Hall effect in a highly inhomogeneous magnetic field distribution

Two-dimensional Hall probes are becoming increasingly popular as “local” magnetometers for ferromagnetic and superconducting materials. In many applications, the magnetic field at a sample surface varies on a length scale much smaller than the Hall probe dimensions, and data interpretation requires a quantitative model of the Hall voltage in this situation. We present here a classical numerical model of the Hall effect in a strongly inhomogeneous magnetic field and show how a response function can be defined to calculate the Hall voltage for an arbitrary magnetic-field distribution. The results are successfully applied to recent scanning Hall probe microscopy data on superconducting vortices.