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We present a novel magnetoelectronic device for application as a nonvolatile memory cell, logic gate, or magnetic field sensor. It comprises a micron scale high mobility semiconducting Hall cross and a single, electrically isolated microstructured ferromagnetic film. The ferromagnetic film has in-plane magnetization and is fabricated with one edge directly over the Hall cross. Magnetic fringe fields from the edge of the film have a large component perpendicular to the plane of the semiconductor (magnitude of the order of kOe), are localized to a submicron region centered beneath the edge, and generate a Hall voltage in the sensor arms of the Hall cross. The sign of the fringe field, as well as the sign of the output Hall voltage, is switched by reversing the magnetization of the ferromagnet.