Effect of Coulomb repulsion on spin and orbital magnetism of cobalt–benzene complex: A relativistic density functional study

Abstract

We have demonstrated electronic configurations and magnetic properties of single Co adatom on benzene (Bz) molecule in the framework of relativistic density functional theory. A sequence of fixed spin moment (FSM) calculations were carried out with and without Coulomb repulsion (U). We have investigated that varying the strength of Coulomb repulsion results to different equilibrium positions for the Co adatom on benzene molecule. It was shown that inclusion of the on-site Coulomb repulsion in the Co 3d orbitals affects significantly the geometry of Co–Bz complex. We also found two stable low-spin and high-spin multiplicities for the complex. The nature of the high-spin configuration was explained according to the Hubbard electron–electron correlation in 3d shell of the Co adatom. Our FSM results indicate that the high-spin state is a global minimum in the presence of Hubbard parameter U. The relativistic spin–orbit coupling and using orbital polarization correction induce considerable orbital magnetism in both low and high spin states of the Co–Bz complex. We have also calculated magnetic anisotropy energies for two spin states and we found out that an out-of-plane magnetic orientation of Co adatom is more favorable in the low spin state whereas the Coulomb repulsion (U = 2 eV and U = 4 eV) predicts an in-plane magnetic orientation for Co adatom. Our findings can be implicitly taken into account for the extended system of added single Co atom on graphene.