  While it is often assumed that the orbital response is suppressed and
short-ranged due to strong crystal field potential and orbital quenching, we
show that the orbital magnetoelectric response can be remarkably long-ranged in
ferromagnets. In a bilayer consisting of a nonmagnet and a ferromagnet, spin
injection from the interface results in spin accumulation and torque in the
ferromagnet, which rapidly oscillate and decay by spin dephasing. In contrast,
we find that even when an external electric field is applied only on the
nonmagnet, we find substantially long-ranged orbital magnetoelectric response
in the FM, which can go far beyond the spin dephasing length. This unusual
feature is attributed to nearly degenerate orbital characters imposed by the
crystal symmetry, which form hotspots for the intrinsic orbital response.
Because only the states near the hotspots contribute dominantly, the induced
orbital angular momentum does not exhibit destructive interference among states
with different momentum as in the case of the spin dephasing. This gives rise
to a distinct type of orbital torque on the magnetization, increasing with the
thickness of the ferromagnet. Such behavior may serve as critical long-sought
evidence of orbital transport to be directly tested in experiments. Our
findings open the possibility of using long-range orbital magnetoelectric
effect in orbitronic device applications.
