Purely electrical detection of a skyrmion in constricted geometry

How to detect the skyrmion position is a crucial problem in future skyrmionics since it corresponds to the reading process of information. We propose a method to detect the skyrmion position purely electrically by measuring the Hall conductance in a constricted geometry. The Hall conductance becomes maximum when a skyrmion is at the lead position. It is possible to detect the skyrmion position even at room temperature. We find an optimized width of the sample determined by the skyrmion radius. We also investigate the effects of elastic and inelastic scatterings, and finite temperature. We find that the local density of states become minimum at the skyrmion position. Our results will be a basis of future skyrmion electronics.