Diffusive transport in a Hall junction with a microinhomogeneous magnetic field

The diffusive classical transport of a two-dimensional electron gas in a four-terminal Hall junction is investigated in the presence of different nonuniform axially symmetric magnetic field profiles. Starting from the continuity equation, we calculate numerically the steady state electrostatic potential and current distributions in the Hall device. The Hall resistance was found to be insensitive to the functional form of the localized magnetic field inhomogeneity in the parameter region $\mu B\ll 1$ and is related to the total magnetic flux in an effective area about twice that of the junction area. The latter is due to the spread of the transport current into the voltage probes. The size of this effective area is different when the voltage probes are wider than the current probes.