Reservoir Computing with Spin Waves in a Skyrmion Crystal*

Skyrmions in chiral magnets are nanometric spin textures characterized by a topological invariant and often emerge as a skyrmion crystal in a magnetic field. We propose that skyrmion crystals possess high potential for reservoir computing, one of the state-of-the-art derivatives of recurrent neural networks. Benefited from the nonlinear interferences and slow relaxations of spin waves propagating in the crystal, the skyrmion reservoir attains several fundamental requirements of reservoir computing, e.g., the generalization ability, short-term memory, and nonlinearity. We demonstrate these properties by performing three standard tasks, i.e., the input-estimation task, short-term memory task, and parity-check task on the skyrmion reservoir. We then extend our study to more nontrivial tasks, including the nonlinear autoregressive moving average task and handwritten digit recognition task. A low mean square error can be achieved, and a digit recognition rate as high as 95% can be reached by the skyrmion crystal with the number of virtual nodes being less than four hundred, consolidating the practical potential of the skyrmion reservoir. Since skyrmion crystals emerge spontaneously in a static magnetic field, the skyrmion reservoir requires no advanced nanofabrication for production, in contrast to other proposed magnetic reservoirs, e.g., spin-torque oscillators. Our work is expected to realize a breakthrough in the research of spintronics reservoir computing.