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SmCo12, with its large magnetic energy product, is a highly promising high-temperature permanent magnet that has attracted significant attention. However, the widely existing ThMn12-type crystal structure in this system faces serious stability problem, which significantly hinders its practical engineering applications. Exploring a novel SmCo12 structure that combines stability and excellent magnetic properties is crucial for breaking through this bottleneck. In this study, the metastable phases of the SmCo12 system are systematically investigated in this work by using a local particle swarm optimization algorithm combined with first-principles calculations. The theoretical calculations reveal a hexagonal phase structure (space group $ P\overline{3}1m $) with a formation energy of 90 meV/atom, which is lower than that of the conventional ThMn12-type SmCo12. Its phonon spectrum shows no imaginary frequencies and its structure remains stable during Nosé-Hoover thermostat simulations at 1200 K, confirming its dynamic stability and thermodynamic stability. The electronic structure reveals that this structure exhibits metallic characteristics, with a total magnetic moment of as high as 21.81µB/f.u. and a magnetocrystalline anisotropy constant of up to 11.10 MJ/m3, significantly exceeding similar high-cobalt-content Sm-Co systems. Furthermore, theoretical predictions indicate that the hexagonal phase SmCo12 structure exhibits exceptionally outstanding magnetic properties, with maximum energy product, anisotropy field, and Curie temperature reaching 54.56 MGOe, 15.01 MA/m, and 1180 K, respectively. The newly discovered hexagonal SmCo12 phase provides a novel direction for solving the stability problem of the ThMn12-type structure.
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Keywords:
- structure prediction /
- first principles calculations /
- high Curie temperature /
- rare earth permanent magnets
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图 1 SmCo12四种候选晶体结构示意图, 红色为Sm原子, 蓝色为Co原子 (a) $ P4 mm $(No.99); (b) $ {P4}/{mmm} $(No.123); (c) ThMn12型$ {I4}/{mmm} $(No.139); (d) $ P\overline{3}1 m $(No.162)
Figure 1. Four candidate crystal structures of SmCo12, red represents Sm atom, blue represents Co atom: (a) $ P4 mm $(No.99); (b) $ P4/mmm $(No.123); (c) ThMn12-type $ I4/mmm $(No.139); (d) $ P\overline{3}1 m $(No.162).
图 2 候选SmCo12结构能量随体积变化曲线
Figure 2. Energy-volume curve of candidate SmCo12 structures.
图 3 二元SmmCon合金形成能及凸包图, 结构搜索候选结构标记为圆点, 稳定结构标记为星号, 亚稳态结构标记为三角形
Figure 3. Formation energy and convex hull of binary SmmCon alloys, candidate structures from structural search are marked as circles, stable structures as stars, and metastable structures as triangles.
图 4 候选SmCo12结构声子谱 (a) $ P4 mm $(No.99); (b) $ P4/mmm $(No.123); (c) ThMn12型$ I4/mmm $(No.139); (d) $ P\overline{3}1 m $(No.162)
Figure 4. The phonon dispersion of candidate SmCo12 structures: (a) $ P4 mm $(No.99); (b) $ P4/mmm $ (No.123); (c) ThMn12-type $ I4/mmm $(No.139); (d) $ P\overline{3}1 m $(No.162).
图 5 在1200 K下, 六方相($ P\overline{3}1 m $) SmCo12分子动力学模拟后 (a) 弛豫后晶体结构; (b) 总势能随模拟时间的变化
Figure 5. At 1200 K, for the hexagonal phase ($ P\overline{3}1 m $) SmCo12 after molecular dynamics simulation: (a) Relaxed crystal structure; (b) total potential energy as a function of simulation time.
图 6 六方相($ P\overline{3}1 m $) SmCo12态密度 (a) 总态密度与各元素贡献; (b) Sm原子态密度以及各轨道贡献; (c) 6$ {k}_{1} $晶位Co原子态密度及各轨道贡献; (d) 6$ {k}_{2} $晶位Co原子态密度及各轨道贡献, 费米能级设为0 eV
Figure 6. The DOS of hexagonal phase ($ P\overline{3}1 m $) SmCo12: (a) The total DOS and the contribution of each element; (b) the Sm atomic DOS and the contribution of each orbital; (c) the Co atomic DOS at 6$ {k}_{1} $ crystal site and the contribution of each orbital; (d) the Co atomic DOS at the 6$ {k}_{2} $ crystal site and the contribution of each orbital. The Fermi level is set to 0 eV.
图 7 六方相SmCo12 (a) 每个原子间交换耦合常数随间距变化曲线; (b) 随温度变化的磁化曲线
Figure 7. Hexagonal SmCo12: (a) Exchange coupling constants between each atom as a function of interatomic distance; (b) magnetization curve as a function of temperature.
表 1 候选SmCo12结构的空间群、焓值、晶胞参数和晶系
Table 1. The candidate SmCo12 structures including their space groups, enthalpy values, unit cell parameters, and crystal systems.
Space Group Enthalpy
/(eV·atom–1)Lattice parameters/Å Wyckoff position Crystal system $ P4 mm $ (No.99) –6.52 a = b = 4.00, c = 10.65
α = β = γ = 90°Sm: 1$ a $
Co: 1$ {a}_{i} $; 1$ {b}_{i} $; 2$ {c}_{i} $ (i = 1, 2, 3)Tetragonal $ I4/mmm $ (No.139) –6.67 a = b = 8.89, c = 4.087
α = β = γ = 90°Sm: 2$ a $
Co: 8$ f $; 8$ i $; 8$ j $Tetragonal $ P\overline{3}1 m $ (No.162) –6.76 a = b = 4.20, c = 10.93
α = β = 90°, γ = 120°Sm: 1$ b $
Co: 6$ {k}_{1} $; 6$ {k}_{2} $Hexagonal $ P4/mmm $ (No.123) –6.79 a = b = 3.54, c = 12.13
α = β = γ = 90°Sm: 1$ a $
Co: 2$ {h}_{i} $ (i = 1, 2); 4$ i $; 2$ h $; 2$ e $Tetragonal 
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表 2 候选SmCo12结构的空间群、平衡状态下的体积、形成能及体积模量
Table 2. The candidate SmCo12 structures include their space groups, equilibrium volumes, formation energies, and bulk modulus.
Space
GroupVolume
/Å3Formation Energy
(meV/atom)Bulk module
/GPa$ {E}_{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}} $ $ {E}_{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}}^{\mathrm{S}\mathrm{m}\mathrm{C}{\mathrm{o}}_{5}} $ $ {E}_{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}}^{\mathrm{S}{\mathrm{m}}_{2}\mathrm{C}{\mathrm{o}}_{17}} $ $ P4 mm $
(No.99)173.22 0 63 67 111.00 $ I4/mmm $
(No.139)323.12 –47 16 21 145.50 $ P\overline{3}1 m $
(No.162)172.16 –137 –74 –69 131.99 $ P4/mmm $
(No.123)161.37 –167 –104 –99 154.33
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表 3 VASP与OpenMX 计算六方相($ P\overline{3}1 m $$ (\mathrm{N}\mathrm{o}.162) $) SmCo12电子磁矩和单离子磁各向异性能对比
Table 3. A comparison of the electronic magnetic moments and single ion magnetic anisotropy energies of hexagonal ($ P\overline{3}1 m $ (No.162)) SmCo12 calculated by using VASP and OpenMX.
Method Atom s p d $ {m}_{i/\mu \mathrm{B}} $ $ {k}_{i} $/meV OpenMX Co 6$ {k}_{1} $ –0.01 –0.08 1.74 1.66 0.19 Co 6$ {k}_{2} $ 0.0 –0.06 1.84 1.76 0.46 Sm 1$ b $ –0.01 –0.04 1.29 1.25 –11.97 VASP Co 6$ {k}_{1} $ –0.02 –0.05 1.67 1.60 0.57 Co 6$ {k}_{2} $ –0.01 –0.04 1.57 1.52 0.4 Sm 1$ b $ –0.01 –0.01 –0.21 –0.23 –8.93
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表 4 六方相($ P\overline{3}1 m $)SmCo12结构自旋磁矩和轨道磁矩
Table 4. Spin magnetic moments and orbital magnetic moments of the hexagonal phase ($ P\overline{3}1 m $) SmCo12 structure.
Atoms Occ. $ {m}_{i}^{s}/{\mu }_{B} $ $ {m}_{i}^{\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{t}}/{\mu }_{B} $ $ {m}_{i}/{\mu }_{B} $ Co 6$ {k}_{1} $ 1.66 0.07 1.73 Co 6$ {k}_{2} $ 1.76 0.08 1.84 Sm 1$ b $ 1.25 0.02 1.27
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表 5 六方相($ P\overline{3}1 m $(No.162)) SmCo12本征磁性与ThMn12型对比
Table 5. Comparison of intrinsic magnetism between hexagonal($ P\overline{3}1 m $(No.162)) SmCo12 and ThMn12-type structure.
Space Group $ {m}^{\mathrm{t}\mathrm{o}\mathrm{t}}/ $($ {\mathrm{\mu }}_{\mathrm{B}} $·f.u.–1) $ {M}_{\mathrm{s}}/ $(MA·m–1) $ (\mathrm{B}\mathrm{H}{)}_{\mathrm{m}\mathrm{a}\mathrm{x}}/ $MGOe $ {H}_{\mathrm{a}}/ $(MA·m–1) $ {T}_{\mathrm{C}}/ $K $ P\overline{3}1 m $ (No.162) SmCo12 21.81 1.17 54.56 15.01 1180 ThMn12-type SmCo12 * 21.90 1.26 62.38 8.70 1150 ThMn12-type SmCo12 [15,38,40,41] 17.4 1.0 39.60 3.91 1300 ThMn12-type SmFe12 [38,41,44] 25.7 1.30 76.0 9.55 554 ThMn12-type Sm(Fe0.8Co0.2)12 [15,43] 24.5 1.35 80 9.55 1100 注: *present work.
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