1. Ⅱ HOMO-LUMO gap and dispersion of HOMO
Electronic structures and spin-orbit coupling effect in (TM=3d, 4d, and 5d atoms) Weiwei Ju and Zhongqin Yang State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai , China
Electronic structures and spin-orbit coupling effect of a single TM impurity encapsulated in an icosahedral Au12 cage with Ih symmetry are studied based on density functional theory (DFT) with generalized gradient approximation (GGA) for exchange-correlation functional. The study shows SOC effect only is a perturbation for Sc, Ti, V, Cr, Mn, Fe, Co, Y, Zr, Nb, Mo, Tc, Lu, Hf, Ta, W, named the first group; whereas for Ni, Ru, Rh, Pd, Re, Os, Ir, Pt, SOC effect has rearranged the original distribution of energy level and causes new sequence of energy level near Fermi level, named the second group. Corresponding results, total magnetic moment and local magnetic moment almost can not be affected for the first group, in the mean time, that of the second group change remarkably after considering SOC effect.
Ⅰ Model and method
The theoretical calculations are done using density functional theory with generalized gradient approximation (GGA) implemented in Vienna ab initio simulation package (VASP). After considering SOC effect, the fully relativistic effects can be included in our calculation because VASP already considers scalar relativistic effects automatically. The left figure is the model used in our calculation.
Ⅱ HOMO-LUMO gap and dispersion of HOMO
Ⅲ Magnetic moment
Ⅳ The partial s-, d-projected density of states (PDOS) for 3d impurity encapsulated in an icosahedral Au12 cage without consideration of SOC. The exchange splitting is obvious for the latter elements of 3d series.
Ⅴ The charge transfer and orbital moment
According to the magnitude of charge transfer, the impurities of the former clusters transfer more charge to Au cage than the latter, so the orbits of former impurities have a strongly delocalized character and their orbital moments are small. However, the latter impurities lose less charge and orbital features are obvious, which is the main reason of their large orbital magnetic moment.
Ⅵ Conclusion
We discuss the total magnetic moment and local magnetic moment in a single 3d, 4d and 5d impurity encapsulated in icosahedral Au cage by means of density functional calculations with and without SOC, finding SOC has more remarkable effect for those clusters at the end of 3d, 4d and 5d series than those at the beginning. In the mean time, the effect of SOC for the HOMO-LUMO gap also obeys same rule to their magnetic moment.