Fig. 3: Magnetization and anomalous Hall effect.

a Magnetization as a function of the magnetic field applied along the [0001] crystal direction at different temperatures. The inset highlights a vanishingly small remanent magnetization within error of 5 mμ_B/u.c. The plot shows the total magnetization of the measured sample, i.e., also including the substrate. The inset also shows the total measured magnetization. However, when recalculating from A/m to mμ_B/u.c., we considered that the remanent signal at zero field is due to the Mn₅Si₃ film alone and has no contribution from the Si substrate (we also considered the same for the small field range around zero plotted in the inset). b Field and temperature dependent anomalous Hall resistivity. The ordinary Hall effect, which is linear in the applied magnetic field, was subtracted (see text). c Decomposition of the anomalous Hall resistivity measured at 50 K into a topological Hall component \({\rho }_{{{{{{{{\rm{H}}}}}}}}}^{{{{{{{{\rm{T}}}}}}}}}\), and a component ascribed to the unconventional d-wave magnetism, \({\rho }_{{{{{{{{\rm{H}}}}}}}}}^{{{{{{{{\rm{U}}}}}}}}}\) (see Methods and Supplementary Fig. 4).). d The decomposition of the spontaneous (zero-field) anomalous Hall resistivity as a function of temperature. e Spontaneous anomalous Hall conductivity corresponding to the component ascribed to the unconventional d-wave magnetism.