Theory of Orbital Hall Effect and Current-Induced Torques by Orbital Current

Abstract

The current-induced torque is one of the most important phenomena in spintronics as it provides a way to control magnetic order parameters by electrical means. So far, most studies on the microscopic mechanisms of the current-induced torque have focused on the role of spin current carried by conduction electrons, which exerts spin-transfer torque on the magnetization upon the injection into a ferromagnet. In solids, however, electronic Bloch states originate from the atomic orbitals of the constituent atoms. Thus, while it is natural to expect that such orbital information may be used to control the magnetization because the orbital degree of freedom carries the angular momentum as the spin degree of freedom does, the role of orbitals in the physics of the current-induced torque has been barely investigated. In recent years, we uncovered mechanisms of generating the electronic current carrying finite orbital angular momentum such as the orbital Hall effect (OHE) [1] and proposed to utilize the orbital current for controlling the magnetization [2]. The latter is shortly denoted by “orbital torque” (OT) nowadays.In this talk, I review recent theoretical progress in the mechanisms of the OHE and the OT. In the first part, I will explain that the OHE arises in various metals regardless of their strength of the spin-orbit coupling, whose magnitude is typically an order of magnitude larger than that of the spin Hall effect (SHE) in heavy metals [3]. In fact, the SHE is a concomitant effect of the OHE, whose hierarchical relation will be explained. In the second part, I will discuss the mechanisms of the OT. The main problem is that it is hard to distinguish the orbital contribution and the spin contribution to the torque on the magnetization in most torque measurements. This is one of the main difficulties to quantify the OT. Theoretically, we recently developed a general theoretical formalism that tracks the transfer of the angular momentum in solids between the lattice, the local magnetic moment, and the electron’s spin and orbital, and successfully implemented it within the density functional theory framework [4]. This enables us to understand the microscopic nature of the OT and quantify different competing contributions. Finally, I will also discuss unique qualitative features of the OT mechanisms: significant dependence of the interface orbital transparency on the crystallinity and long-range transport and dephasing in a ferromagnet [5].