We present ab initio density functional calculations of the magnetic anisotropy of dimers of the transition-metal atoms from groups 8 to 10 of the Periodic Table. Our calculations are based on a noncollinear implementation of spin-density functional theory (DFT) where spin-orbit coupling (SOC) is included self-consistently. The physical mechanism determining the sign and magnitude of the magnetic anisotropy energy (MAE) is elucidated via an analysis of the influence of SOC on the spectrum of the Kohn-Sham eigenvalues of the dimers. The possible influence of orbital-dependent electron-electron interactions has been investigated by performing calculation with a hybrid functional (mixing Hartree-Fock and DFT exchanges) and with a $\text{DFT}+U$ Hamiltonian introducing an orbital-dependent on-site Coulomb repulsion $U$. The results demonstrate that the MAE is stable with respect to the addition of such orbital-dependent interactions.

• Received 2 March 2009

DOI:https://doi.org/10.1103/PhysRevB.79.224418