The relationship between the sign of exchange bias and the magnetization depth profile of Co/FeF$_{2}$

We have used the unique spatial sensitivity of polarized neutron beams in reflection geometry to measure the depth dependence of magnetization across the interface between a ferromagnet (Co) and an antiferromagnet (FeF$_{2})$. Our Co/FeF$_{2}$ bilayer sample is one that exhibits either positive or negative exchange bias depending upon the magnitude of the cooling field. For positive exchange bias, pinned magnetization at the Co/FeF$_{2}$ interface is directed opposite to the cooling field, while in the FeF$_{2}$ bulk, the net pinned magnetization is parallel to the cooling field. For negative exchange bias, the net pinned magnetization near the Co/FeF$_{2}$ interface is parallel to the direction of the cooling field. We propose a model that explains the cooling field dependence of the sign of exchange bias. Work at LANL and UCSD was funded by the U.S. Department of Energy, BES-DMS, and by a University of California Campus-Laboratory Collaboration grant.