The origin of exchange bias in multigranular non-collinear IrMn$_3$/CoFe thin films

Antiferromagnetic spintronic devices have the potential to outperform conventional ferromagnetic devices due to their ultrafast dynamics and high data density. A challenge in designing these devices is the control and detection of the orientation of the anti-ferromagnet. One of the most promising ways to achieve this is through the exchange bias effect. This is of particular importance in large scale multigranular devices. Due to the large system sizes, previously, only micromagnetic simulations have been possible, these have an assumed distribution of antiferromagnetic anisotropy directions. Here, we use an atomistic model where the distribution of antiferromagnetic anisotropy directions occurs naturally and the exchange bias occurs due to the intrinsic disorder in the antiferromagnet. We perform large scale simulations, generating realistic values of exchange bias. We find a strong temperature dependance of the exchange bias, which approaches zero at the blocking temperature while the coercivity has a peak at the blocking temeprature due to the superparamagnetic flipping of the antiferromagnet during the hysteresis loop. We find a large discrepancy between the exchange bias predicted from a geometric model of the antiferromagnetic interface indicating the importance of grain edge effects in multigranular exchange biased systems. The grain size dependence shows the expected peak due to a competition between the superparamagnetic nature of small grains and reduction in the statistical imbalance in the number of interfacial spins for larger grain sizes. Our simulations confirm the existence of single antiferromagnetic domains within each grain. The model gives insights into the physical origin of exchange bias and provides a route to developing optimised nanoscale antiferromagnetic spintronic devices.