Possible high-spin states in hydrogenated C 60 molecules

Atoms with principal quantum number smaller than 2 are traditionally regarded to be nonmagnetic, but recent appealing advances in the understanding of ferromagnetism in materials such as graphene nanoribbons with zigzag edges and triangular graphene nanoflakes pave a novel way to investigate magnetism in materials merely with $s$ and $p$ orbitals. Opening the $p$ shell turns out to be essential for the production of unpaired electrons, and the normal chemical treatment is to modify the molecules with various atoms and groups such as hydrogen. In this paper, we combine first-principles calculations with the Hubbard model to investigate magnetic properties in hydrogenated ${\mathrm{C}}_{60}$ (${\mathrm{C}}_{60}{\mathrm{H}}_{n}$). For the enumerated ${\mathrm{C}}_{60}{\mathrm{H}}_{2}$ structures, there are nine configurations with ferromagnetic ground states and one configuration with an antiferromagnetic ground state. We have proposed a pair magnetic interaction model to predict the magnetic order, as well as a general rule to screen the maximum local magnetic moments for given $n$. When $n=3$ and 4, our model can give a good prediction of magnetic order, which is confirmed by the first-principles calculations. We find that the maximum number of unpaired electrons in ${\mathrm{C}}_{60}{\mathrm{H}}_{n}$ is smaller than the number of hydrogen atoms when $n\ensuremath{\ge}6$.