We demonstrate that electronic and magnetic properties of graphene can be tuned via proximity of multiferroic substrate. Our first-principles calculations performed both with and without spin-orbit coupling clearly show that by contacting graphene with bismuth ferrite BiFeO$_3$ (BFO) film, the spin-dependent electronic structure of graphene is strongly impacted both by the magnetic order and by electric polarization in the underlying BFO. Based on extracted Hamiltonian parameters obtained from the graphene band structure, we propose a concept of six-resistance device based on exploring multiferroic proximity effect giving rise to significant proximity electro- (PER), magneto- (PMR), and multiferroic (PMER) resistance effects. This finding paves a way towards multiferroic control of magnetic properties in two dimensional materials.
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