Scaling of anomalous Hall effect in amorphous CoFeB films with accompanying quantum correction

Scaling of anomalous Hall effect in amorphous CoFeB films with thickness ranging from 2 to 160 nm has been investigated. We have found that the scaling relationship between longitudinal (ρxx) and anomalous Hall (ρAH) resistivity is distinctly different in the Bloch and localization regions. For ultrathin CoFeB films, the sheet resistance (Rxx) and anomalous Hall conductance (GAH) received quantum correction from electron localization showing two different scaling relationships at different temperature regions. In contrast, the thicker films show a metallic conductance, which have only one scaling relationship in the entire temperature range. Furthermore, in the dirty regime of localization regions, an unconventional scaling relationship σAH∝σxxα with α=1.99 is found, rather than α=1.60 predicted by the unified theory.