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. (C) 1998 American Institute of Physics. [S0021-8979(98)08511-9]