  Over the past two decades, the magnetic ground states of all rare earth
titanate pyrochlores have been extensively studied, with the exception of
Sm$_2$Ti$_2$O$_7$. This is, in large part, due to the very high absorption
cross-section of naturally-occurring samarium, which renders neutron scattering
infeasible. To combat this, we have grown a large, isotopically-enriched single
crystal of Sm$_2$Ti$_2$O$_7$. Using inelastic neutron scattering, we determine
that the crystal field ground state for Sm$^{3+}$ is a dipolar-octupolar
doublet with Ising anisotropy. Neutron diffraction experiments reveal that
Sm$_2$Ti$_2$O$_7$ orders into the all-in, all-out magnetic structure with an
ordered moment of 0.44(7) $\mu_B$ below $T_N=0.35$ K, consistent with
expectations for antiferromagnetically-coupled Ising spins on the pyrochlore
lattice. Zero-field muon spin relaxation measurements reveal an absence of
spontaneous oscillations and persistent spin fluctuations down to 0.03 K. The
combination of the dipolar-octupolar nature of the Sm$^{3+}$ moment, the
all-in, all-out ordered state, and the low-temperature persistent spin dynamics
make this material an intriguing candidate for moment fragmentation physics.
