Hopfield neural network in magnetic textures with intrinsic Hebbian learning

Macroscopic spin ensembles with brainlike features such as nonlinearity, stochasticity, self-oscillations, memory effects, and plasticity, form attractive platforms for neuromorphic computing. We propose an artificial neural network consisting of electric contacts on conducting films with tunable magnetic textures that is superior to conventional implementations, because it does not require resource-demanding external computations during training. Simulations show that the feedback between anisotropic magnetoresistance and current-induced spin-transfer torque in malleable magnetic textures autonomously trains the network according to the Hebbian learning principle. We illustrate the idea by simulating the pattern recognition by a four-node Hopfield neural network.