Echo state property and memory capacity of artificial spin ice

Physical reservoir computing by using artificial spin ice (ASI) has been proposed on the basis of both numerical and experimental analyses. ASI is a many-body system consisting of ferromagnets with various interactions. Recently, fabricating magnetic tunnel junctions (MTJs) as ferromagnets in an ASI was achieved in the experiment, which enables an electrical detection of magnetic state of each MTJ independently. However, performing a recognition task of time-dependent signal by such an MTJ-based ASI has not been reported yet. In this work, we examine numerical simulation of a recognition task of time-dependent input and evaluate short-term memory and parity-check capacities. These capacities change significantly when the magnitude of the input magnetic field is comparable to a value around which the magnetization alignment is greatly affected by the dipole interaction. It implies that the presence of the dipole interaction results in a loss of echo state property. This point was clarified by evaluating Lyapunov exponent and confirming that the drastic change of the memory capacities appears near the boundary between negative and zero exponents, which corresponds to the edge of echo state property.