Fig. 3. Field dependence of χ, b_z, and ${\tilde{\mathbf{\sigma }}}_{\mathit{x}\mathit{y}}$ (a quantity that is proportional to the anomalous Hall conductivity) calculated by MC simulation.

The numbers in square brackets are the magnetic field in Tesla, assuming the upper critical field to be 12 T, which is the case for MnGe. The temperatures are at (A) T/J_H = 0.1 (~20 K) and (B) T/J_H = 0.5 (~100 K) with γ = 2. The definition and description of ${\tilde{\mathrm{\sigma }}}_{\mathit{x}\mathit{y}}$ are given in Eq. 26 and the paragraphs above it. In the figure, the blue and yellow shading indicates helical and skyrmion crystal phases, respectively. See the main text for details. (C) Experimental measurement of Hall conductivity in MnGe at 50 and 100 K. Reproduced from data from the work of Kanazawa et al. (29).