Anomalous, spin, and valley Hall effects in graphene deposited on ferromagnetic substrates
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/ferromagnetic metal (cobalt or nickel), and (ii) graphene/magnetic insulator (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 are shown to have universal values when the Fermi level is inside the energy gap in the electronic spectrum.