Ferromagnetic phase in graphene-based planar heterostructures induced by charged impurity

The spontaneous self-consistent generation of axial current and corresponding dipole-like magnetic field in a planar electron-positron system similar to graphene and related hetero-structures doped by charged impurity with charge $Z$ is explored. It is shown that this effect takes place for $Z \geq Z^{\ast}$ with $Z^{\ast}$ being a peculiar analogue of the Curie point in ferromagnetics. The properties of induced ferromagnetic state are studied in detail. It is shown also that the arising this way magnetic dipole leads to a significant decrease of the total Casimir (vacuum) energy of the system, which in turn provides its spontaneous generation above the "Curie point" $Z \geq Z^{\ast}$.