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Contact between a Co∕ Pt multilayer and an IrMn film leads to perpendicular exchange bias. The exchange bias field does not depend on the degree of (111) film texture and for Co∕ Pt multilayers with IrMn at the bottom it can be enhanced by magnetic field annealing. The perpendicular exchange bias of the Co∕ Pt–Ir Mn system is limited by a misalignment between the Co spins and the film normal, which is due to a negative magnetic anisotropy contribution from the Co∕ Ir Mn interface (K S Co∕ Ir Mn=− 0.09 mJ∕ m 2)⁠. The insertion of a 3 Å thick Pt layer at the Co∕ Ir Mn interface maximizes the perpendicular exchange-bias field.