Modeling the exchange bias interaction in ferromagnetic/antiferromagnetic films and nanostructures

A novel approach to model the exchange bias (EB) effect in ferromagnetic (FM)/antiferromagnetic (AFM) continuous films and nanodots is presented. The aim is to study both the EB magnetothermal stability and spatial confinement effects, key features for modern spintronic devices. The EB is due to the exchange coupling at the FM/AFM interface, and is featured by the exchange bias field (Hex), i.e. the horizontal shift of the hysteresis loop. To model the exchange coupling we used the three-dimensional Object Oriented MicroMagnetic Framework. The AFM phase was described as a collection of both fixed and rotatable spins (FSs and RSs, respectively) both interacting with the FM phase: the FSs have the role of pinning centers, i.e. they mirror the presence of regions with high anisotropy energy in the AFM phase, so they increase Hex; the RSs change their orientation following the FM magnetization, so they do not contribute to Hex. The calculations were performed for a continuous film and for squared dots with size (D) ranging from 1200 nm down to 300 nm. By changing the FSs to RSs relative fraction we accounted for confinement effects, confirming a reduction of the anisotropy energy for the AFM grains at the dot border. Moreover, by introducing spatial correlations among FSs we modeled the proven existence of a low temperature frozen collective regime of the interfacial AFM spins and its interplay with D. A good agreement was found between the results of the calculations and the experimental data [1]. Finally, we tested our model for the description of the dynamical properties of the FM/AFM system; we will present our results regarding the spin wave frequency dependence on the external magnetic field.