Origin of magnetocrystalline anisotropy oscillations in (001) face-centred-cubic Co thin films and effect of sp-d hybridization

摘要

Magnetocrystalline anisotropy (MA) energy of (001) face-centred-cubic Co(N) films is calculated for film thicknesses N = 1-28 in a realistic tight-binding model with and without sp-d orbital hybridization included. The obtained results show that the average MA energy is not largely influenced by the sp-d hybridization. On the other hand, the oscillation pattern is remarkably changed when the sp-d hybridization is included: in this case the MA energy has oscillations with a clear period of 2 atomic layers (AL), similar to the previous ab initio calculations (Szunyogh L, Ujfalussy B, Blaas C, Pustugova U, Sommers C and Weinberger P 1997 Phys. Rev. B 56 14036). A careful analysis in k- and N-spaces reveals that the total MA oscillations are a superposition of two oscillatory contributions: one coming from the neighbourhood of the (&UGamma;) over bar -point with period close to 2 AL (regardless whether the sp-d hybridization is present or not) and the other originating in the region around the M-point. The (M) over bar -point contribution has a larger period and its amplitude is significantly smaller than that of the (&UGamma;) over bar -point contribution when the sp-d hybridization is included so that the 2 AL (&UGamma;) over bar -point contribution is dominant in this case. The two oscillatory MA contributions are attributed to quantum-well states and the corresponding oscillation periods are related to the extremal radii of the minority-spin bulk Co Fermi surface. [References: 43]