We study electronic transport in systems comprising square graphene nanorings with a ferromagnetic insulator layer on top of them. The rings are connected symmetrically or asymmetrically to contacts. The proximity exchange interaction of electrons with agnetic ions results in spin-dependent transport properties. When a nanoring is connected asymmetrically, the occurrence of Fano-like antiresonances in the transmission coefficient can induce abrupt changes in the spin polarisation under minute variations of the Fermi energy. We also demonstrate that the spin polarization can be efficiently controlled by a side-gate voltage. This opens a possibility to use these effects for fabricating tunable sources of polarised electrons.
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