The jump phenomenon in the angular dependence of the off-aligned exchange bias

Based on the principle of minimal energy, the angular dependence of exchange bias has been investigated in detail with noncollinear easy axes of unidirectional and uniaxial anisotropies in the ferromagnetic/antiferromagnetic bilayers. The competition between unidirectional and uniaxial anisotropies divides the initial magnetization state of the bilayers into monostable state and bistable state, which determine the angular dependence of exchange bias directly. When the external field is applied along the intrinsic easy axes and intrinsic hard axes, it is found that one of the coercive fields at the descending or ascending branch of the hysteresis loop makes an abrupt change, whereas the other coercive field keeps continuity by analyzing the magnetization reversal processes. Consequently, the exchange bias field and the coercivity will show the jump phenomenon in the angular dependence of exchange bias. This jump phenomenon of the exchange bias is found to be an intrinsic property of the bilayers which is dependent on the relative magnitudes and orientations between unidirectional and uniaxial anisotropies. The numerical calculations indicate that both the exchange bias field and the coercivity are larger in the magnitude at the points of the jumps. At the jumping points of the intrinsic easy axes, the coercivity reaches the maximum; at the jumping points of the intrinsic hard axes, the exchange bias field reaches the maximum, at the meantime the coercivity can vanish itself suddenly. These features of the jump phenomenon are useful in the technological applications to achieve the largest exchange bias field.