A magnetoresistive sensor having a longitudinal field that is produced along its axis and that stabilizes the sensor. The longitudinal field is produced by the current in conductors that are connected to the magnetoresistive sensor elements. By controlling the direction and distribution of the current in the conductors, a longitudinal field is produced that has the required direction and magnitude to stabilize the single domain state of the sensor. The resulting lack of domain wall motion in the sensor during operation prevents instabilities in its electrical output, commonly known as Barkhausen noise. Four different sensor designs are provided that include two single element sensors with two conductors, a dual element sensor with four conductors, and a dual element sensor with three conductors. The ease of implementation makes the stabilized sensor of the present invention superior to conventional approaches that rely on permanent magnets or exchange coupled layers to provide longitudinal bias.