  $\mathrm {^{151}Eu^{3+}}$-doped yttrium silicate ($\mathrm
{^{151}Eu^{3+}:Y_2SiO_5}$ ) crystal is a unique material that possesses
hyperfine states with coherence time up to 6 h. Many efforts have been devoted
to the development of this material as optical quantum memories based on the
bulk crystals, but integrable structures (such as optical waveguides) that can
promote $\mathrm {^{151}Eu^{3+}:Y_2SiO_5}$-based quantum memories to practical
applications, have not been demonstrated so far. Here we report the fabrication
of type 2 waveguides in a $\mathrm {^{151}Eu^{3+}:Y_2SiO_5}$ crystal using
femtosecond-laser micromachining. The resulting waveguides are compatible with
single-mode fibers and have the smallest insertion loss of $4.95\ dB$.
On-demand light storage is demonstrated in a waveguide by employing the
spin-wave atomic frequency comb (AFC) scheme and the revival of silenced echo
(ROSE) scheme. We implement a series of interference experiments based on these
two schemes to characterize the storage fidelity. Interference visibility of
the readout pulse is $0.99\pm 0.03$ for the spin-wave AFC scheme and $0.97\pm
0.02$ for the ROSE scheme, demonstrating the reliability of the integrated
optical memory.
