The magnetic properties of zig-zag graphene nanoflakes (ZGNF) are investigated within the framework of the dynamical mean-field theory. At half-filling and for realistic values of the local interaction, the ZGNF is in a fully compensated antiferromagnetic (AF) state, which is found to be robust against temperature fluctuations. Introducing charge carriers in the AF background drives the ZGNF metallic and stabilizes a magnetic state with a net uncompensated moment at low temperature. The change in magnetism is ascribed to the delocalization of the doped holes in the proximity of the edges, which mediate ferromagnetic correlations between the localized magnetic moments. Depending on the hole concentration, the magnetic transition may display a pronounced hysteresis over a wide range of temperature, indicating the coexistence of magnetic states with different symmetry. This suggests the possibility of achieving the electrostatic control of the magnetic state of ZGNFs to realize a switchable spintronic device.
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