A universal scaling law of exchange bias training effect

Exchange bias training effect in ferromagnetic/antiferromagnetic bilayers is investigated. In some systems the evolution of the exchange bias field $H_E$ with the number of cycle $n$ cannot be fitted by the empirical $1/\sqrt{n}$ function. A unified expression is derived from a discretized Landau-Khalatnikov equation in the framework of the thermodynamics model which is proposed by Ch.\ Binek. This generalized model describes well training effect independent of the magnetization reversal mechanism in the ferromagnetic layers.