Fig. 3

Correlation of MR(θ _zy ) and AHE. a MR(θ _zy ) results for co-sputtered (Fe_1−xMn _x )_0.6Pt_0.4 with x = 0.22–0.65. b–c Mn composition dependence of ρ _xx , \(\rho _{xy}^{{\mathrm{AH}}}\) and M_s, respectively. d \(\rho _{xy}^{{\mathrm{AH}}}/M_{\mathrm{s}}\) as a function of ρ _xx . e MR ratio as a function of θ_AH for a variety of samples including Fe, Fe_1−xPt _x , (Fe_1-xMn _x )_0.6Pt_0.4, and Fe_1−xMn _x . Solid lines in a are fittings based on the angle dependence. Inset of d shows the full range of \(\rho _{xy}^{{\mathrm{AH}}}/M_{\mathrm{s}}\) vs. ρ _xx plot, and solid line in d serves as a guide for the eye. The shadowed area in e is the calculated AHMR ratio range using different combinations of β: 0.4–0.6 and l_s: 2–5 nm, and dotted line in e is the fitting results using β = 0.55 and l_s = 3.5 nm. The error bars in d are from the linear fitting to determine \(\rho _{xy}^{{\mathrm{AH}}}\) from ρ _xy