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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>3</a:mn><a:mi>d</a:mi></a:mrow></a:math> 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.