Hall Resistance of a Two-Dimensional Electron Gas in the Presence of Magnetic Clusters with Large Perpendicular Magnetization

Abstract

The Hall and magnetoresistance of a two-dimensional electron gas (2DEG) placed a small distance from a random distribution of identical perpendicular magnetized ferromagnetic clusters is studied. The magnetic clusters are modeled both by magnetic dipoles, and by thin magnetic disks. The electrons in the 2DEG are scattered by the magnetic field profiles as created by the magnetic clusters.

Although the average magnetic field is zero, we find a nonzero Hall resistance (R _xy), which increases with k _F, for small Fermi energies (E _F = ħ² k ² _F/2m), but which tends to zero for higher energies. For magnetic disks we find resonances in both the Hall and the magnetoresistance (R _xx) as function of the Fermi wave vector. The physical reason is that quasi bound electron states are formed in the nonhomogeneous magnetic field profiles, and so electrons are trapped underneath the magnetic disk. Such resonances enhance R _xx, but reduce R _xy.