It has been found that the insertion of a copper laminate within CoFe, or a CoFe/NiFe composite, leads to higher values of CPP GMR and DRA. However, this type of structure exhibits very negative magnetostriction, in the range of high -10.sup.-6 to -10.sup.-5. This problem has been overcome by giving the copper laminates an oxygen exposure treatment When this is done, the free layer is found to have a very low positive magnetostriction constant. Additionally, the value of the magnetostriction constant can be adjusted by varying the thickness of the free layer and/or the position and number of the oxygen treated copper laminates.