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Impurity-induced magnetic moments on the graphene-lattice Hubbard model: an inhomogeneous cluster DMFT study

Defect-induced magnetic moments are at the center of the research effort on spintronic applications of graphene. Here we study the problem of a nonmagnetic impurity in graphene with a new theoretical method, inhomogeneous cluster dynamical mean field theory (I-CDMFT), which takes into account interaction-induced short-range correlations while allowing long-range inhomogeneities. The system is described by a Hubbard model on the honeycomb lattice. The impurity is modeled by a local potential. For a large enough potential, interactions induce local antiferromagnetic correlations around the impurity and a net total spin $\frac12$ appears, in agreement with Lieb's theorem. Bound states caused by the impurity are visible in the local density of states (LDOS) and have their energies shifted by interactions in a spin-dependent way, leading to the antiferromagnetic correlations. Our results take into account dynamical correlations; nevertheless they qualitatively agree with previous mean-field and density functional theory (DFT) studies. Moreover, they provide a relation between impurity potential and on-site repulsion $U$ that could in principle be used to determine experimentally the value of $U$.