  We show that dynamics of the magnetization in ferromagnets can pump the
orbital angular momentum, which we denote by orbital pumping. This is the
reciprocal phenomenon to the orbital torque that induces magnetization dynamics
by the orbital angular momentum in non-equilibrium. The orbital pumping is
analogous to the spin pumping established in spintronics but requires the
spin-orbit coupling for the orbital angular momentum to interact with the
magnetization. We develop a formalism that describes the generation of the
orbital angular momentum by magnetization dynamics within the adiabatic
perturbation theory. Based on this, we perform first-principles calculation of
the orbital pumping in prototypical $3d$ ferromagnets, Fe, Co, and Ni. The
results show that the ratio between the orbital pumping and the spin pumping
ranges from 5 to 15 percents, 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.
