First-principles study on magnetism of different dimensional Ru systems

The magnetism, the magnetocrystalline anisotropy and the optical properties of the monolayer and atomic chain of 4d transition-metal Ru are investigated by using the full-potential linearized-augmented-plane-wave method in a generalized gradient approximation. The magnetic moments are 1.039 \mu_B/atom and 1.130 \mu_B/atom for the monolayer and atomic chain, respectively. Both systems have large magnetocrystalline anisotropy energy (MAE). The magnetic easy axis is normal to the monolayer and perpendicular to the chain axis in the atomic chain. The optical properties of the two low-dimensional Ru systems are investigated by calculating the complex optical conductivity tensor. Both systems exhibit anisotropy in photoconductivity, especially for the atomic chain. The physical origins of MAE and photoconductivity are studied based on electronic structures. It is found that the changes in crystal field caused by different symmetry-breaking mechanisms in the two low-dimensional Ru systems result in MAE through spin--orbit coupling, while the anisotropy in photoconductivity mainly comes from the crystallographic anisotropy.