A physical model of exchange bias in [Pd/Co]5/FeMn thin films with perpendicular anisotropy

Abstract

A physical model of perpendicular exchange bias (PEB) has been established based on the total energy equation per unit area of an exchange bias system by assuming coherent rotation of the magnetization. The anisotropy energy of antiferromagnetic (AFM) layer, KAFM×tAFM, as well as ferromagnetic (FM) multilayers, KFM,eff×tFM, and the interfacial exchange coupling energy, Jex were considered as primary physical parameters in building up the physical model of PEB phenomenon. It was proposed that the PEB is a result of the energy competition between KAFM×tAFM, KFM,eff×tFM, and Jex; where KAFM×tAFM≥Jex, is a critical condition to observe exchange bias in the system. In particular, it was revealed that Jex is directly relevant to the net magnetization of FM and AFM spin structure, Jex∝cos αAFM×cos βFM, in the perpendicular direction rather than the magnetization angle difference observed in an in-plane system. The physical role of perpendicular anisotropy energy, KFM,eff×tFM was also found to be significant to enhance the PEB. These physical characteristics are completely different from those are observed from an exchange bias system with in-plane anisotropy. The physical validity of the proposed PEB model was confirmed using different structures of exchange biased [Pd/Co]5/FeMn thin films with perpendicular anisotropy. The experimentally analyzed results demonstrated that the physical model of PEB proposed in this work is agreed well with the experimentally observed PEB phenomenon. Furthermore, the proposed model was found to be effective to design and to predict a new PEB system for the advanced spintronics applications.