Scattering of electrons at a magnetic protuberance of submicron size

We have studied transport of 2D electrons through individual magnetic inhomogeneities of the height up to 1 T and the size down to 100 nm. Such magnetic fields were created by placing dysprosium microtablets on top of a near-surface 2D electron gas (2DEG). The cyclotron orbit for such inhomogeneities becomes smaller than their size and incident electrons are strongly deflected. We report an inversion of the sign of the Hall effect: a positively magnetised micromagnet on top of a 2DEG gives rise to a Hall signal which corresponds to a negative field applied to the 2DEG. This dramatic anomaly is attributed to the fact that 2D electrons are not able to reach the central, strongest part of the magnetic field and, therefore, the dominant contribution to the Hall effect comes from a stray field having the opposite sign.