An antiferromagnetically exchange-coupled structure for use in a magnetic device, such as a magnetoresistive sensor, includes an enhancement layer formed of a chemically-ordered tetragonal-crystalline alloy, a chemically-ordered tetragonal-crystalline Mn-alloy antiferromagnetic layer in contact with the enhancement layer, and a ferromagnetic layer exchange-coupled with the antiferromagnetic layer. The enhancement layer is an alloy selected from the group consisting of alloys of AuCu, FePt, FePd, AgTi3, Pt Zn, PdZn, IrV, CoPt and PdCd, and the antiferromagnetic layer is an alloy of Mn with Pt, Ni, Ir, Pd or Rh. The enhancement layer enhances the transformation of the Mn alloy from the chemically-disordered phase to the chemically-ordered phase.