Orbital polarization effects on the magnetic anisotropy and orbital magnetism of clusters, films, and surfaces:: A comparative study within tight-binding theory

The effects of orbital polarizations on the magnetic properties of transition-metal nanostructures are investigated in the framework of a self-consistent tight-binding theory. Three different approximations to the intra-atomic two-center Coulomb interactions are considered: (i) full orbital dependence of the direct and exchange Coulomb interactions U-mm(') and J(mm)(') as given by atomic symmetry, (ii) orbital independent interactions U=U-mm(') and J=J(mm)('), and (iii) orbital polarization (OP) approximation of the form H-OP=-(B/2)Sigma L-i(i)2, where L-i refers to the orbital momentum operator at atom i and B to the Racah coefficient. Results are given for the local orbital magnetic moments < L-i delta > along high-symmetry magnetization directions delta and for the corresponding magnetic anisotropy energies Delta E-delta gamma of surfaces, films, and clusters of Fe, Co, and Ni. The quantitative differences between the approximations allow us to quantify the effects of orbital polarizations on < L-i delta > and Delta E-delta gamma. One observes that, with an appropriate choice of B, the OP ansatz yields a very good agreement with the rigorous orbital dependent calculations. The simplest orbital independent approach underestimates < L-i delta > and Delta E-delta gamma systematically. However, it provides a good qualitative description of the main general trends as a function of dimensionality, local environment, and d-band filling. Advantages and limitations of the various approaches are discussed.