Rotatable anisotropy and coercivity in exchange-bias bilayers

A phenomenological approach for polycrystalline exchange-bias bilayers is proposed which explains the coercivity enhancement as well as its temperature and coupling strength dependences. In the model, it is assumed that uncompensated interfacial antiferromagnetic grains can switch their magnetizations irreversibly, producing a rotatable anisotropy. A preferential distribution of the antiferromagnetic easy axes is also considered. An inhomogeneous ferromagnetic magnetization reversal is allowed, assuming that the ferromagnet is divided into domains, each coupled to a stable antiferromagnetic grain only. The antiferromagnetic anisotropy distribution affects the angular dependence of the coercivity, reducing its value in the vicinity of the exchange-bias direction, also smoothing the loop shift variations, more notably for small ferromagnetic uniaxial anisotropy. The inclusion of the rotatable anisotropy changes the shape of the magnetization curves and their characteristics. The larger the relative contribution of the rotatable anisotropy to the effective uniaxial anisotropy, the closer the loop shift angular variation gets to a pure cosine behavior, and no significant effect on the coercivity for strong coupling is detected. The frequently observed peak in the temperature variation of the coercivity is also explained considering the variation of the rotatable anisotropy, which is directly connected to the temperature dependence of the unstable antiferromagnetic grains' magnetization.