Prediction and magnetic study of a new stable SmCo<sub>12</sub> structure

DAI Yudong; LIU Yicong; LI Zhenqing; YANG Zhixiong; ZHANG Weibing

doi:10.7498/aps.74.20250389

Abstract

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 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 90 meV/atom 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 21.81 μ_B/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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Authors and contacts

Corresponding author: YANG Zhixiong, clyzx@csust.edu.cn ; ZHANG Weibing, zhangwb@csust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874092), the Fok YingTong Education Foundation, China (Grant No. 161005), and the Science Fund for Distinguished Young Scholars of Hunan Province, China (Grant No. 2021JJ10039).

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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: $ 1a $ 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: $ 2a $ 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); $ 4i $; $ 2h $; $2 e $	Tetragonal

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Space group	Volume /Å³	Formation energy (meV/atom)			Bulk module /GPa
Space group	Volume /Å³	$ {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}} $	Bulk module /GPa
$ 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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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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Atoms	Occ.	$ {m}_{i}^{s}/{\mu }_{{\mathrm{B}}} $	$ {m}_{i}^{\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{t}}/{\mu }_{{\mathrm{B}}} $	$ {m}_{i}/{\mu }_{{\mathrm{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

DownLoad: CSV

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(Fe_0.8Co_0.2)₁₂ ^[15,43]	24.5	1.35	80	9.55	1100
注: *present work.

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Vol. 74, Issue 17 - 2025-09-05

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