In one embodiment a magnetic head includes a sensor thin film adapted for producing a planar Hall voltage, the sensor thin film having a thickness along a down-track direction that is greater than a thickness along a cross-track direction. The down-track direction is in a direction of travel of a magnetic medium relative to the sensor thin film, and the cross-track direction is perpendicular to the down-track direction. In another embodiment, at least one magnetic head as described above is included in a magnetic data storage system, which includes a magnetic medium, a drive mechanism for passing the magnetic medium over the at least one magnetic head, and a controller electrically coupled to the at least one magnetic head for controlling operation of the at least one magnetic head. Other heads and systems are described according to various other embodiments.