Orbital Pumping Incorporating Both Orbital Angular Momentum and Position

We develop a theory of adiabatic orbital pumping, highlighting qualitative differences from spin pumping. An oscillating magnetic field pumps not only orbital angular momentum current but also orbital angular position current. The latter, which has no spin counterpart, underscores the incompleteness of existing orbital torque theories. Importantly, both types of orbital currents can be detected as transverse electric voltages, which contain considerable second harmonic components unlike in spin pumping. Moreover, orbital currents can be pumped by lattice dynamics that carry phonon angular momentum, implying that orbital currents can, in turn, induce phonon angular momentum. Our work open up new possibilities for generating orbital currents and provides a broader understanding of the interplay between spin, orbital, and phonon dynamics.