Analytic treatment of the incomplete ferromagnetic domain-wall model for exchange bias

Abstract The incomplete ferromagnetic domain-wall model we proposed recently is solved analytically. We derive the dependence of the exchange bias field ( H EB ) on the different parameters that characterize the magnetic bilayer system. Excellent agreement with the numerical solutions is achieved. Moreover, the model yields a crossover from a t F −1 dependence of H EB for thin ferromagnetic films, to a t F −1.9 dependence for thick films, where t F is the ferromagnetic film thickness. Our results are in agreement with experiment.