Electron-electron interaction correction to the skew scattering contribution to the anomalous Hall effect in ultrathin FeCo films

Electron-electron interaction (EEI), a quantum effect that occurs in low-dimensional or disordered systems at low temperatures, is an important issue in electron transport phenomena, especially in the anomalous Hall effect (AHE). Nevertheless, the role of EEI correction to the AHE is overlooked in conventional magnetic metal systems and the scaling exponents of the power-law fits are not consistently at the systems with sufficiently high disorder. Here, we demonstrate that EEI does correct to the AHE and cause $\text{ln}T$-type temperature dependence of sheet resistance ${R}_{xx}$ (conductance ${G}_{xx}$), anomalous Hall resistance ${R}_{\mathrm{AH}}$, and anomalous Hall conductance ${G}_{\mathrm{AH}}$ in ultrathin high-quality FeCo films in the low-temperature region. Furthermore, the scaling exponent \ensuremath{\gamma} \ensuremath{\sim} 1 is acquired through the power-law fits of ${G}_{\mathrm{AH}}\ensuremath{\sim}{G}_{xx}^{\ensuremath{\gamma}}$ by varying temperature or thickness, suggesting that EEI corrects to skew scattering and definitely results in skew scattering dominating AHE in the bad metal regime (${\ensuremath{\sigma}}_{xx}<1\ifmmode\times\else\texttimes\fi{}{10}^{4}$ S/cm).