Non-monotonic variation of anomalous Hall effect with spin orbit coupling strength

For L1(0) FePt films, the anomalous Hall resistivity is found to be proportional to spontaneous magnetization $M_{\mathrm{S}}$. After the $M_{\mathrm{S}}$ temperature effect is eliminated, $\rho_{\mathrm{xyo}}$ can be fitted by $\rho_{\mathrm{xyo}}=a_{\mathrm{o}}\rho_{\mathrm{xx}}+ b_{\mathrm{o}}\rho_{\mathrm{xx}}^{\mathrm{2}}$. $a_{\mathrm{o}}$ and $b_{\mathrm{o}}$ change non-monotonically with chemical long range ordering degree $S$. Accordingly, it is indicated that for L1(0) FePt films the spin orbit coupling strength increases monotonically with increasing $S$.