| Calculation of the Hall conductivity for a model of MnSi within the $sd$ model is presented. The classical spin Hamiltonian chosen to describe the spin states of MnSi is shown, upon varying the anisotropy strength and magnetic field, to exhibit a rich phase diagram containing the multiple spin spiral (or skyrme crystal) phase of square, rectangular, and hexagonal symmetries. The Hall conductivity $\sigma_$ is calculated in the $sd$ model for varying types of magnetic states. While $\sigma_$ 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 regardless of the field orientation. |
|