  We explore spin dynamics of isotopically purified $^{166}$Er:$^{7}$LiYF$_4$
crystal below 1 Kelvin and at weak magnetic fields $<$0.3 T. Crystals grown in
our lab demonstrate record-narrow inhomogeneous optical broadening down to
16~MHz. Solid state atomic ensembles with such narrow linewidths are very
attractive for the implementation of off-resonant Raman quantum memory and for
the interfacing of superconducting quantum circuits and telecom C-band optical
photons. Both applications require low magnetic field of $\sim10$ mT. However,
at conventional experimental temperatures $T>1.5$ K and time scales of $\mu$s,
spin coherence of Er:LYF crystal appears only at magnetic fields above 1 Tesla.
In the present work, we demonstrate spin coherence of Er:LYF crystals at the
field range compatible with ZEFOZ transitions of $^{167}$Er isotope and with
working conditions of superconducting quantum circuits.
