  Spin, anomalous, and valley Hall effects in graphene-based hybrid structures
are studied theoretically within the Green function formalism and linear
response theory. Two different types of hybrid systems are considered in
detail: (i) graphene/boron nitride/cobalt(nickel), and (ii) graphene/YIG. The
main interest is focused on the proximity-induced exchange interaction between
graphene and magnetic substrate and on the proximity-enhanced spin-orbit
coupling. The proximity effects are shown to have a significant influence on
the electronic and spin transport properties of graphene. To find the spin,
anomalous and valley Hall conductivities we employ certain effective
Hamiltonians which have been proposed recently for the hybrid systems under
considerations. Both anomalous and valley Hall conductivities have universal
values when the Fermi level is inside the energy gap in the electronic
spectrum.
