Influence of W thickness on Perpendicular Magneto-crystalline Anisotropy of Pt/Co/W(111) Superlattices

Tri-layer superlattice with reflection asymmetry in the spirit of Rashba effect has been
explored in spintronics. Pt/Co/W (111) superlattice is investigated by employing first-principles calculations to clarify experimental results, where perpendicular magnetocrystalline anisotropy (PMA) depends on W thickness. Moreover, the enhancement of PMA with respect to Pt/Co due to non-magnetic W is examined. Our calculation results show that the thickness dependence of PMA is evident, whose maximum occurs when W is three monolayers, where the orbital hybridization at interfaces with W is responsible for PMA. Surprisingly, W contributes to PMA with appreciable orbital magnetic anisotropy, which follows the so-called Bruno relation, E_PMA ~ m^⊥_orb - m^∥_orb. To clarify the physics origin, PMA is analyzed in the framework of second-order perturbation theory, where 〈m=-2|L_z|m=+2〉 dominates. In addition, k-resolved PMA demonstrates that contribution is from the Γ with d orbitals of m = ±2, where m is the magnetic quantum number.