Fig. 4: Angle and temperature dependent DC Transport measurements.

a Temperature dependence of \({\rho }_{{xy}}^{\perp }\) with OOP \(\vec{{{\boldsymbol{H}}}}\). b Temperature dependence of \({\rho }_{{xy}}^{{THE}}\). \({\rho }_{{xy}}^{{THE}}\) is extracted by subtracting the OHE and AHE contributions from \({\rho }_{{xy}}^{\perp }\). c LTEM images at \(300\,{K}\) for \({\mu }_{0}{H}_{0}=0\), \(80\),\(\,220\), and \(320\,{mT}\) in the OOP configuration. d PHE measurements of \({\rho }_{{xy}}^{\parallel }\) for IP \(\vec{{{\boldsymbol{H}}}}\) applied at \({\theta }_{H}=\) \({0}^{\circ }\), \(3{0}^{\circ }\),\(\,6{0}^{\circ }\), and \(9{0}^{\circ }\) with respect to the \([100]\) axis. Inset presents calculated magnetic textures for \({\theta }_{H}={0}^{\circ }\) and \(3{0}^{\circ }\). e Extraction of the topological contribution, \({\rho }_{{xy}}^{{TPHE}}\), at \({\theta }_{H}=3{0}^{\circ }\). Upper panel: Measurement of \({\rho }_{{xy}}^{\parallel }\) (green solid line) together with the measured \({R}_{s}^{\parallel }{\mu }_{0}{M}_{z}\) (red line) at \({\theta }_{H}={30}^{\circ }\). \({M}_{z}\) was measured using a MOKE setup at \({\theta }_{H}={30}^{\circ }\) (red line). \({R}_{s}^{\parallel }\) was determined from \({\rho }_{{xy}}^{\parallel }\) at the saturated magnetization regime. Saturation conditions were verified by calculating \({M}_{z}\) at \({\theta }_{H}={30}^{\circ }\) (red dashed line) and by measuring \({M}_{{xy}}\) using a VSM (blue solid line). Calculated \({M}_{{xy}}\) (blue dashed line) reproduces the measured \({M}_{{xy}}\) in saturation. Lower panel presents the extracted \({\rho }_{{xy}}^{{TPHE}}\).