**Dongwook Go**

Spin current is one of the central concepts in spintronics. While early studies of giant magnetoresistance and spin-transfer torque have shown good agreement between the theory and experiment, recent experiments of current-induced torques in spin-orbit coupled systems imply that we need a theory which goes beyond “spin current picture”. In general, angular momentum can be carried by other degrees of freedom as well as the spin. For electrons, the angular momentum is encoded in not only the spin but also orbital part of the wave function, thus one can think of transport of orbital angular momentum carried by electrons in analogy to the spin transport.

In this talk, I will explain how to electrically generate orbital current and utilize it to exert a torque on the magnetization. As a way to generate the orbital current, I introduce a mechanism of orbital Hall effect, which is defined as orbital current response along transverse directions to an external electric field [1]. Then I show that injection of the orbital current to a ferromagnet can excite magnetization dynamics, which we call orbital torque [2]. One advantage of utilizing the orbital current is that it does not require spin-orbit coupling for electrical generation, which is in contrast to spin current generation, e.g., by spin Hall effect. Thus, the orbital torque mechanism predicts sizable current-induced torque even for weakly spin-orbit coupled materials. However, since the spin and orbital angular momenta transform in the same way upon symmetry operations, it is challenging to disentangle the orbital transport effect from the spin transport effect in experiments. For this purpose, we recently developed a general theory which can track angular momentum transfer between different angular-momentum-carrying degrees of freedom, which include not only the spin and orbital of the electron but also crystal lattice and local magnetic moment [3]. From a first-principles implementation of the formalism, we show that the orbital torque mechanism behaves qualitatively different from the “conventional” contribution caused by the spin Hall effect. This provides microscopic understanding of the orbital torque in terms of the electronic structure. Finally, I discuss further experimental implications and conceptual difference between the orbital transport and spin transport.

We acknowledge funding under SPP 2137 “Skyrmionics” (project MO 1731/7-1) and TRR 173 − 268565370 (project A11) of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation).

[2] D. Go and H.-W. Lee, Orbital Torque: Torque Generation by Orbital Current Injection, Phys. Rev. Res. 2, 013177 (2020).

[3] D. Go, F. Freimuth, J.-P. Hanke, F. Xue, O. Gomonay, K.-J. Lee, S. Blügel, P. M. Haney, H.-W. Lee, and Y. Mokrousov, Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems, arXiv:2004.05945.