Probing the Magnetic State of a Kitaev Material with Graphene

Single layer $\alpha$-ruthenium trichloride ($\rm\alpha-RuCl_3$) has been proposed as a potential quantum spin liquid. Graphene/$\rm RuCl_3$ heterobilayers have been extensively studied with a focus on their large interlayer electron transfer driven by a chemical potential difference, which dopes both materials. Here we examine the possibility of probing the magnetic state of the \ce{RuCl_3} layer by measuring transport in an adjacent graphene layer. We perform self-consistent Hartree-Fock calculations on a Hubbard-Kanamori model of the $4d^5$ $t_{2g}$ electrons of $\rm \alpha-RuCl_3$ and confirm that out-of-plane ferromagnetic and zigzag antiferromagnetic states are energetically competitive. We show that the influence of hybridization between graphene and $\rm RuCl_3$ bands is strongly sensitive to the magnetic configuration of $\rm RuCl_3$ and the relative orientations of the two layers, and argue that it can alter the conductivity of the graphene layer. Our analysis can be applied to any van der Waals heterobilayer system with weak interlayer hybridization and allows for arbitrary lattice constant mismatch and relative orientation.