Magnetization distribution in exchange spring bilayers with mutually orthogonal anisotropies

A soft/hard bilayer system with mutually orthogonal anisotropies is considered in this paper. The easy axis of the hard layer is perpendicular to the film plane, and the easy axis of the soft layer is parallel to the film plane. Pt84Co16 is chosen as the soft layer material, and TbFeCo is chosen as the hard layer material. The one-dimensional continuum micromagnetic model is used. The characteristics of nucleation fields, angular distribution and hysteresis loops are studied. The calculation results show that the nucleation field decreases rapidly and even turns negative with increasing soft layer thickness. This negative nucleation field is caused by the demagnetizing field and the easy axis orientation of the soft layer which is parallel to the film plane. Both of these two factors can induce an effective in-plane uniaxial anisotropy, which will tend to align the magnetization of the soft layer parallel to the film plane. As the magnetocrystalline anisotropy constant K of the soft layer is very small, the negative nucleation field mainly comes from the demagnetizing field of the soft layer. The angular distribution calculation shows that the change rate of magnetization deviation angle (degree per nanometer) along z axis in the soft layer is faster than that in the hard layer. The angular change rate could be adjusted by varying the anisotropy constant ratio, exchange energy constant ratio, or external field. When the anisotropy constant ratio Ks/Kh (soft/hard) or exchange energy constant ratio As/Ah (soft/hard) increases, the angular change rate ratio (soft/hard) decreases. Especially when both Ks/Kh and As/Ah increase at the same time, the angular change rate in the hard layer could become faster than that in the soft layer. If the anisotropy constant Ks becomes larger, it is more difficult for the magnetization in the soft layer to deviate from its easy axis than before. This will also enhance the pinning effect of the magnetization in the soft layer, and reduce the difference in deviation angle between the two boundaries of the soft layer. When the exchange energy constant As increases, the magnetization tends to become parallel to the neighboring magnetization, which also reduces the angular change of magnetization in the soft layer. As the anisotropy constant is roughly proportional to the square of spontaneous magnetization, the effect of spontaneous magnetization on the angular change rate comes from the anisotropy constant change. The simulation for the hysteresis loops shows that the saturation field strength increases while the remanence decreases with increasing both the values of Ks and As.