Does carrier localization affect the anomalous Hall effect?

The effect of carrier localization due to electron-electron interaction in anomalous Hall effect is elusive and there are contradictory results in the literature. To address the issue, we report here the detailed transport study including the Hall measurements on $\beta$-Mn type cubic compound Co$_7$Zn$_7$Mn$_6$ with chiral crystal structure, which lacks global mirror symmetry. The alloy orders magnetically below $T_c$ = 204 K, and reported to show spin glass state at low temperature. The longitudinal resistivity ($\rho_{xx}$) shows a pronounced upturn below $T_{min}$ = 75 K, which is found to be associated with carrier localization due to quantum interference effect. The upturn in $\rho_{xx}$ shows a $T^{1/2}$ dependence and it is practically insensitive to the externally applied magnetic field, which indicate that electron-electron interaction is primarily responsible for the low-$T$ upturn. The studied sample shows considerable value of anomalous Hall effect below $T_c$. We found that the localization effect is present in the ordinary Hall coefficient ($R_0$), but we failed to observe any signature of localization in the anomalous Hall resistivity or conductivity. The absence of localization effect in the anomalous Hall effect in Co$_7$Zn$_7$Mn$_6$ may be due to large carrier density, and it warrants further theoretical investigations, particularly with systems having broken mirror symmetry.