  We propose spin valves where a 2D non-magnetic conductor is intercalated
between two ferromagnetic insulating layers. In this setup, the relative
orientation of the magnetizations of the insulating layers can have a strong
impact on the in-plane conductivity of the 2D conductor. We first show this for
a graphene bilayer, described with a tight-binding model, placed between two
ferromagnetic insulators. In the anti-parallel configuration, a band gap opens
at the Dirac point, whereas in the parallel configuration, the graphene bilayer
remains conducting. We then compute the electronic structure of graphene
bilayer placed between two monolayers of the ferromagnetic insulator CrI$_3$,
using density functional theory. Consistent with the model, we find that a gap
opens at the Dirac point only in the antiparallel configuration.
