Evidence of tunable magnetic coupling in hydrogenated graphene

A lot of efforts have been devoted to understanding the origin and effects of magnetic moments induced in graphene with carbon atom vacancy, or light adatoms like hydrogen or fluorine. At the meantime, the large negative magnetoresistance (MR) widely observed in these systems is not well understood, nor had it been associated with the presence of magnetic moments. In this paper, we study the systematic evolution of the large negative MR of in-situ hydrogenated graphene in ultra-high vacuum (UHV) environment. We find for most combination of electron density ($n_e$) and hydrogen density ($n_H$), MR at different temperature can be scaled to $\alpha=(\mu_BB)/[k_B(T-T^*)]$, where $T^*$ is the Curie-Weiss temperature. The sign of $T^*$ indicates the existence of tunable ferromagnetic-like ($T^* >0$) and anti-ferromagnetic-like ($T^* <0$) coupling in hydrogenated graphene. However, the lack of hysteresis of MR or anomalous Hall effect below $|T^*|$ points to the fact that long-range magnetic order did not emerge, which we attribute to the competition of different magnetic orders and disordered arrangement of magnetic moments on graphene. We also find that localized impurity states introduced by H adatoms could modify the capacitance of hydrogenated graphene. This work provides a new way to extract information from large negative MR behavior and can be a key to help understanding interactions of magnetic moments in graphene.