Long-Range Orbital Magnetoelectric Torque in Ferromagnets

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.