Weak ferromagnetism of antiferromagnetic domains in graphene with defects

Magnetic properties of graphene with randomly distributed magnetic defects/vacancies are studied in terms of the Kondo Hamiltonian in the mean field approximation. It has been shown that graphene with defects undergoes a magnetic phase transition from a paramagnetic to a antiferromagnetic (AFM) phase once the temperature reaches the critical point $T_{N}$. The defect straggling is taken into account as an assignable cause of multiple nucleation into AFM domains. Since each domain is characterized by partial compensating magnetization of the defects associated with different sublattices, together they reveal a super-paramagnetic behavior in a magnetic field. Theory qualitatively describe the experimental data provided the temperature dependence of the AFM domain structure.