Fig. 2. Electrical detection of the Néel vector of Mn₅Si₃ by the AHE.

(A) Hysteresis of Hall resistivity ρ_yx and (B) magnetization M under out-of-plane magnetic field at 150 K, within the cAFM phase of Mn₅Si₃. M can be decomposed into DMI-induced m as blue line and defect-induced M-m as black line. (C) Comparison between ρ_yx and m of Mn₅Si₃ thin films with different thickness at 150 K. The numbers in parentheses indicate the thickness of the film in nanometer. (D) Simulated hysteresis of out-of-plane net moment m_z under out-of-plane magnetic field at 150 K. (E) Simulated trajectories of 180° switching of Néel vector n and net moment m by out-of-plane magnetic field from 15 kOe to −15 kOe at 150 K. m and n are defined on the basis of the AFM sublattice of Mn₅Si₃ and averaged over all of simulation cells (Materials and Methods). (F) Calculated σ_xy near the Fermi level for the Néel vector along n₊ or n₋ with net moment along m₊ or m₋ at 150 K. (G) Calculated σ_xy at the Fermi level for n along any direction at 150 K.