An apparatus, according to one embodiment, includes: a tape head having: a write module, a read module, and a plurality of tunnel valve read transducers arranged in an array extending along the read module. Each of the tunnel valve read transducers includes: a sensor structure, an upper and lower magnetic shield, an upper conducting spacer layer between the sensor structure and the upper magnetic shield, a lower conducting spacer layer between the sensor structure and the lower magnetic shield, and electrically insulating layers opposite the sensor structure. The sensor structure includes a cap layer, a free layer, a tunnel barrier layer, a reference layer and antiferromagnetic layer. A height of the free layer measured in a direction perpendicular to a media bearing surface of the read module is less than a width of the free layer measured in a cross-track direction perpendicular to an intended direction of media travel.