  Rare-earth ion doped crystals have proven to be solid platforms for
implementing quantum memories. Their potential use for integrated photonics
with large multiplexing capability and unprecedented coherence times is at the
core of their attractiveness. The best performances of these ions are however
usually obtained when subject to a dc magnetic field, but consequences of such
fields on the quantum memory protocols have only received little attention. In
this article, we focus on the effect of a dc bias magnetic field on the
population manipulation of non-Kramers ions with nuclear quadrupole states,
both in the spin and optical domains, by developing a simple theoretical model.
We apply this model to explain experimental observations in a
${}^{151}$Eu:Y$_2$SiO$_5$ crystal, and highlight specific consequences on the
AFC spin-wave protocol. The developed analysis should allow to predict optimal
magnetic field configurations for various protocols.
