Training of the exchange-bias effect: A simple analytic approach

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, μ₀HEB(n), 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 μ₀HEB 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 μ₀HEB(n) 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 n1. The full capability of the theory is explored in comparison with experimental results obtained recently on a NiO(001)∕Fe(110) heterostructure.