Effect of probe geometry on the Hall response in an inhomogeneous magnetic field: A numerical study

The effect of probe geometry on the classical Hall response to a weak perpendicular inhomogeneous magnetic field is studied numerically. An electric potential equation based on a classical model of the two-dimensional Hall effect is solved numerically for a generalized flux distribution to find the Hall response function. We find that the magnitude and shape of this response function is strongly affected by probe geometry. Asymmetric cross-shaped Hall probes, with one narrow voltage lead, have a strongly peaked response more localized than in symmetric probe arrangements. This suggests novel lithographic patterns that may improve the spatial resolution of Hall magnetometry and scanning Hall probe microscopy.