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 nonmagnetic 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.

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