way to another phase. The field dependence of the susceptibility of this second phase, which extends to about 0.6~T, indicates the presence of a weak magnetization plateau below 50~mK, as has been predicted by a single-tetrahedron four-spin model, giving support to the underlying proposal that the disordered low-field ground state of Tb$_2$Ti$_2$O$_7$ is a quantum spin ice.