  The extreme versatility of two-dimensional van der Waals (vdW) materials
derives from their ability to exhibit new electronic properties when assembled
in proximity with dissimilar crystals. For example, although graphene is
inherently non-magnetic, recent work has reported a magnetic proximity effect
in graphene interfaced with magnetic substrates, potentially enabling a pathway
towards achieving a high-temperature quantum anomalous Hall effect. Here, we
investigate heterostructures of graphene and chromium trihalide magnetic
insulators (CrI$_3$, CrBr$_3$, and CrCl$_3$). Surprisingly, we are unable to
detect a magnetic exchange field in the graphene, but instead discover
proximity effects featuring unprecedented gate-tunability. The graphene becomes
highly hole-doped due to charge transfer from the neighboring magnetic
insulator, and further exhibits a variety of atypical transport features. These
include highly extended quantum Hall plateaus, abrupt reversals in the Landau
level filling sequence, and hysteresis over at least days-long time scales. In
the case of CrI$_3$, we are able to completely suppress the charge transfer and
all attendant atypical transport effects by gating. The charge transfer can
additionally be altered in a first-order phase transition upon switching the
magnetic states of the nearest CrI$_3$ layers. Our results provide a roadmap
for exploiting the magnetic proximity effect in graphene, and motivate further
experiments with other magnetic insulators.
