Anomalous magnetism in hydrogenated graphene

We revisit the problem of the local moment formation due to the functionalization of graphene by an individual chemisorbed Hydrogen atom. We first study the average spin magnetization as a function of the applied field, and we find that in the non-interacting case at $T=0$, the $m_s(H)$ curve is non-linear for small $H$ (at $T=0$) which makes it impossible to define a spin susceptibility. Second, we compute the net magnetic moment within the mean field Hubbard approximation. In contrast with all previous work that use finite simulation cells that give a magnetic moment of $S=1/2$, we use an embedding method that allows the modeling of a single impurity in infinite pristine graphene. Our results give a magnetic moment smaller than $1/2$. Our results highlight that the spin physics of a single Hydrogen is different from localized spin moments in gapped systems for which magnetic moment is quantized and from conductors, for which the $T=0$ spin susceptibility do exist.