Novel mechanism for weak magnetization with high Curie temperature observed in H-adsorption on graphene

To elucidate the physics underling magnetism observed in nominally nonmagnetic materials with only $sp$-electrons, we built an extreme model to simulate H-adsorption (in a straight-line form) on graphene. Our first principles calculations for the model produce a ferromagnetic ground state with a magnetic moment of one Bohr magneton per H atom and an estimated Curie temperature above 250~K. The removal of the $p_z$-orbitals from sublattice B of graphene introduces $p_z$-vacancies. The $p_z$-vacancy-induced states are not created from changes in interatomic interactions but are created because of a $p_z$-orbital imbalance between two sublattices (A and B) of a conjugated $p_z$-orbital network. Therefore, there are critical requirements for the creation of these states (denoted as $p_z^{\rm imbalance}$) to avoid further imbalances and minimize the effects on the conjugated $p_z$-orbital network. The requirements on the creation of $p_z^{\rm imbalance}$ are as follows: 1) $p_z^{\rm imbalance}$ consists of $p_z$-orbitals of only the atoms in sublattice A, 2) the spatial wavefunction of $p_z^{\rm imbalance}$ is antisymmetric, and 3) in principle, $p_z^{\rm imbalance}$ extends over the entire crystal without decaying, unless other $p_z$-vacancies are crossed. Both the origin of spin polarization and the magnetic ordering of the model arise from the aforementioned requirements.