Understanding of exchange bias in ferromagnetic/antiferromagnetic bilayers

In this chapter, we present the theoretical analysis and numerical simulation of the exchange bias (EB) phenomenon in the ferromagnetic/antiferromagnetic bilayers (FM/AFM) [1-3]. The EB phenomenon was discovered experimentally by Meiklejohn and Bean in 1956 [1]. The phenomenon has numerous applications in nanoelectronics and spintronics. A comprehensive explanation of the EB does not exist yet [4-17]. The effect manifests itself in the shift of the magnetization dependence on the external magnetic field M(H) along the field axis. The shift of the hysteresis loop is proportional to the exchange interaction through the FM/AFM interface J 0, whereas the width of the hysteresis loop is proportional to the magnetic anisotropy in the FM layer. The phenomenon appears in the systems with contacting FM/AFM subsystems: layered systems, nanoparticles [2], multiferroics [18]. In the simplest model of EB, the AFM is assumed to be a hard magnetic material [19,20], the AFM interface is uncompensated, and the FM film has a uniform magnetization. The easy-plane anisotropy and an additional weak anisotropy in the easy plane are taken into account. The model of the phenomenon gives an expression for the EB H bias = J 0 S_AFMS_FM/L_FM_F, where S_AFM and S_FM are the AFM and FM magnetic moments, respectively, MFM is the magnetization of the FM that is constant along the FM/AFM interface, and J 0 is the interlayer exchange interaction. Such an expression for H _bias, however, gives a significantly larger value of the hysteresis loop shift than that observed in experiments. It is important to note that the same value of the shift is observed in the case of compensated FM/AFM interface [21-23]. Since EB was discovered, a lot of theoretical models have been proposed [4]. Among them, the possibility of the domain walls appears both in the FM and the AFM subsystems [7,8,24]; the impact of the interface defects on the EB effect [5], the influence of the domain and polycrystalline structure of materials [6]. In References [25,26], the authors presented an explanation of the nature of EB phenomenon in systems with a compensated FM/AFM interface. The recent works also study the geometrical frustration in the FM/AFM-layered system and its impact on the shift of the magnetization curves [27-29]. Recently, new features of the EB phenomenon were observed experimentally [30-33]. The shifted hysteresis loop becomes asymmetric M(2H _bias-H) ≠ -M(H) and additional horizontal plateaus appear [31,33]. The slope of the magnetization curve is different on different parts of the curve. These features can be explained by different spin-flip kinetics in different magnetic configurations. Here, we propose an explanation to the magnetization curves features, such as horizontal plateaus, asymmetry, split of the hysteresis loop. We use the assumption that these features can be associated with an inhomogeneous magnetization distribution in the FM film. We consider the cases of the perfect and rough FM/AFM interface. The horizontal plateaus, asymmetry, and other features of the magnetic hysteresis loops are obtained in the framework of such models.