High-performance combinatorial optimization based on classical mechanics.

Quickly obtaining optimal solutions of combinatorial optimization problems has tremendous value but is extremely difficult. Thus, various kinds of machines specially designed for combinatorial optimization have recently been proposed and developed. Toward the realization of higher-performance machines, here, we propose an algorithm based on classical mechanics, which is obtained by modifying a previously proposed algorithm called simulated bifurcation. Our proposed algorithm allows us to achieve not only high speed by parallel computing but also high solution accuracy for problems with up to one million binary variables. Benchmarking shows that our machine based on the algorithm achieves high performance compared to recently developed machines, including a quantum annealer using a superconducting circuit, a coherent Ising machine using a laser, and digital processors based on various algorithms. Thus, high-performance combinatorial optimization is realized by massively parallel implementations of the proposed algorithm based on classical mechanics.

Magnetization switching of a perpendicular nanomagnet induced by vertical nonlocal injection of pure spin current.

Injection of pure spin current using a nonlocal geometry is a promising method for controlling magnetization in spintronic devices from the viewpoints of increasing freedom in device structure and avoiding problems related to charge current. Here, we report an experimental demonstration of magnetization switching of a perpendicular magnetic nanodot induced by vertical injection of pure spin current from a spin polarizer with perpendicular magnetization. In comparison with direct spin injection, the current amplitude required for magnetization switching is of the same order and shows smaller asymmetry between parallel-to-antiparallel and antiparallel-to-parallel switching. Simulation of spin accumulation reveals that, in the case of nonlocal spin injection, the spin torque is symmetric between the parallel and antiparallel configuration because current flows through only the spin polarizer, not the magnetic nanodot. This characteristic of nonlocal spin injection is the origin of the smaller asymmetry of the switching current and can be advantageous in spintronic applications.

Zero-dc-field rotation-direction-dependent magnetization switching induced by a circularly polarized microwave magnetic field.

Magnetization switching of high-anisotropy nanomagnets by a small magnetic field is a key challenge in developing future magnetic nanodevices. In this paper, we experimentally demonstrate magnetization switching of a perpendicularly magnetized nanomagnet induced solely by an in-plane circularly polarized microwave magnetic field. Applying a microwave field with an amplitude below 5% of the anisotropy field induces large ferromagnetic resonance excitation, which results in magnetization switching even in the absence of a dc field. This kind of magnetization switching is induced by a microwave field with a duration of 0.5 ns and is clearly dependent on the rotation direction of the microwave field.