First-principles study of magnetic disordering and alloying effects on phase stability and elastic constants of Co2CrZ (Z = Ga, Si, Ge) alloys

Yang Shun-Jie; Li Chun-Mei; Zhou Jin-Ping

doi:10.7498/aps.71.20212254

Abstract

Using the exact Muffin-Tin orbital method combined with the coherent potential approximation, the effects of magnetic disordering and alloying effects on the phase stability of L2₁- and D0₂₂-Co₂CrZ (Z = Ga, Si, Ge) alloys are systematically investigated at 0 K in the present work. It is shown that at 0 K, the lattice parameter, bulk modulus, magnetic moments, and elastic constants of the studied L2₁ alloys are in line with the available theoretical and experimental data. In the ferromagnetic state, these alloys possess L2₁ structure; with the magnetic disordering degree (y) increasing, the energy of the phase increases relatively and finally turns from lower than D0₂₂ phase to higher than D0₂₂ phase. As a result, when y ≥ 0.1 (0.2), then Z = Si and Ge (Z = Ga) alloys are stabilized by the D0₂₂ phase. With y increasing, the tetragonal shear elastic modulus (C' = (C₁₁–C₁₂)/2) also turns soft, indicating that the magnetic disorderingis conducive to the lattice tetragonal deformation in the three alloys from both the energetic view and the mechanical view. The electronic origination of the magnetic disordering effect on the stabilities of the L2₁ and D0₂₂ phases can be ascribed to the Jahn-Teller instability effect. In the FM L2₁-Co₂CrGa_1–xSi_x and L2₁-Co₂CrGa_1–xGe_x quaternary alloys, with x increasing, the total magnetic moment increases monotonically according to the Slater-Pauling rule, and C' also stiffens, reflecting that the adding of Si and Ge can promote the mechanical stability of L2₁-Co₂CrGa alloy, thereby depressing the lattice tetragonal deformation.

Keywords:

Authors and contacts

College of Physical Science and Technology, Shenyang Normal University, Shenyang 110034, China

Corresponding author: Li Chun-Mei, cmli@synu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12174269)

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References

[1]	Heusler F 1903 Deut. Phys. Ges. 5 219
[2]	Ram S, Kanchana V 2013 AIP. Conf. Proc. 1512 1102 Google Scholar
[3]	AlgethamiO A, 李歌天, 柳祝红, 马星桥 2020 物理学报 69 058102 Google Scholar Algethami O A, Li G T, Liu Z H, Ma X Q 2020 Acta Phys. Sin. 69 058102 Google Scholar
[4]	赵昆, 张坤, 王家佳, 于金, 吴三械 2011 物理学报 60 127101 Google Scholar Zhan K, Zhang K, Wang J J, Yu J, Wu S X 2011 Acta Phys. Sin. 60 127101 Google Scholar
[5]	Krenke T, Acet M, Wassermann E F 2006 Phys. Rev. B. 73 174413 Google Scholar
[6]	杜音, 王文洪, 张小明, 刘恩克, 吴光恒 2012 物理学报 61 147304 Google Scholar Du Y, Wang W H, Zhang X M, Liu E K, Wu G H 2012 Acta Phys. Sin. 61 147304 Google Scholar
[7]	Terada M, Fujita Y, Endo K 1974 J. Phys. Soc. 36 620 Google Scholar
[8]	Ritcey S P, Dunlap R A 1984 J. Appl. Phys. 55 2050 Google Scholar
[9]	Li Y, Xin Y, Chai L, Ma Y Q, Xu H B 2010 Acta. Mater. 58 3655 Google Scholar
[10]	Guezlane M, Baaziz H, Ei Haj Hassan F, Charifi Z, Djaballah Y 2016 J. Magn. Magn. Mater. 414 219 Google Scholar
[11]	Hirata K, Xu X, Omori T, Nagasako M, Kainuma R 2015 J. Alloys Compd. 642 200 Google Scholar
[12]	Rai D P, Thapa R K 2012 J. Alloys Compd. 542 257 Google Scholar
[13]	Liu C Q, Li Z, Zhang Y L, Huang Y S, Ye M F, Sun X D, Zhang G J, Gao Y M 2018 Appl. Phys. Lett. 112 211903 Google Scholar
[14]	Shinpei F, Shoji I, Setsuro A 1989 J. Phys. Soc. Jpn. 58 3657 Google Scholar
[15]	Manfred W, Jian L, Corneliu C 2001 Scr. Mater. 40 2393
[16]	Xu X, Omori T, Nagasako M, Okubo A, Umetsu R Y, Kanomata T, Ishida K, Kainuma R 2013 Appl. Phys. Lett. 103 164104 Google Scholar
[17]	Hirata K, Xu X, Omori T, Kainuma R 2019 J. Magn. Magn. Mater. 500 166311 Google Scholar
[18]	Umetus R Y, Okubo A, Xu X, Kainuma R 2014 J. Alloys Compd. 588 153 Google Scholar
[19]	Bentouaf A, Mebsout R, Aissa B 2019 J. Alloys Compd. 77 1062
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[24]	Li C M, Zhang Y, Feng W J, Huang R Z, Gao M 2020 Phys. Rev. B 101 054106 Google Scholar
[25]	Vitos L, Abrilsosv I A, Johansson B 2001 Phys. Rev. Lett. 87 156401 Google Scholar
[26]	Gyorff B L 1972 Phys. Rev. B 5 2382 Google Scholar
[27]	Dutta B, Bhandary S, Ghosh S, Sanyal B 2012 Phys. Rev. B 86 024419 Google Scholar
[28]	Li C M, Hu Q M, Yang R, Johansson B, Vitos L 2010 Phys. Rev. B 82 094201 Google Scholar
[29]	胡岩菲 2020 硕士学位论文 (沈阳: 沈阳师范大学) Hu Y F 2020 M. S. Dissertation (Shenyang: Shangyang Normal University)(in Chinese)
[30]	张扬 2021硕士学位论文 (沈阳: 沈阳师范大学) Zhang Y 2021 M. S. Dissertation (Shenyang: Shangyang Normal University)(in Chinese)
[31]	Perdew J P, Burke K, Emzerhof M 1996 Phys. Rev. Lett. 77 3865
[32]	Vitos L 2007 Computational Quantum Mechanics for Materials Engineers (London: Spring-Verlag) pp98–121
[33]	Seema K, Kumar R 2015 J. Magn. Magn. Mater. 377 70 Google Scholar
[34]	Ram S, Chauhan M R, Agarwal K, Kanchana V 2011 Phil. Mag. Lett. 91 545 Google Scholar
[35]	Umetsu R Y, Okubo A, Xu X, Kainuma R 2014 Journal of Alloys and Compounds 588 153 Google Scholar
[36]	Chen X Q, Podloucky R, Rogl P 2006 J. Appl. Phys. 100 113901 Google Scholar
[37]	Bai Z Q, Lu Y H, Shen L, Ko V Han G C, Feng Y P 2012 J. Appl. Phys. 111 093911 Google Scholar
[38]	Rai D P, Shankar A, Sandeep, Ghimire M P, Thapa R K 2012 Material Science Research India 9 155 Google Scholar
[39]	Li C M, Hu Q M, Yang R, Johansson B, Vitos L 2015 Phys. Rev. B 91 174112 Google Scholar
[40]	Umetsu R Y, Kobayashi K, Kainuma R, Yamaguchi Y, Ohoyama K, Sakuma A, Ishida K 2010 J. Alloys Compd. 499 1 Google Scholar
[41]	Galanakis I, Dederichs P H 2002 Phys. Rev. B 66 174429 Google Scholar
[42]	Roy T, Pandey D, Chakrabarti A 2016 Phys. Rev. B 93 184102 Google Scholar
[43]	Ayuela A, Enkovaara J, Ullakko K, Nieminen E M 1999 J. Phys. Condens. Matter. 11 2017 Google Scholar

Cited By

图 1 Co₂CrZ (Z = Ga, Si, Ge)合金晶格结构:　(a) L2₁相; (b) D0₂₂相

Figure 1. Crystal structures of Co₂CrZ (Z = Ga, Si, Ge) alloys: (a) L2₁ phase; (b) D0₂₂ phase.

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图 2 铁磁状态下L2₁-Co₂CrGa_1–xSi_x和L2₁-Co₂CrGa_1–xGe_x(0 ≤ x ≤ 1)合金晶格常数和体弹性模量随x的变化关系与文献[12, 18, 33, 34, 38]的理论和实验结果的对比　(a) a; (b) B

Figure 2. x-dependence of the lattice constant and bulk modulus of the FM L2₁-Co₂CrGa_1–xSi_x and L2₁-Co₂CrGa_1–xGe_x (0 ≤ x ≤ 1) alloys are in comparison with the available theoretical and experimental data from Refs. [12, 18, 33, 34, 38]: (a) a; (b) B.

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图 3 Co₂CrZ(Z = Ga, Si, Ge)合金ΔE随四方晶格c/a的变化关系, 本文ΔE的计算以各合金FM状态下L2₁相(即y = 0, c/a = 1)的电子总能作为参考值　(a) Z = Ga; (b) Z = Si; (c) Z = Ge

Figure 3. ΔE of Co₂CrZ(Z = Ga, Si, Ge) alloys change with respect to the c/a of tetragonal lattice, here, the electronic energy of the FM L2₁ structure (y = 0, c/a = 1) is as reference for ΔE calculations of each alloy: (a) Z = Ga; (b) Z = Si; (c) Z = Ge.

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图 4 FM状态下Co₂CrZ(Z = Ga, Si, Ge)合金总磁矩(μ_tot)及Co(μ_Co), Cr(μ_Cr)原子局域磁矩随四方晶格c/a的变化关系、及其顺磁PM状态下μ_Cr绝对值大小随c/a的变化关系　(a) FM-μ_tot; (b) FM-μ_Co; (c) FM-μ_Cr; (d) PM-μ_Cr

Figure 4. μ_tot and μ_Co and μ_Cr atoms of the FM Co₂CrZ(Z = Ga, Si, Ge) alloys change with respect to c/a, together with the trends of μ_Cr-x of the three PM alloys in their absolute values: (a) FM-μ_tot; (b) FM-μ_Co; (c) FM-μ_Cr; (d) PM-μ_Cr.

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图 5 FM状态下L2₁-Co₂CrGa_1–xSi_x和L2₁-Co₂CrGa_1–xGe_x (0 ≤ x ≤ 1)合金μ_tot与μ_Co, μ_Cr原子磁矩随x的变化关系、及其与Slater-Pauling(S-P)定律计算给出μ_tot-x关系的对比

Figure 5. μ_tot and μ_Co, μ_Cr atoms of the FM L2₁-Co₂CrGa_1–xSi_x and L2₁-Co₂CrGa_1–xGe_x (0 ≤ x ≤ 1) alloys change with respect to x, in comparison with their calculated trends of μ_tot-x according to the Slater-Pauling (S-P) rule.

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图 6 FM状态下L2₁-Co₂CrZ (Z = Ga, Si, Ge)合金单晶弹性常数(C₄₄和C '=(C₁₁– C₁₂)/2)和A = C₄₄/C随y的变化关系　(a) (b) Z = Ga; (c) (d) Z = Si; (e) (f) Z = Ge

Figure 6. Single-crystal elastic constants (C₄₄ and C ' = (C₁₁– C₁₂)/2) and elastic anisotropy (A = C₄₄/C ') of the FM L2₁-Co₂CrZ (Z = Ga, Si, Ge) alloys change with respect to the magnetic disordering degree (y): (a) (b) Z = Ga; (c)(d) Z = Si; (e) (f) Z = Ge.

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图 7 FM状态下L2₁-Co₂CrGa_1–xSi_x和L2₁-Co₂CrGa_1–xGe_x (0 ≤ x ≤ 1)合金单晶弹性常数(C₄₄和C ' = (C₁₁–C₁₂)/2)、A = C₄₄/C及G和E随x的变化关系　(a) C₄₄–x; (b) C ' –x和A–x; (c)G–x; (d) E–x

Figure 7. Single-crystal elastic constants (C₁₁, C₁₂, C₄₄, and C ' = (C₁₁–C₁₂)/2), elastic anisotropy (A = C₄₄/C'), polycrystal shear modulus (G), and Young’ modulus (E) of the FM L2₁-Co₂CrGa_1–xSi_x and L2₁-Co₂CrGa_1–xGe_x (0 ≤ x ≤ 1) alloys change with respect to x: (a) C₄₄–x; (b) C ' –x and A–x; (c) G–x; (d) E–x.

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图 8 FM和PM状态下L2₁-和D0₂₂-Co₂CrZ (Z = Ga, Si, Ge)合金电子总态密度(DOS)及Co, Cr和Z原子局域DOS的对比: (a)—(d) Z = Ga; (e)—(h) Z = Si; (i)—(l) Z = Ge

Figure 8. Total electronic density of states (DOS) and local density of states of Co, Cr and Z atoms of the Co₂CrZ (Z = Ga, Si, Ge) alloys with both the FM and PM L2₁ and D0₂₂ phases: (a)–(d) Z = Ga; (e)–(h) Z = Si; (i)–(l) Z = Ge.

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表 1 铁磁(FM)和顺磁(PM)状态下L2₁-Co₂CrZ (Z = Ga, Si, Ge)合金晶格常数和体弹性模量的EMTO计算结果与其他源于文献[12, 33-38]理论和实验值的对比

Table 1. Lattice constant and bulk modulus of the FM and PM L2₁-Co₂CrZ (Z = Ga, Si, Ge) alloys calculated with the EMTO program are in comparison with the other theoretical and experimental data from Refs. [12, 33-38].

Alloys	Phases	Methods	a/Å	B/GPa
Co₂CrGa	FM L2₁	EMTO	5.736	203.5
		The.^[12]	5.802	208.8
		The.^[33]	5.797	204.8
		The.^[34]	5.720	—
		Exp.^[35]	5.760	—
	PM L2₁	EMTO	5.749	177.8
Co₂CrSi	FM L2₁	EMTO	5.651	234.3
		The.^[36]	5.630	227.0
		Exp.^[37]	5.650	—
	PM L2₁	EMTO	5.652	202.4
Co₂CrGe	FM L2₁	EMTO	5.755	207.7
		The.^[38]	5.770	250.4
		The.^[33]	5.754	227.1
	PM L2₁	EMTO	5.764	180.4

DownLoad: CSV

表 2 FM状态下L2₁-Co₂CrZ (Z = Ga, Si, Ge)合金单晶弹性常数(C₁₁, C₁₂, C₄₄, C ' = (C₁₁– C₁₂)/2)、A = C₄₄/C及多晶G和E的EMTO计算结果与源于文献[36, 42]理论值的对比

Table 2. Single-crystal elastic constants (C₁₁, C₁₂, C₄₄, and C ' = (C₁₁ – C₁₂)/2), elastic anisotropy (A = C₄₄/C '), G, and E of the FM L2₁-Co₂CrZ (Z = Ga, Si, Ge) alloys are shown in comparison with the available theoretical results from Refs. [36, 42]

Alloys	Methods	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	C '/GPa	A	G/GPa	E/GPa
Co₂CrGa	EMTO	241.27	184.65	136.96	28.31	4.84	71.07	190.99
Co₂CrGa	FPLAPW^[42]	233.00	182.80	136.80	25.10	5.45	67.30	—
Co₂CrSi	EMTO	306.87	196.56	155.88	55.15	2.83	102.04	267.17
Co₂CrSi	FPLAPW^[36]	297	193	145	52	—	—	—
Co₂CrGe	EMTO	268.28	177.35	128.81	45.47	2.83	54.06	147.74

DownLoad: CSV

[1]	Heusler F 1903 Deut. Phys. Ges. 5 219
[2]	Ram S, Kanchana V 2013 AIP. Conf. Proc. 1512 1102 Google Scholar
[3]	AlgethamiO A, 李歌天, 柳祝红, 马星桥 2020 物理学报 69 058102 Google Scholar Algethami O A, Li G T, Liu Z H, Ma X Q 2020 Acta Phys. Sin. 69 058102 Google Scholar
[4]	赵昆, 张坤, 王家佳, 于金, 吴三械 2011 物理学报 60 127101 Google Scholar Zhan K, Zhang K, Wang J J, Yu J, Wu S X 2011 Acta Phys. Sin. 60 127101 Google Scholar
[5]	Krenke T, Acet M, Wassermann E F 2006 Phys. Rev. B. 73 174413 Google Scholar
[6]	杜音, 王文洪, 张小明, 刘恩克, 吴光恒 2012 物理学报 61 147304 Google Scholar Du Y, Wang W H, Zhang X M, Liu E K, Wu G H 2012 Acta Phys. Sin. 61 147304 Google Scholar
[7]	Terada M, Fujita Y, Endo K 1974 J. Phys. Soc. 36 620 Google Scholar
[8]	Ritcey S P, Dunlap R A 1984 J. Appl. Phys. 55 2050 Google Scholar
[9]	Li Y, Xin Y, Chai L, Ma Y Q, Xu H B 2010 Acta. Mater. 58 3655 Google Scholar
[10]	Guezlane M, Baaziz H, Ei Haj Hassan F, Charifi Z, Djaballah Y 2016 J. Magn. Magn. Mater. 414 219 Google Scholar
[11]	Hirata K, Xu X, Omori T, Nagasako M, Kainuma R 2015 J. Alloys Compd. 642 200 Google Scholar
[12]	Rai D P, Thapa R K 2012 J. Alloys Compd. 542 257 Google Scholar
[13]	Liu C Q, Li Z, Zhang Y L, Huang Y S, Ye M F, Sun X D, Zhang G J, Gao Y M 2018 Appl. Phys. Lett. 112 211903 Google Scholar
[14]	Shinpei F, Shoji I, Setsuro A 1989 J. Phys. Soc. Jpn. 58 3657 Google Scholar
[15]	Manfred W, Jian L, Corneliu C 2001 Scr. Mater. 40 2393
[16]	Xu X, Omori T, Nagasako M, Okubo A, Umetsu R Y, Kanomata T, Ishida K, Kainuma R 2013 Appl. Phys. Lett. 103 164104 Google Scholar
[17]	Hirata K, Xu X, Omori T, Kainuma R 2019 J. Magn. Magn. Mater. 500 166311 Google Scholar
[18]	Umetus R Y, Okubo A, Xu X, Kainuma R 2014 J. Alloys Compd. 588 153 Google Scholar
[19]	Bentouaf A, Mebsout R, Aissa B 2019 J. Alloys Compd. 77 1062
[20]	Odaira T, Xu X, Miyake A, Omori T, Tokunaga M, Kainuma R 2018 Scr. Mater. 153 35 Google Scholar
[21]	Hu Q M, Li C M, Yang R, Kulkova S E, Bazhanov D I, Johansson B, Vitos L 2009 Phys. Rev. B 79 144112 Google Scholar
[22]	Li C M, Luo H B, Hu Q M, Yang R, Johansson B, Vitos L 2010 Phys. Rev. B 82 024201 Google Scholar
[23]	孙凯晨, 刘爽, 高瑞瑞, 时翔宇, 刘何燕, 罗鸿志 2021 物理学报 70 137101 Google Scholar Sun K C, Liu S, Gao R R, Shi X Y, Liu H Y, Luo H Z 2021 Acta Phys. Sin. 70 137101 Google Scholar
[24]	Li C M, Zhang Y, Feng W J, Huang R Z, Gao M 2020 Phys. Rev. B 101 054106 Google Scholar
[25]	Vitos L, Abrilsosv I A, Johansson B 2001 Phys. Rev. Lett. 87 156401 Google Scholar
[26]	Gyorff B L 1972 Phys. Rev. B 5 2382 Google Scholar
[27]	Dutta B, Bhandary S, Ghosh S, Sanyal B 2012 Phys. Rev. B 86 024419 Google Scholar
[28]	Li C M, Hu Q M, Yang R, Johansson B, Vitos L 2010 Phys. Rev. B 82 094201 Google Scholar
[29]	胡岩菲 2020 硕士学位论文 (沈阳: 沈阳师范大学) Hu Y F 2020 M. S. Dissertation (Shenyang: Shangyang Normal University)(in Chinese)
[30]	张扬 2021硕士学位论文 (沈阳: 沈阳师范大学) Zhang Y 2021 M. S. Dissertation (Shenyang: Shangyang Normal University)(in Chinese)
[31]	Perdew J P, Burke K, Emzerhof M 1996 Phys. Rev. Lett. 77 3865
[32]	Vitos L 2007 Computational Quantum Mechanics for Materials Engineers (London: Spring-Verlag) pp98–121
[33]	Seema K, Kumar R 2015 J. Magn. Magn. Mater. 377 70 Google Scholar
[34]	Ram S, Chauhan M R, Agarwal K, Kanchana V 2011 Phil. Mag. Lett. 91 545 Google Scholar
[35]	Umetsu R Y, Okubo A, Xu X, Kainuma R 2014 Journal of Alloys and Compounds 588 153 Google Scholar
[36]	Chen X Q, Podloucky R, Rogl P 2006 J. Appl. Phys. 100 113901 Google Scholar
[37]	Bai Z Q, Lu Y H, Shen L, Ko V Han G C, Feng Y P 2012 J. Appl. Phys. 111 093911 Google Scholar
[38]	Rai D P, Shankar A, Sandeep, Ghimire M P, Thapa R K 2012 Material Science Research India 9 155 Google Scholar
[39]	Li C M, Hu Q M, Yang R, Johansson B, Vitos L 2015 Phys. Rev. B 91 174112 Google Scholar
[40]	Umetsu R Y, Kobayashi K, Kainuma R, Yamaguchi Y, Ohoyama K, Sakuma A, Ishida K 2010 J. Alloys Compd. 499 1 Google Scholar
[41]	Galanakis I, Dederichs P H 2002 Phys. Rev. B 66 174429 Google Scholar
[42]	Roy T, Pandey D, Chakrabarti A 2016 Phys. Rev. B 93 184102 Google Scholar
[43]	Ayuela A, Enkovaara J, Ullakko K, Nieminen E M 1999 J. Phys. Condens. Matter. 11 2017 Google Scholar

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Vol. 71, Issue 10 - 2022-05-20

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First-principles study of magnetic disordering and alloying effects on phase stability and elastic constants of Co₂CrZ (Z = Ga, Si, Ge) alloys

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Corresponding author: Li Chun-Mei, cmli@synu.edu.cn

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