Magnetocrystalline anisotropy of interfaces: first-principles theory for Co-Cu interface and interpretation by an effective ligand interaction model

The state tracking method proposed recently is employed for the first-principles local density determination of interface magnetocrystalline anisotropy (MCA) energy by the full potential linearized augmented plane wave method. The interface MCA mechanism involving Co is studied with the Co-Cu interface as an example. The free standing Co monolayer is found to exhibit a strong negative MCA (easy axis in the layer plane), -1.35 meV, due to the spin-orbit coupling between spin-down bonding z² and anti-bonding xz or yz states along Δ in the Brillouin zone, and between anti-bonding z² and bonding xz and yz states near M̄. At the Co-Cu interface, the out-of-plane Co bonding z², xz and yz states interact strongly with the Cu states, giving rise to the main change: a decrease in the magnitude of this negative contribution. Together with the effect of changes in band filling and the contribution from the spin-orbit coupling between opposite spins, the interface MCA energy of a Co layer is -0.38 meV for a Co overlayer on a Cu(001) substrate, and near zero (-0.01 meV) for a Co layer sandwiched between a Cu(001) matrix. These results are in very good agreement with recent in situ experimental measurements. An effective ligand interaction model is developed which successfully interprets the first principles results and further shows how the interface MCA depends on the energy of the d orbitals of the interface atoms and the strength of the interface bonds.