Theoretical study of interfacial damping in perpendicular anisotropy superlattices along multiple crystal orientations

Damping, representing the loss of magnetic energy from the electrons to the lattice through the spin-orbit interaction, is calculated for Co/Pt and Co/Pd superlattices grown along the (001), (111), and (011) orientations. The damping consists of two contributions: interfacial and, usually, bulk. The interfacial damping shows dependence on the superlattice orientation. The origin of the interfacial damping is due to both the distorted electronic states at the interface and the spin-orbit interaction in the weakly polarized nonmagnetic Pt/Pd layers deposited on Co layers. The density of states around the Fermi level provides the spin-flip channels and closely correlates with the damping value. The damping shows asymmetry in the two transverse directions of the spin for spins at most angles. The damping for out-of-plane magnetization can be as much as 1.7 times larger than that of in-plane magnetization.