The Hall effect of an inhomogeneous magnetic field in mesoscopic structures

We present a simulation of the motion of electrons in a mesoscopic Hall bar, scattered by a local inhomogeneous magnetic field. In the low-field regime, the Hall resistance is found to be determined precisely by the average magnetic field in the cross junction, which implies a valuable device application of non-invasive access for measuring magnetic flux, like SQUIDs do, but on a rather small (submicron) scale. The bending resistance is found to depend sensitively on the local magnetic field profile, which may also imply certain device applications, such as detecting the local magnetic properties of small objects. We also discuss briefly the asymmetric effect due to non-identical leads and asymmetric location of the field profile in the cross junction.