Theory of proximity induced exchange coupling in graphene on hBN/(Co, Ni)

A route towards an applicable spintronics device are van der Waals heterostructures\footnote{A. K. Geim and I. V. Grigorieva, Nature 499, 419 (2013).} with two-dimensional materials, such as graphene and hexagonal boron nitride (hBN). We perform systematic first-principles calculations of the proximity exchange coupling, induced by cobalt and nickel in graphene, via a few layers of hBN. We find that the induced spin splitting of the graphene bands is significant, even for two layers of hBN. By employing a pseudospin-dependent exchange model Hamiltonian, we can describe the first-principles data. This model can be used to study transport in graphene with proximity exchange\footnote{K. Zollner, M. Gmitra, T. Frank, and J. Fabian, Phys. Rev. B 94, 155441 (2016).}. We will also present more recent data on the proximity exchange in other two-dimensional materials and topological insulators.