Micromagnetic simulation in two antiferromagnetically coupled ferromagnetic layers separated by a spacer

On the basis of a micromagnetic model, magnetization reversal in two antiferromagnetically coupled ferromagnetic layers $\text{(10\hspace{0.05em}}\mathrm{nm}{\mathrm{ t}}_1\text{/0.9\hspace{0.05em}}\mathrm{nm}{\mathrm{M/t}}_2 \mathrm{nm}$ films with $t_2\text{=2,}$ 3, 4, 5 nm, here $t_1$ and $t_2$ are the top and bottom layers, respectively, and M the spacer) with the same random anisotropy arrangement can be represented by a computer simulation. The calculation indicates that the appearance of a full antiferromagnetic coupling at remanence requires the antiferromagnetic coupling constant $\text{j=−3.5\hspace{0.05em}}{\mathrm{erg/cm}}^{\mathrm{2}}$ for the $\text{10\hspace{0.05em}}\mathrm{nm}{\mathrm{ t}}_1\text{/0.9\hspace{0.05em}}\mathrm{nm}\text{M/3\hspace{0.05em}}\mathrm{nm}{\mathrm{ t}}_2,$ films and it needs a large j value if $t_2$ increases for the case of $K_{\text{u2}}{\mathrm{=K}}_{\text{u1}}{\text{=1×10}}^6 {\mathrm{erg/cm}}^{\mathrm{3}}$ and $M_{\text{s1}}{\mathrm{=M}}_{\text{s2}}\text{=400\hspace{0.05em}}{\mathrm{emu/cm}}^{\mathrm{3}}.$ $H_c$ follows the equation $H_c{\text{=−0.755j/M}}_s{t}_1$ $\text{(j<0).}$ Why the calculated $H_c$ values deviate from $H_c^{\max }{\mathrm{=-j/M}}_s{t}_1$ is discussed.