<title>Quenching of the hall effect in localised high magnertic field region</title>

We report the suppression of the Hall effect in a mesoscopic Hall cross with a strong magnetic field only in the center and vanishingly small outside. The local magnetic field is produced by placing Dy pillar on top of a structure with high-mobility two-dimensional electron gas (2DEG). The effect is found to be due to a sharp increase of the number of back-scattered and quasi-localized electron orbits. The possibility of localizing electrons inside the magnetic inhomogeneity region is discussed.