No abstract

Unequal transmissions of spin waves along opposite directions provide useful functions for signal processing. So far, the realization of such nonreciprocal spin waves has been mostly limited at a gigahertz frequency in the coherent regime via microwave excitation. Here we show that, in a magnetic bilayer stack with chiral coupling, tunable nonreciprocal propagation can be realized in spin Hall effect-excited incoherent magnons, whose frequencies cover the spectrum from a few gigahertz up to terahertz. The sign of nonreciprocity is controlled by the magnetic orientations of the bilayer in a nonvolatile manner. The nonreciprocity is further verified by measurements of the magnon diffusion length, which is unequal along opposite transmission directions. Our findings enrich the knowledge on magnetic relaxation and diffusive transport and can lead to the design of a passive directional signal isolation device in the diffusive regime.

The Ising machine is an unconventional computing architecture that can solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann computing architectures. The spin Hall nano-oscillator has potential as a building block for a high-speed, low-power Ising machine based on its GHz operating frequency, sub-micron dimensions, and high degree of tunability. We develop an analytical framework describing how the dynamics of an electrically coupled array of spin Hall oscillators can be mapped to the Ising Hamiltonian based on the device characteristics. Our analytical model is integrated into a lightweight and versatile Verilog-A device that is used to model the nonlinear spin Hall oscillator's phase dynamics in SPICEbased circuit simulators. Finally, by integrating this device model with off-the-shelf electronic amplifier models, we analyze the Ising machine performance at the circuit level considering phase noise and scalability of the coupled network. The physics-based analytical models and quantitative tools presented in this work will enable future experimental realization of an electrically coupled spin Hall oscillator-based Ising machine operating with a high degree of time, space, and energy efficiency.

The introduction of magnetic moments to topological materials provides rich opportunities for studying the interplay among magnetism, electron correlation, and topological orders, which can give rise to exotic magnetoelectric effects and allow one to manipulate the topological band structure via spintronic approaches. Here, we report current-induced switching in a thin film of ferromagnetic Weyl semimetal Co2MnGa with perpendicular magnetic anisotropy, via the spin–orbit torque from a neighboring heavy metal Pt. The reversal of the large anomalous Hall signal indicates an effective electrical control of the Berry curvatures associated with the Weyl nodes in the topological band structure. The efficiency of the spin–orbit torque switching is calibrated to be comparable to that in conventional ferromagnets. Given the compatibility of Co2MnGa films with various spintronic devices and techniques, our work represents an essential step toward memory and computing devices built by topological ferromagnetic materials.

The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks which provide programmable connectivities among arbitrary pairs of nodes are highly desirable for the development of practical oscillator-based Ising machines. Here we propose using an electrically coupled array of GHz spin Hall nano-oscillators to realize such a network. By developing a general analytical framework that describes injection locking of spin Hall oscillators with large precession angles, we explicitly show the mapping between the coupled oscillators' properties and the Ising model. We integrate our analytical model into a versatile Verilog-A device that can emulate the coupled dynamics of spin Hall oscillators in circuit simulators. With this abstract model, we analyze the performance of the spin Hall oscillator network at the circuit level using conventional electronic components and considering phase noise and scalability. Our results provide design insights and analysis tools toward the realization of a CMOS-integrated spin Hall oscillator Ising machine operating with a high degree of time, space, and energy efficiency.