Intrinsic torques emerging from anomalous velocity in magnetic textures

磁気構造中の異常速度に起因した内因性トルク

荒木 康史   ; 家田 淳一   

Araki, Yasufumi; Ieda, Junichi

We present a theory of current-induced torques on magnetic textures in the presence of strong spin-orbit coupling (SOC). It has been broadly discussed that nontrivial topology in real and momentum spaces contributes to anomalous transport phenomena of electrons. Magnetic textures such as skyrmions give rise to the topological Hall effect in magnetic metals, due to the real-space Berry curvature acting as an effective magnetic field for electrons. The momentum-space Berry curvature, which arises from band inversion by SOC in topological insulators (TIs) and Weyl semimetals (WSMs), leads to the intrinsic anomalous Hall effect (AHE) via the anomalous velocity in response to an applied electric field. Here we propose that the topological characteristics intertwined in real and momentum spaces contribute also to dynamics of magnetic textures driven by electric fields. Based on spin-momentum locking (SML) due to strong SOC, we phenomenologically classify the electrically induced torques, and derive the contributions from magnetic textures and the anomalous velocity. As a result, we find the "intrinsic" torques that arise from the spin polarization converted from the anomalous velocity by SML. The intrinsic torques are distinct from the conventional spin-transfer torque (STT) and the spin-orbit torque (SOT), both of which come from the electron spins in transport current. They are hence independent of the transport relaxation time and are robust against disorder or thermal fluctuation. We especially point out the intrinsic torque arising only in magnetic textures, which we call the "topological Hall torque (THT)". The THT is induced by the cooperation of the real-space magnetic texture and the momentum-space Berry curvature, and can emerge dominantly in bulk crystals. Such an enhanced torque is capable of driving dynamics of the magnetic texture at high speed, which may make the spintronics device highly efficient without building any complex heterostructures.