Adiabatic Spin and Orbital Pumping in Metallic Heterostructures

In this study, we investigate the spin and orbital densities induced by magnetization dynamics in a planar bilayer heterostructure. To do this, we employed a theory of adiabatic pumping using the Keldysh formalism and Wigner expansion. We first conduct simulations on a model system to determine the parameters that control the spin and orbital pumping into an adjacent non-magnetic metal. We conclude that, in principle, the orbital pumping can be as significant as spin pumping when the spin-orbit coupling is present in the ferromagnet. We extend the study to realistic heterostructures involving heavy metals (W, Pt, Au) and light metals (Ti, Cu) by using first-principles calculations. We demonstrate that orbital pumping is favored in metals with $d$ states close to the Fermi level, such as Ti, Pt, and W, but is quenched in materials lacking such states, such as Cu and Au. Orbital injection is also favored in materials with strong spin-orbit coupling, leading to large orbital pumping in Ni/(Pt, W) bilayers.