  We find clear signatures of spin-dependent negative differential resistance
in compound systems comprising a graphene nanoribbon and a set of ferromagnetic
insulator strips deposited on top of it. The periodic array of ferromagnetic
strips induces a proximity exchange splitting of the electronic states in
graphene, resulting in the appearance of a superlattice with a spin-dependent
energy spectrum. The electric current through the device can be highly
polarized and both the current and its polarization manifest non-monotonic
dependence on the bias voltage. The device operates therefore as an Esaki spin
diode, which opens possibilities to design new spintronic circuits.
