Analytical solutions for exchange bias and coercivity in ferromagnetic/antiferromagnetic bilayers

Abstract

Analytical expressions have been derived for the exchange bias field, coercivity, and effective anisotropy field in ferromagnetic/antiferromagnetic bilayers in the framework of a model assuming the formation of a planar domain wall at the antiferromagnetic side of the interface with the reversal of the ferromagnetic orientation. It is shown that there are five different sets of analytical expressions for the hysteresis loop displacement and coercivity, which depend on the interfacial exchange coupling strength and ferromagnetic anisotropy, and only one expression for the effective anisotropy field. These expressions are compared with the previously reported theoretical results, and the validity of the latter is discussed. It is shown that in the framework of the present model, the hysteresis loop, ac susceptibility, and ferromagnetic resonance measurements of exchange anisotropy should give the same values for the exchange bias field. The difference between the exchange bias field values, estimated experimentally by ac susceptibility and through hysteresis loop measurements for Co/CoO bilayers, is explained as well.