Hall anomaly of diffusive magnetic waveguides

We report on the Hall resistance in a diffusive two-dimensional (2D) electron channel incorporating a strong magnetic barrier at its center. An external magnetic field was tilted in the plane perpendicular to the barrier to separate magnetization effects due to ferromagnetic elements from effects of magnetic channeling in the 2D electron gas. In the presence of an inhomogeneous current distribution, the Hall resistance is found to measure the trapping of electrons in or out of magnetic edge states rather than the magnetization average over the Hall cross. A simple formula for the Hall resistance in this regime is proposed.