Atomistic origin of exchange anisotropy in $\gamma$-IrMn$_3$-CoFe bilayers

The exchange interaction determines the ferromagnetic (FM) or antiferromagnetic (AFM) ordering of atomic spins. When ferromagnets and antiferromagnets are coupled together, they often exhibit the exchange bias effect, a unidirectional interface exchange field causing a shift of the magnetic hysteresis loop. The effective magnitude of this interface exchange field is at most a few percent of the bulk exchange, arising from pinned interfacial spins in the antiferromagnet. The pinned spins are known to comprise a small fraction of the total number of interface spins, yet their exact nature and physical origin has so far been elusive. Here we show that in the technologically important $\gamma - IrMn_3/CoFe$ structure the pinned interface spins are in fact delocalised over the whole interface layer. The pinned spins arise from the small imbalance of the number of spins in each magnetic sublattice in the antiferromagnet due to the natural atomic disorder. These pinned spins are strongly coupled to the bulk antiferromagnet explaining their remarkable stability. Moreover, we find that the ferromagnet strongly distorts the interface spin structure of the antiferromagnet, causing a large reversible interface magnetisation that does not contribute to exchange bias. The unexpected delocalised nature of the pinned interface spins explains both their small number and their stability, uncovering the mysterious microscopic origin of the exchange bias effect.