In one illustrative example of the invention, a spin valve sensor of a magnetic head has a sensor stack structure which includes a free layer structure and an antiparallel (AP) pinned layer structure separated by a spacer layer. A capping layer structure formed over the sensor stack structure includes a layer of cobalt (e.g. pure cobalt, oxidized cobalt, or cobalt-iron) as well as a layer of tantalum formed over it. Advantageously, the cobalt layer in the capping layer structure enhances the GMR and soft magnetic properties for thinner freelayer structures while maintaining a desirable slightly negative magnetostriction.