Skyrmions and Anomalous Hall Effect in a Dzyloshinskii-Moriya Spiral Magnet

TL;DR

This study uses Monte Carlo simulations to explore the phase diagram and Hall conductivity in a Dzyaloshinskii-Moriya spiral magnet, revealing how magnetic fields induce nonzero Hall effects in various spin spiral phases.

Contribution

It provides a detailed phase diagram of spiral and skyrmion phases and analyzes the conditions for Hall conductivity onset under magnetic fields in a classical spin model.

Findings

Multiple spin spiral phases with different symmetries identified.

Hall conductivity emerges only above a critical magnetic field in certain phases.

Zero Hall conductivity at zero field, with field-induced nonzero Hall response.

Abstract

Monte Carlo simulation study of a classical spin model with Dzylosinskii-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 Hall conductivity $\sigma_{xy}$ is calculated within the $sd$ model for each of the phases. While $\sigma_{xy}$ is zero in the absence of external magnetic field, applying a field strength $H$ larger than a threshold value $H_c$ leads to the simultaneous onset of nonzero chirality and Hall conductivity. We find $H_c = 0$ for the multiple spin spiral states, but $H_c > 0$ for a single spin spiral state regardless of the field orientation. Relevance of the present results to MnSi is discussed.