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The field shift of the hysteresis loop, called exchange bias field, in ferromagnetic/antiferromagnetic (F/AF) Co/IrMn bilayers, or (Pt/Co),,/IrMn structures, appears only above a critical thickness of IrMn, which is related to the IrMn magnetocrystalline anisotropy and to the interfacial coupling between the F and AF layers. In this letter, we show that this critical IrMn thickness can be considerably reduced by sandwiching the IrMn layer between two F layers or multilayers having parallel or orthogonal anisotropy, i.e., the first being magnetized in plane and the second out of plane. An in-plane exchange bias field of 20 mT could be measured in structures of the form (Pt/Co)3/IrMn/Co (5 nm) having an IrMn layer as thin as 3 nm at room temperature. Several explanations are proposed and discussed. The first is associated with structural variations of texture resulting in changes in the antiferromagnet grains' anisotropy energy. The second is based on an enhancement of the stability of the antiferromagnet spin lattice resulting from an indirect intergrain coupling. The third relies on a decrease of the Co/IrMn interfacial coupling due to an out-of-plane canting of the interfacial spin.