Skyrmions and anomalous Hall effect in a Dzyaloshinskii-Moriya spiral magnet

Monte Carlo simulation study of a classical spin model with Dzyalosinskii-Moriya interaction and the spin anisotropy under the magnetic field is presented. We found a rich phase diagram containing the multiple spin spiral (or Skyrme crystal) phases of square, rectangular, and hexagonal symmetries in addition to the spiral spin state. The Skyrme crystal states are stabilized by a spin anisotropy or a magnetic field. The Hall conductivity sigma(xy) is calculated within the sd model for each of the phases. Applying a magnetic field induces nonzero uniform chirality and the anomalous Hall conductivity simultaneously. The field dependence of sigma(xy) is shown to be a sensitive probe of the underlying magnetic structure. Relevance of the present results to several recent experiments on MnSi is discussed.