Spin-based logic architectures provide nonvolatile data retention, near-zero leakage, and scalability, extending the technology roadmap beyond complementary metal-oxidesemiconductor (CMOS) logic [1][2][3][4][5][6][7][8][9][10][11][12][13] . Architectures based on magnetic domain-walls take advantage of fast domain-wall motion, high density, non-volatility, and flexible design in order to process and store information 1,3,14-16 . Such schemes, however, rely on domain-wall manipulation and clocking using an external magnetic field, which limits their implementation in dense, large scale chips. Here we demonstrate a concept to perform allelectric logic operations and cascading in domain-wall racetracks. We exploit the chiral coupling between neighbouring magnetic domains induced by the interfacial Dzyaloshinskii-Moriya interaction 17-20 to realize a domain-wall inverter, the essential basic building block in all implementations of Boolean logic. We then fabricate reconfigurable NAND and NOR logic gates, and perform operations with current-induced domain-wall motion. Finally, we cascade several NAND gates to build XOR and full adder gates, demonstrating electrical control of magnetic data and device interconnection in logic circuits. Our work provides a viable platform for scalable all-electric magnetic logic, paving the way for memory-in-logic applications.

Magnetically coupled nanomagnets have multiple applications in nonvolatile memories, logic gates, and sensors. The most effective couplings have been found to occur between the magnetic layers in a vertical stack. We achieved strong coupling of laterally adjacent nanomagnets using the interfacial Dzyaloshinskii-Moriya interaction. This coupling is mediated by chiral domain walls between out-of-plane and in-plane magnetic regions and dominates the behavior of nanomagnets below a critical size. We used this concept to realize lateral exchange bias, field-free current-induced switching between multistate magnetic configurations as well as synthetic antiferromagnets, skyrmions, and artificial spin ices covering a broad range of length scales and topologies. Our work provides a platform to design arrays of correlated nanomagnets and to achieve all-electric control of planar logic gates and memory devices.

Memory and logic devices that encode information in magnetic domains rely on the controlled injection of domain walls to reach their full potential. In this work, we exploit the chiral coupling induced by the Dzyaloshinskii-Moriya interaction between in-plane and out-of-plane magnetized regions of a Pt/Co/AlO x trilayer in combination with current-driven spin-orbit torques to control the injection of domain walls into magnetic conduits. We demonstrate that the current-induced domain nucleation is strongly inhibited for magnetic configurations stabilized by the chiral coupling and promoted for those that have the opposite chirality. These configurations allow for 1 arXiv:2003.11805v1 [cond-mat.mes-hall] 26 Mar 2020 efficient domain wall injection using current densities of the order of 4×10 11 Am −2 , which are lower than those used in other injection schemes. Furthermore, by setting the orientation of the in-plane magnetization using an external field, we demonstrate the use of a chiral domain wall injector to create a controlled sequence of alternating domains in a racetrack structure driven by a steady stream of unipolar current pulses. Main TextThe nucleation of magnetic domains underpins magnetization reversal processes and, consequently, the functioning of most types of magnetic storage devices. Domain wall (DW) racetrack memory and logic devices, in particular, require reliable control over domain nucleation and current-induced DW propagation in order to work efficiently. 1-3 The problem of domain nucleation was first addressed by modifying the magnetic anisotropy of the nucleation sites using altered shapes 4-6 or ion irradiation of magnetic structures, 7-12 which favor magnetization reversal at specific locations. These methods are commonly used in field-induced domain nucleation and DW propagation studies. [13][14][15][16] Current-induced domain nucleation techniques based on the Oersted field produced by a narrow write line, 17 spin-transfer torque switching using magnetic tunnel junctions 18 and using magnetization boundaries where the magnetization of the two adjacent regions are orthogonally aligned 19 have been shown to mitigate the shortcomings of field nucleation. These methods offer faster and more localized domain nucleation at the cost of higher device complexity.A significant leap forward in magnetic writing was made with the advent of spin-orbit torques (SOTs), 20-24 which emerge at ferromagnet/heavy metal interfaces. 25 Ever since the