  Gate-induced magnetic switching in bilayer CrI$_3$ has opened new ways for
the design of novel low-power magnetic memories based on van der Waals
heterostructures. The proposed switching mechanism seems to be fully dominated
by electrostatic doping. Here we explain, by first-principle calculations, the
ferromagnetic transition in doped bilayer CrI$_3$. For the case of a very small
electron doping, our calculations predict the formation of magnetic polarons
("ferrons", "fluctuons") where the electron is self-locked in a ferromagnetic
droplet in an antiferromagnetic insulating matrix. The self-trapping of holes
is impossible, at least, within our approximation.
