It is generally believed that free-standing graphene does not demonstrate any ferroic properties. In the present work we revise this statement and show that single graphene sheet with a pair of magnetic adatoms can be driven into ferroelectric (FE) and multiferroic (MF) phases by tuning the Dirac cones slope. The transition into the FE phase occurs gradually, but an anomalous MF phase appears abruptly by means of a Quantum Phase Transition. Our findings suggest that such features should exist in graphene recently investigated by Scanning Tunneling Microscopy (Science 352, 437 (2016)).
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