  Rare-earth ion-doped crystals are of great interest for quantum memories, a
central component in future quantum repeaters. To assess the promise of 1$\%$
Tm$^{3+}$-doped yttrium gallium garnet (Tm:YGG), we report measurements of
optical coherence and energy-level lifetimes of its $^3$H$_6$ $\leftrightarrow$
$^3$H$_4$ transition at a temperature of around 500 mK and various magnetic
fields. Using spectral hole burning, we find hyperfine ground-level (Zeeman
level) lifetimes of several minutes at magnetic fields of less than 1000 G. We
also measure coherence time exceeding one millisecond using two-pulse photon
echoes. Three-pulse photon echo and spectral hole burning measurements reveal
that due to spectral diffusion, the effective coherence time reduces to a few
$\mu$s over a timescale of around two hundred seconds. Finally, temporal and
frequency-multiplexed storage of optical pulses using the atomic frequency comb
protocol is demonstrated. Our results suggest Tm:YGG to be promising for
multiplexed photonic quantum memory for quantum repeaters.
