Low-Energy Magnetic States of Tb Adatom on Graphene

Electronic structure and magnetic interactions of a Tb adatom on graphene are investigated from first principles using combination of density functional theory and multiconfigurational quantum chemistry techniques including spin-orbit coupling. We determine that the six-fold symmetry hollow site is the preferred adsorption site and we investigate electronic spectrum for different adatom oxidation states including Tb$^{3+}$, Tb$^{2+}$, Tb$^{1+}$, and Tb$^{0}$. For all charge states, the Tb $4f^8$ configuration is retained with other adatom valence electrons being distributed over $5d_{xy}$, $5d_{x2+y2}$, and $6s/5d_0$ single-electron orbitals. We find strong intra-site adatom exchange coupling that ensures that the $5d6s$ spins are parallel to the $4f$ spin. For Tb$^{3+}$, the energy levels can be described by the $J=6$ multiplet split by the graphene crystal field. For other oxidation states, the interaction of $4f$ electrons with spin and orbital degrees of freedom of $6s5d$ electrons in the presence of spin-orbit coupling results in the low-energy spectrum composed closely lying effective multiplets that are split by the graphene crystal field. Stable magnetic moment is predicted for Tb$^{3+}$ and Tb$^{2+}$ adatoms due to uniaxial magnetic anisotropy and effective anisotropy barrier around 440 cm$^{-1}$ controlled by the temperature assisted quantum tunneling of magnetization through the third excited doublet. On the other hand, in-plane magnetic anisotropy is found for Tb$^{1+}$ and Tb$^{0}$ adatoms. Our results indicate that the occupation of the $6s5d$ orbitals can dramatically affect the magnetic anisotropy and magnetic moment stability of rare earth adatoms.