Title: Strongly asymmetric magnetization switching and programmable complete Boolean logic enabled by long-range intralayer Dzyaloshinskii-Moriya interaction

Abstract: Electrical switching of magnetization is central to spintronics. Despite the enormous efforts on the spin torques and the Dzyaloshinskii-Moriya interaction (DMI) effects, some fundamental physics for electrical switching of magnetization is still missing as indicated by a number of remarkable long-standing puzzles. Here, we report the discovery of the long-range intralayer DMI effect widely existing in magnetic heterostructure, which is distinct from the yet-known DMI effects as it describes the chiral coupling of two orthogonal magnetic domains within the same magnetic layer via the mediation of an adjacent heavy metal layer. The long-range intralayer DMI generates a strong perpendicular effective magnetic field (H_DMI^z) on the perpendicular magnetization. Characteristically, H_DMI^z varies with the sign/magnitude of the interfacial DMI constant, the applied in-plane magnetic fields, and the distribution of the perpendicular magnetic anisotropy. The long-range intralayer DMI results in striking consequences including the strongly asymmetric current/field switching of perpendicular magnetization, hysteresis loop shift of perpendicular magnetization in the absence of in-plane direct current, and sharp, complete switching of perpendicular magnetization purely by an in-plane magnetic field. Utilizing the long-range intralayer DMI effect, we demonstrate programable, complete Boolean logic operations (i.e., AND, NAND, NOT, OR, and NOR) within a single spin-orbit torque device. These results will stimulate the investigation of the long-range intralayer DMI effect and its impacts on a variety of spintronic devices.