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

Analytical expressions have been derived for the exchange bias field, coerc ivity, and effective anisotropy field in ferromagnetic/antiferromagnetic bi layers in the framework of a model assuming the formation of a planar domai n wall at the antiferromagnetic side of the interface with the reversal of the ferromagnetic orientation. It is shown that then are five different set s of analytical expressions for the hysteresis loop displacement and coerci vity, which depend on the interfacial exchange coupling strength and ferrom agnetic anisotropy, and only one expression for the effective anisotropy fi eld. These expressions are compared with the previously reported theoretica l 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 gi ve the same values for the exchange bias field. The difference between the exchange bias field values, estimated experimentally by ac susceptibility a nd through hysteresis loop measurements for Co/CoO bilayers, is explained a s well.