The angular dependence of the exchange bias under the planar domain wall model

Based on the principle of minimal energy, the angular dependence of exchange bias (ADEB) under planar domain wall model has been investigated in detail. Three different types of the initial states, monostable, bistable and tristable states, will be formed in exchange-biased systems by adjusting the relative strength of the uniaxial anisotropy, unidirectional anisotropy and the planar domain wall energy. These initial states determine the ADEB directly. The jump phenomena were still existent in the ADEB. Additionally, it can be found that the magnetization reversal mode is sensitive to the orientation of the magnetic field. Two distinct modes of the magnetization rotation, half-plane rotation and whole-plane rotation, can be observed when the applied field points along different orientations. These modes of the magnetization rotation can be identified by different features of the transverse hysteresis loops. Our investigations about the ADEB and the magnetization reversal modes are helpful to interpret the magnetic behaviors of some exchange-biased systems, which can be described by planar domain wall model