Anomalous magnetism in hydrogenated graphene

We revisit the problem of local moment formation in graphene due to chemisorption of individual atomic hydrogen or other analogous sp$^3$ covalent functionalizations. We describe graphene with the single orbital Hubbard model, so that the H chemisorption is equivalent to a vacancy in the honeycomb lattice. In order to circumvent artefacts related to periodic unit cells, we use either huge simulation cells of up to $8\times10^5$ sites, or an embedding scheme that allows the modelling of a single vacancy in an otherwise pristine infinite honeycomb lattice. We find three results that stress the anomalous nature of the magnetic moment ($m$) in this system. First, in the non-interacting ($U=0$), zero temperature ($T=0$) case, the $m(B)$ is a continuous smooth curve with divergent susceptibility, different from the step-wise constant function found for a single unpaired spins in a gapped system. Second, for $U=0$ and $T>0$, the linear susceptibility follows a power law $\propto{T}^{-\alpha}$ with an exponent of $\alpha=0.77$ different from conventional Curie's law. For $U>0$, in the mean field approximation, the integrated moment is smaller than $m=1\mu_B$, in contrast with results using periodic unit cells. These three results highlight that the magnetic response of the local moment induced by sp$^3$ functionalizations in graphene is different both from that of local moments in gaped systems, for which the magnetic moment is quantized and follows a Curie law, and from Pauli paramagnetism in conductors, for which a linear susceptibility can be defined at $T=0$.