A magnetic head for reading information from a magnetic medium is provided. The magnetic head includes a substrate, having a substrate thermal coefficient of expansion, and a read element positioned above the substrate. The head also includes a shield, positioned above the substrate and adjacent the read element, which has a shield thermal coefficient of expansion that substantially matches the substrate thermal coefficient of expansion. The shield absorbs stray magnetic fields from the magnetic medium, which emanate from stored data that is adjacent to a data element that is directly beneath and read by the magnetoresistive read element. This shield may also serve to provide electrical contact for the read element. The magnetic thermal coefficient of expansion and electrical properties of the shield may be suitably optimized through appropriate choice of component materials and structure.