The Anomalous Hall Effect in Ultra-Thin Amorphous CNi3 Films

The anomalous Hall resistance in homogeneous CNi$_3$ films with sheet resistance near the quantum resistance was studied. Tunneling measurements show that the saturation behavior is commensurate with the emergence of the 2D Coulomb gap, suggesting that e-e interactions mediate the high-disorder phase. The saturation of anomalous Hall resistance is associated with the crossover from the weak- localization regime to that of a 2D correlated insulator. In the weak-localization regime, where the sheet conductance G $\gg e^2/h$, the anomalous Hall resistance of the films increases with increasing disorder and the Hall conductance scales as G$_{xy} \propto G^\varphi$ with $\varphi$ = 1.6. However, at sufficiently high disorder the system begins to enter the 2D correlated insulator regime, at which point the Hall resistance R$_{xy}$ abruptly saturates and the scaling exponent becomes $\varphi$ = 2. The crossover is also clearly evident in the scaling behavior of the Hall conductivity as well as in the tunneling density of states.