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.

Current-induced spin-transfer torques (STT) and spin-orbit torques (SOT) enable the electrical switching of magnetic tunnel junctions (MTJs) in nonvolatile magnetic random access memories. In order to develop faster memory devices, an improvement of the timescales underlying the currentdriven magnetization dynamics is required. Here we report all-electrical time-resolved measurements of magnetization reversal driven by SOT in a three-terminal MTJ device. Single-shot measurements of the MTJ resistance during current injection reveal that SOT switching involves a stochastic two-step process consisting of a domain nucleation time and propagation time, which have different genesis, timescales, and statistical distributions compared to STT switching. We further show that the combination of SOT, STT, and voltage control of magnetic anisotropy (VCMA) leads to reproducible sub-ns switching with a spread of the cumulative switching time smaller than 0.2 ns. Our measurements unravel the combined impact of SOT, STT, and VCMA in determining the switching speed and efficiency of MTJ devices. Switching nanomagnets by current injection offers unparalleled scalability, as well as low power and high speed operation compared to control via external magnetic fields 1-3. Spin-transfer torques (STT) 1,4 are presently employed in memory and spin logic applications 5,6 to control the state of magnetic tunnel junctions (MTJ) via an electric current passing through the reference and free magnetic layers, which allows also for efficient readout of the MTJ through the tunnel magnetoresistance (TMR). Time-resolved studies of magnetization reversal in spin valve 7,8 and MTJ devices 9-12 have shown that STT enables switching on a timescale of 100 to 1 ns, depending on the driving current 13 and external field 14. However, STT switching is characterized by nonreproducible dynamic paths and incubation times up to several tens of ns long, which limit the reliability and speed of the reversal process to about 10-20 ns, even when mitigation strategies based on large driving currents or noncollinear spin injection are employed 13,15,16. These limitations may be overcome by magnetization reversal driven by spin-orbit torques (SOT) 3,17-19 , which has been recently demonstrated in three-terminal MTJs with in-plane 20,21 as well as out-of-plane magnetization 22-25. SOT switching combines an in-plane current injection geometry with charge-to-spin conversion due to the spin Hall effect and interfacial spin scattering 3. Such a geometry decouples the write and read current paths, improving the MTJ endurance and operation speed by minimizing electrical stress of the tunnel barrier and allowing for tuning the barrier thickness for high TMR, fast read-out, and minimal read disturbances. Moreover, in devices with perpendicular magnetization, the injected spin current is orthogonal to the quiescent magnetization of the free layer, thus providing an "instant on" torque that is expected to minimize the switching incubation time 25-27 .

Magnonics is gaining momentum as an emerging technology for information processing. The wave character and Joule heating-free propagation of spin-waves hold promises for highly efficient computing platforms, based on integrated magnonic circuits. The realization of such nanoscale circuitry is crucial, although extremely challenging due to the difficulty of tailoring the nanoscopic magnetic properties with conventional approaches. Here we experimentally realize a nanoscale reconfigurable spin-wave circuitry by using patterned spin-textures. By space and time-resolved scanning transmission X-ray microscopy imaging, we directly visualize the channeling and steering of propagating spin-waves in arbitrarily shaped nanomagnonic waveguides, with no need for external magnetic fields or currents. Furthermore, we demonstrate a prototypic circuit based on two converging nanowaveguides, allowing for the tunable spatial superposition and interference of confined spin-waves modes. This work paves the way to the use of engineered spin-textures as building blocks of spin-wave based computing devices.

We use three-terminal magnetic tunnel junctions (MTJs) designed for field-free switching by spin-orbit torques (SOTs) to systematically study the impact of dual voltage pulses on the switching performances. We show that the concurrent action of an SOT pulse and an MTJ bias pulse allows for reducing the critical switching energy below the level typical of spin transfer torque while preserving the ability to switch the MTJ on the sub-ns time scale. By performing dc and real-time electrical measurements, we discriminate and quantify three effects arising from the MTJ bias: the voltagecontrolled change of the perpendicular magnetic anisotropy, current-induced heating, and the spin transfer torque. The experimental results are supported by micromagnetic modeling. We observe that, depending on the pulse duration and the MTJ diameter, different effects take a lead in assisting the SOTs in the magnetization reversal process. Finally, we present a compact model that allows for evaluating the impact of each effect due to the MTJ bias on the critical switching parameters. Our results provide input to optimize the switching of three-terminal devices as a function of time, size, and material parameters.

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