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, mu(0)H(EB)(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 mu(0)H(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(EB)(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 ngreater than or equal to1. The full capability of the theory is explored in comparison with experimental results obtained recently on a NiO(001)/Fe(110) heterostructure.