Apparatus and method for providing a magnetic head that includes a magnetoresistive read sensor disposed between first and second magnetic shields. The shields are configured to reduce protrusion of the shields from a polished flat air bearing surface of the magnetic head upon increases in temperature. This configuration for the shields therefore at least reduces differences in thermal expansion of the shields relative to other parts of the magnetic head forming the air bearing surface. These shields according to some embodiments include one or more ferromagnetic layers exchange coupled with an antiferromagnetic layer. Further, in a particular embodiment, all the ferromagnetic layers within each of the shields can have a combined thickness per shield of less than 500 angstroms.