Simple mechanism for a positive exchange bias

We argue that the interface coupling, responsible for the positive exchange bias ${(H}_E)$ observed in ferromagnetic/compensated antiferromagnetic (FM/AF) bilayers, favors an antiferromagnetic alignment. At low cooling field this coupling polarizes the AF spins close to the interface, where spin configuration persists after the sample is cooled below the Néel temperature. This pins the FM spins as in Bean’s model and gives rise to a negative $H_E.$ When the cooling field increases, it eventually dominates and polarizes the AF spins in an opposite direction to the low-field one. This results in a positive $H_E.$ The size of $H_E$ and the crossover cooling field are estimated. We explain why $H_E$ is mostly positive for an AF single crystal, and discuss the role of interface roughness on the magnitude of $H_E,$ and the quantum aspect of the interface coupling.