Competing interfacial exchange and Zeeman energies in exchange biased bilayers

The exchange bias in antiferromagnet $\left({\mathrm{MnF}}_2\right)$/ferromagnet (Fe) bilayers has been studied as a function of temperature, cooling field, and interfacial roughness. Positive exchange bias is observed under certain conditions, along with a nonmonotonic roughness dependence. The unusual cooling field dependence can be understood within a simple model in which the exchange bias is determined by a competition between a roughness-dependent average exchange energy and a Zeeman energy for the antiferromagnet surface spins. Our results are consistent with the existence of a domain wall parallel to the interface in the Fe layer, contrary to earlier theoretical models.