Training of the exchange bias effect in antiferro-/ferromagnetic heterostructures is considered in the theoretical framework of spin configurational relaxation, which is activated through consecutively cycled hysteresis loops. The corresponding exchange bias fields, ${\mu }_0{H}_{\text{EB}}\left(n\right)$, reveal relaxation from the initial state, $n=1$, of high antiferromagnetic interface magnetization to the equilibrium state of reduced magnetization in the limit of large $n$. The evolution of ${\mu }_0{H}_{\text{EB}}$ vs $n$ is calculated with the help of a discretized Landau-Khalatnikov equation, where the continuous time parameter is replaced by the loop index $n$. The result reveals the origin of the well established but hitherto unexplained power-law decay of ${\mu }_0{H}_{\text{EB}}\left(n\right)$ for $n>1$. Moreover, in contrast with the breakdown of the power-law behavior at $n=1$, the relaxation approach describes the training effect for $n⩾1$. The full capability of the theory is explored in comparison with experimental results obtained recently on a $\mathrm{NiO}\left(001\right)∕\mathrm{Fe}\left(110\right)$ heterostructure.

• Received 2 December 2003

DOI:https://doi.org/10.1103/PhysRevB.70.014421