Disordered Quantum Spin Ice Ground State of Tb$_2$Sn$_{2-x}$Ti$_x$O$_7$

Inelastic neutron scattering, AC magnetic susceptibility and $\mu$SR measurements have been performed on polycrystalline solid solutions of the pyrochlore magnet, Tb$_2$Sn$_{2-x}$Ti$_x$O$_7$ for seven samples with x between 0 and 2. These measurements probe the crystal field states, low energy spin dynamics and phase behavior to temperatures less than 0.1K. Tb$_2$Ti$_2$O$_7$ is proposed to display a quantum variant of the spin ice ground state, stabilized by virtual excitations between the Tb$^{3+}$ crystal field ground state doublet and its low lying excited state doublet. Isostructural, Tb$_2$Sn$_2$O$_7$, displays ``soft'' spin ice order and its Tb$^{3+}$ ground and excited crystal field states are known to be interchanged relative to those in Tb$_2$Ti$_2$O$_7$. These measurements of the solid solutions of Tb$_2$Sn$_{2-x}$Ti$_x$O$_7$ focus on crystal field excitations between 1meV and 50meV, and show greatly enhanced spin dynamics at low energies for samples with intermediate x. All magnetic order is absent for x$>$0.1, leaving behind a highly fluctuating, disordered spin ice ground state.