图 1  本文基本方案为t ^s + t ⁱ + t ^h = 15 nm, 计算范围从–t ^s到t ^h. 计算模型　(a) 易轴平行膜面; (b) 易轴垂直膜面

Fig. 1.  The basic scheme in our work, with regions calculated from –t ^s to t ^h when t ^s + t ⁱ + t ^h = 15 nm. Fig. 1(a) and (b) show the model for the calculation of the easy axis parallel and perpendicular to the film plane, respectively.

图 2  界面层厚度tⁱ不同时SmCo(5 nm)/Fe(10–tⁱ nm)双层膜的退磁曲线　(a) 易轴平行膜面; (b) 易轴垂直膜面. 插图是H_N, H_P 和H_C随tⁱ的变化曲线

Fig. 2.  Demagnetization curves of SmCo(5 nm)/Fe(10–tⁱ nm) bilayers for various interface layer thicknesses tⁱ. Fig. 2(a) and 2(b) show the demagnetization curves of the easy axis parallel and perpendicular to the film plane, respectively. The inset shows the change curves of the H_N, H_P and H_C as functions of tⁱ.

图 3  $ t^{\rm i} $ = 4 nm时SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜在不同外磁场下膜厚方向上的自旋分布　(a) 易轴平行膜面; (b) 易轴垂直膜面. 插图是四个关键角$ {\theta }^{\text{s}}$, $ {\theta }^{{\text{i}}_{\text{1}}} $, $ {\theta ^{{{\text{i}}_{\text{2}}}}} $和$ {\theta ^{\text{h}}} $随外磁场的变化曲线

Fig. 3.  Spin distributions in the thickness direction for the SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayer with $ t^{\rm i} $ = 4 nm under various applied magnetic fields. Fig. 3(a) and (b) show the spin distributions of the easy axis parallel and perpendicular to the film plane, respectively. The inset shows the evolution of four key angles, i.e., $ {\theta ^{\text{s}}} $, $ {\theta ^{{{\text{i}}_{\text{1}}}}} $, $ {\theta ^{{{\text{i}}_{\text{2}}}}} $ and $ {\theta ^{\text{h}}} $ as functions of the applied magnetic field.

图 4  $ t^{\rm i} $ = 4 nm时易轴平行膜面SmCo(5 nm)/Fe(10–$ t^{\rm i} $nm)双层膜在不同外磁场下一些膜面内的自旋分布　(a) H = –5.3 kOe时的软磁层表面; (b) H = –8.7 kOe时的软磁层表面; (c) H = –10.7 kOe时的硬磁层与界面层第二界面; (d) H = –11.3 kOe时的硬磁层表面. 显示比例为1∶12, 即图中的每一个磁矩代表12 × 12个计算的磁矩

Fig. 4.  The spin distributions within some film planes for the parallel SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayer with $ t^{\rm i} $ = 4 nm under various applied magnetic fields: (a) H = –5.3 kOe, the soft layer surface; (b) H = –8.7 kOe, the soft layer surface; (c) H = –10.7 kOe, the second interface between the hard and interface layers; (d) H = –11.3 kOe, the hard layer surface. The adopted ratio 1∶12 for presentation. This means that one displayed magnetic moment at the figure stands for 12 × 12 calculated moments.

图 5  $ t^{\rm i} $ = 4 nm时易轴垂直膜面取向SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜不同外磁场下四个关键角对应膜面内的自旋分布　(a) H = 10.7 kOe时的软磁层表面; (b) H = 10.7 kOe时的软磁层与界面层第一界面; (c) H = 2.7 kOe时的硬磁层与界面层第二界面; (d) H = –14.0 kOe时的硬磁层表面. 显示比例为1∶12, 即图中的每一个磁矩代表12 × 12个计算的磁矩

Fig. 5.  The spin distributions corresponding to four key angles within the film plane for the perpendicular SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayer with $ t^{\rm i} $ = 4 nm under various applied magnetic fields: (a) H = 10.7 kOe, the soft layer surface; (b) H = 10.7 kOe, the first interface between the soft and interface layers; (c) H = 2.7 kOe, the second interface between the hard and interface layers; (d) H = –14.0 kOe, the hard layer surface. The adopted ratio 1∶12 for presentation. This means that one displayed magnetic moment at the figure stands for 12 × 12 calculated moments.

图 6  界面层厚度$ t^{\rm i} $不同时SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜的磁能积(BH)　(a) 易轴平行膜面; (b) 易轴垂直膜面

Fig. 6.  Energy products (BH) of SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayers for various interface layer thicknesses $ t^{\rm i} $: (a) and (b) show the energy products of the easy axis parallel and perpendicular to the film plane, respectively.

图 7  界面层厚度$ t^{\rm i} $不同时易轴平行膜面SmCo(20 nm)/Fe(20–$ t^{\rm i} $ nm)双层膜的磁能积(BH)　(a)实验测量^[30]; (b)理论计算

Fig. 7.  Energy products (BH) in parallel SmCo(20 nm)/Fe(20–$ t^{\rm i} $ nm) bilayers for various interface layer thicknesses $ t^{\rm i} $: (a) The experimental measurement^[30]; (b) the theoretical calculation.

图 8  易轴平行膜面SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜, 当$ t^{\rm i} $ = 4 nm时SmCo原子的扩散比例为10%, 30%, 50%, 70%和90%的　(a) 成核场H_N、钉扎场H_P和矫顽力H_C; (b)剩磁M_r和最大磁能积 (BH)_max.

Fig. 8.  (a) Calculated nucleation field H_N, pinning field H_P, and coercivity H_C; (b) remanence Mr and maximum energy product (BH)_max as functions of t ⁱ for parallel SmCo (5 nm)/Fe(10–$ t^{\rm i} $ nm) with $ t^{\rm i} $ = 4 nm when the ratio of SmCo atomic diffusion are 10%, 30%, 50%, 70% and 90%, respectively.

图 9  界面层厚度$ t^{\rm i} $不同时SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm)双层膜的成核场H_N随界面交换耦合常数A^int的变化曲线　(a) 易轴平行膜面; (b) 易轴垂直膜面

Fig. 9.  Nucleation field H_N as a function of the interface exchange energy constant A^int for various interface layer thicknesses $ t^{\rm i} $ in SmCo(5 nm)/Fe(10–$ t^{\rm i} $ nm) bilayers. (a) and (b) show the curves of the easy axis parallel and perpendicular to the film plane, respectively.