Unified nonequilibrium dynamical theory for exchange bias and training effects

We have investigated the exchange bias and training effect in the ferromagnetic/antiferromagnetic (FM/AF) heterostructures using a unified Monte Carlo dynamical approach. The magnetization of the uncompensated AF layer is still open after the first field cycling is finished. Our simulated results show obvious shift of hysteresis loops (exchange bias) and cycling dependence of exchange bias (training effect) when the temperature is below 45 K. The exchange bias field decreases with decreasing cooling rate or increasing temperature and the number of the field cycling. Essentially, these two effects can be explained on the basis of the microscopical coexistence of both reversible and irreversible moment reversals of the AF domains. Our simulations are useful to understand the real magnetization dynamics of such magnetic heterostructures.