An apparatus, according to one embodiment, includes: a module; and a plurality of tunnel valve read transducers arranged in an array extending along the module. Each of the tunnel valve read transducers includes: a sensor structure having a tunnel barrier layer and a free layer. Moreover, each of the tunnel valve read transducers includes a pair of hard bias magnets which sandwich the respective sensor structure therebetween, the hard bias magnets being positioned on opposite sides of the sensor structure along a cross-track direction. Furthermore, a thickness of each of the hard bias magnets at a thickest portion thereof is at least 10 times greater than a thickness of the free layer. Other systems, methods, and computer program products are described in additional embodiments.