Cooling-field dependence of dipole-induced loop bias

In ferromagnet/antiferromagnet bilayers and core/shell nanoparticles, an exchange-bias-like loop bias phenomenon in the ferromagnet is observed solely due to the long-range dipolar interactions between ferromagnet and antiferromagnet. With increasing cooling field, the loop bias field may increase from zero in the bilayers or from a negative value in the core/shell nanoparticles to a positive saturated value, depending on the interfacial dipolar interaction and/or ferromagnetic/antiferromagnetic thickness. Using a modified Monte-Carlo method and the Meiklejohn-Bean model, the interfacial dipole fields (up to several teslas) and the domain sizes imprinted on the interfacial antiferromagnet are explicitly calculated to elucidate the cooling field dependence of loop bias, which is governed by distinct mechanisms at the flat and curved interfaces. Finally, through simply discussing the roles of lattice structure, ferromagnetic dipolar interaction, and simulation time, it is evidenced that the dipole-induced loop bias is ubiquitous and applicable for stabilizing a ferromagnet, irrespective of the interface mismatch and the undeterministic diffusion between different ingredients. This work helps us to develop the spintronic devices with nonatomic-contact nanostructure assemblies.