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Orbital pumping by magnetization dynamics in ferromagnets

We show that dynamics of the magnetization in ferromagnets can pump orbital angular momentum, a

phenomenon we refer to as orbital pumping. This is the reciprocal phenomenon to orbital torque that induces

magnetization dynamics by the orbital angular momentum in nonequilibrium. The orbital pumping is analogous

to the spin pumping established in spintronics, but it requires spin-orbit coupling for the orbital angular

momentum to interact with magnetization. We develop a formalism that describes the generation of orbital

angular momentum by magnetization dynamics within the adiabatic perturbation theory. Based on this, we

perform first-principles calculations of orbital pumping in prototypical 3d ferromagnets, Fe, Co, and Ni. Results

show that the ratio between orbital pumping and spin pumping ranges from 5% to 15%, being smallest in Fe

and largest in Ni. This implies that ferromagnetic Ni is a good candidate for measuring the orbital pumping.

Implications of our results on experiments are also discussed.

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