Fig. 1. The illustration of core ((Nd_0.7, Ce_0.3)₂Fe₁₄B) - shell (Nd₂Fe₁₄B) model of which the shell thickness is a constant of 6 nm while the core size is variable.

Fig. 2. (a) The relevance of the coercivity to the core size (side length x); (b) the demagnetization curves of grains with different core size (side length x) when t = 6 nm.

Fig. 3. Comparisons of the total demagnetization energy E_d of grains with various core size (side length).

Fig. 4. Illustration of core ((Nd_0.7, Ce_0.3)₂Fe₁₄B) - shell (Nd₂Fe₁₄B) model of which the core size is a constant of 200 nm × 200 nm × 200 nm while the shell thickness t is variable.

Fig. 5. (a) The relevance of the coercivity to the shell thickness; (b) the demagnetization curves of grains with different shell thicknesses when the core size is kept at 200 nm × 200 nm × 200 nm.

Fig. 6. Illustration of the nucleation points for t = 2−20 nm (view ofx-z plane) (The dotted lines represent the boundary between the core and the shelll; the point in the magnified area specifically indicates the nucleation point of the model; the blue arrow indicates that the magnetic moment is the same as the initial magnetization direction, that is, the magnetic moment is not reflected. Reversal, the magnetic moment of the red arrow has reversed).

Fig. 7. The reversal process for t = 6 nm (view of x-z plane at y = 21 nm) under external field of 48.25 kOe (equal to the coercivity) (The dotted lines represent the boundary between the core and the shelll; the blue arrow indicates that the magnetic moment is the same as the initial magnetization direction, that is, the magnetic moment is not reflected. Reversal, the magnetic moment of the red arrow has reversed).

Fig. 8. The reversal process for t =16 nm (view of x-z plane at y = 1 nm) under external field of 50.25 kOe (equal to the coercivity) (The dotted lines represent the boundary between the core and the shelll; the blue arrow indicates that the magnetic moment is the same as the initial magnetization direction, that is, the magnetic moment is not reflected. Reversal, the magnetic moment of the red arrow has reversed).

Fig. 9. The change of the total demagnetization energy E_d for grains with different shell thicknesses under varying external field.

Fig. 10. Illustration of six types of core ((Nd_0.7, Ce_0.3)₂Fe₁₄B)-shell (Nd₂Fe₁₄B) model, from left to right: a_x type, the shell is evenly distributed on the two x-planes (the plane perpendicular to the x-axis) of the core; a_z type, the shell is evenly distributed on the two z-planes (the plane perpendicular to the z-axis) of the core; b_xy type, the shell is evenly distributed on the x-planes and the y-planes of the core; b_xz type, the shell is evenly distributed on the x-planes and the z-planes of the core; c type, the shell is evenly distributed on the x-planes, y-planes and the z-planes of the core (evenly distributed around the core); c' type, both the shell thicknesses for the x-planes and the y-planes of the core are 1 nm, and the shell thickness for the z-planes of the core is variable with changing total shell volume (The size shown in the figure takes V_shell/V_grain ≈ 50% as an example).

Fig. 11. Comparisons for the coercivity of six types of core-shell grain structure with the same shell volume.

Fig. 12. The reversal magnetization processes of six types of grains when V_shell/V_grain ≈ 50% (view of x-z plane): (a) a_z type (x-z plane position: y = 0.5 nm; external field is 59.75 kOe, same as coercive force); (b) c' type (x-z plane position: y = 0.5 nm; external field is 59.25 kOe, and the coercive force is the same); (c) b_xz type (x-z plane position: y = 0.5 nm; the external field is 58.75 kOe, which is the same as the coercive force); (d) c type (x-z plane position: y = 0.5 nm; the external field is 57.75 kOe, which is the same as the coercive force; (e) b_xy type (x-z plane position: y = 18.5 nm; the external field is 54.75 kOe, which is the same as the coercive force); (f) a_x type (x-z plane position: y = 0.5 nm; the external field is 51.25 kOe, which is the same as the coercive force).

Fig. 13. The demagnetization curves for four types of grains.

Fig. 14. (a) Comparisons for the demagnetization field in z-axis direction H_dz of the nucleation points; (b) the total demagnetization energy E_d of four types of grains.