A giant magnetoresistance (GMR) sensor with strongly pinning and pinned layers is described for magnetic recording at ultrahigh densities. The pinning layer is an antiferromagnetic (AFM) iridium-manganese-chromium (Ir--Mn--Cr) film having a Mn content of approximately from 70 to 80 atomic percent and having a Cr content of approximately from 1 to 10 atomic percent. The first pinned layer is preferably a ferromagnetic Co--Fe having an Fe content of approximately from 20 to 80 at % and having high, positive saturation magnetostriction. The second pinned layer is preferably a ferromagnetic Co--Fe having an Fe content of approximately from 0 to 10 atomic percent. The net magnetic moment of the first and second pinned layers is designed to be nearly zero in order to achieve a pinning field of beyond 3,000 Oe.