Structure and half-metallic ferromagnetism of quaternary Heusler compounds CoMnZn<i>Z</i>

Xu Jia-Ling; Jia Li-Yun; Jin Xiao-Qing; Hao Xing-Nan; Ma Li; Hou Deng-Lu

doi:10.7498/aps.68.20190207

Abstract

Using the first principle full-potential linearized augmented wave method we study the electronic structure and elastic and magnetic properties of CoMnZnZ (Z = Si, Ge, Sn, Pb) LiMgPdSn-type Heusler alloys. These compounds have the composition CoMnZnZ with 1︰1︰1︰1 stoichiometry, where Z denotes the main group element Si, or Ge, or Sn, or Pb. The exchange-correlations are treated within the generalized gradient approximation of Perdewe-Burke-Ernzerhof. For each of all studied Heusler alloys, the ferromagnetic state is considered to be more stable than the paramagnetic state, judged by the energy. The total energy of the magnetic calculation is lower than that of the nonmagnetic state for each of all three serise compounds at the equilibrium lattice constant, indicating that the magnetic state is more stable than the nonmagnetic state. We determine the elastic constants C₁₁, C₁₂ and C₄₄, which have not been established previously in experiment nor in theory. The elastic constant indicates the weakened resistance to sheardeformation compared with the resistance to unidirectional compression. We derive other mechanical parameters, i.e., the shear modulus G, Young’s modulus E, Poisson’s ratio ν, and shear anisotropic factor A, which are the important elastic moduli for applications. These compounds each have a lower anisotropy and possess a low probability to develop micro-crack or structural defect in its growing process. The sound velocity and Debye temperature for each of the CoMnZnZ (Z = Si, Ge, Sn, Pb) compounds in their stable structure are calculated. The CoMnZnPb exhibits the lowest Debye temperature, and the highest value is observed for CoMnZnGe. The electronic structure calculations show that CoMnZnZ (Z = Si, Ge, Sn) each exhibit a gap in the band of minority states, and they are clearly half-metallic ferromagnets, except for the CoMnZnPb. The CoMnZnZ (Z = Si, Ge, Sn) compounds and their magnetic moments are in reasonable agreement with the Slater-Pauling rule, and they comply with a Slater-Pauling rule of M_t = Z_t – 28, which indicates the half metallicity and high spin polarization for these compounds. The CoMnZnSi compound has the largest half-metallic gap value and the gap is about 0.66 eV. The magnetic properties are primarily determined by the Mn atoms, which contribute the highest magnetic moments. The localmoment of the Z element atom is negligibly small. The hybridization of the d orbitals between Co and Mn can explain the origin of the Slater-Pauling rule in half-metallic quaternary Heusler alloys. The half-metallic gap comes mainly from the interaction between the Co and Mn atoms.

Keywords:

Authors and contacts

1.
Department of Mathematics and Physics, Hebei Instituteof Architecture Civil Engineering, Zhangjiakou 075000, China
2.
College of Physics and Information Engineering, Hebei Normal University, Shijiazhuang 050024, China

Corresponding author: Jia Li-Yun, jliyun@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11504247), the Hebei Natural Science Foundation, China (Grant Nos. A2018205144, E2016205268), the Department of Science and Technology of Hebei Province Scientific and Technological Research Project, China (Grant Nos. 13211032, 15211036), the Financial Support from Science and Technology Plan Projects of Zhangjiakou City, China (Grant No. 1611070A), and the Ph. D. Programs Foundation of Hebei Institute of Architecture Civil Engineering, China.

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References

[1]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[2]	Galanakis I, Dederichs P H, Papanikolaou N 2002 Phys. Rev. B 66 174429 Google Scholar
[3]	Skaftouros S, Ozdogan K, Sasioglu E, Galanakis I 2013 Phys. Rev. B 87 024420 Google Scholar
[4]	Luo H, Meng F, Liu H, Li J, Liu E, Wu G, Zhu X, Jiang C 2012 J. Magn. Magn. Mater. 324 2127 Google Scholar
[5]	Luo H, Liu G, Meng F, Wang L, Liu E, Wu G, Zhu X, Jiang C 2011 Computat. Mater. Sci. 50 3119 Google Scholar
[6]	Gao Q, Li L, Lei G, Deng J B, Hun X R 2015 J. Magn. Magn. Mater. 379 288 Google Scholar
[7]	Bainsla L, Mallick A I, Coelho A A, Nigam A K, Varaprasad B, Takahashi Y K, Alam A, Suresh K G, Hono K 2015 J. Magn. Magn. Mater. 394 82 Google Scholar
[8]	Berri S, Maouche D, Ibrir M, Zerarga F 2014 J. Magn. Magn. Mater. 354 65 Google Scholar
[9]	Ozdogan K, Sasioglu E, Galanakis I 2013 J. Appl. Phys. 113 193903 5
[10]	Halder M, Mukadam M D, Suresh K G, Yusuf S M 2015 J. Magn. Magn. Mater. 377 220 Google Scholar
[11]	Venkateswara E Y, Gupta S, Varma M R, Singh P, Suresh K G, Alam A 2015 Phys. Rev. B 92 224413
[12]	Bainsla L, Yadav A K, Venkateswara Y, Jha S N, Bhattacharyya D, Suresh K G 2015 J. Alloys Compounds 651 509 Google Scholar
[13]	Al-zyadi J M K, Gao G Y, Yao K L 2015 J. Magn. Magn. Mater. 378 1 Google Scholar
[14]	姚仲瑜, 孙丽, 潘孟美, 孙书娟, 刘汉军 2018 67 217501 Google Scholar Yao Z Y, Sun L, Pan M M, Sun S J, Liu H J 2018 Acta Phys. Sin. 67 217501 Google Scholar
[15]	黄海深, 孙剑, 吴波, 杨秀德, 李平 2018 材料导报 32 2124 Google Scholar Huang H S, Sun J, Wu B, Yang X D, Li P 2018 Mater. Reports 32 2124 Google Scholar
[16]	Alijani V, Ouardi S, Fecher G H, Winterlik J, Naghavi S S, Kozina X, Stryganyuk G, Felser C, Ikenaga E, Yamashita Y, Ueda S, Kobayashi K 2011 Phys. Rev. B 84 224416 Google Scholar
[17]	Klaer P, Balke B, Alijani V, Winterlik J, Fecher G H, Felser C, Elmers H J 2011 Phys. Rev. B 84 144413 Google Scholar
[18]	Vajiheh A, Juergen W, Gerhard H F, Naghavi S S, Stanislav C, Thomas G, Claudia F 2012 J. Phys.: Condens. Matter 24 046001 Google Scholar
[19]	Benkabou M, Rached H, Abdellaoui A, Rached D, Khenata R, Elahmar M H, Abidri B, Benkhettou N, Bin-Omran S 2015 J. Alloys Compd. 647 276 Google Scholar
[20]	Jia L Y, Xu J L, Zhao R B, Pan H, Shen J L, Yuan L Y, Li G K, Ma L, Zhen C M, Hou D L 2018 J. Supercond. Nov. Magn. 31 1067 Google Scholar
[21]	辛月朋, 马悦兴, 郝红月, 孟凡斌, 刘何燕, 罗鸿志 2016 65 147102 Google Scholar Xin Y P, Ma Y X, Hao H Y, Meng F B, Liu H Y, Luo H Z 2016 Acta Phys. Sin. 65 147102 Google Scholar
[22]	Murnaghan F 1944 Proc. Nat. Acad. Sci. USA 50 697
[23]	Rached H, Rached D, Khenata R, Reshak A H, Rabah M 2009 Phys. Status Solidi (b) 246 1580 Google Scholar
[24]	Rached H, Rached D, Rabah M, Khenata R, Reshak A H 2010 Physica B: Condens. Matter 405 3515 Google Scholar
[25]	Pettifor D G 1992 Mater. Sci. Technol. 8 345 Google Scholar
[26]	Kanchana V, Vaitheeswaran G, Ma Y, Xie Y, Svane A, Eriksson O 2009 Phys. Rev. B 80 125108 Google Scholar
[27]	Pugh S F 1954 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 45 823 Google Scholar
[28]	Haines J, Leger J, Bocquillon G 2001 Ann. Rev. Mater. Res. 31 1 Google Scholar
[29]	Biskri Z E, Rached H, Bouchear M, Rached D 2014 J. Mech. Behav. Biomed. Mater. 32 345 Google Scholar
[30]	Anderson O L 1963 J. Phys. Chem. Solids 24 909 Google Scholar

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图 1 LiMgPdSb型Heusler合金的结构示意图

Figure 1. Structure of LiMgPdSn-type Heusler alloys.

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图 2 四个化合物的态密度图, 其中最上方的是TDOS, 下方分别为各原子的PDOS　(a) CoMnZnSi; (b) CoMnZnGe; (c) CoMnZnSn; (d) CoMnZnPb

Figure 2. Totals and Partials density of states (TDOS, PDOS) in their stable structure: (a) CoMnZnSi; (b) CoMnZnGe; (c) CoMnZnSn; (d) CoMnZnPb.

DownLoad: Full-Size Img PowerPoint

图 3 自旋向下轨道填充状态示意图

Figure 3. Sketch of the spin-down orbital’s occupied states.

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表 1 CoMnZnSi, CoMnZnGe, CoMnZnSn, CoMnZnPb四种化合物对应的平衡晶格常数a₀、体积弹性模量B、压力导数B'和平衡能量E₀

Table 1. Calculated equilibrium lattice parameters a₀, bulk modulus B, its pressure derivative B' and equilibrium energy E₀ for CoMnZnZ (Z = Si, Ge, Sn, Pb) compounds.

Material	a₀/Å	B/GPa	B'	E₀/Ryd
CoMnZnSi	5.81	163.57	4.56	－9276.59
CoMnZnGe	5.93	154.83	3.78	－12894.68
CoMnZnSn	6.18	122.29	5.20	－21054.64
CoMnZnPb	6.35	67.80	10.15	－50552.93

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表 2 计算得到的各化合物的单晶弹性常数C_ij、多晶剪切模量G、杨氏模量E、泊松比ν和剪切各向异性常数A

Table 2. Calculated single crystal elastic constants C_ij and polycrystalline elastic modulus (shear modulus G, Young’s modulus E, Poisson’s ratio ν) shear anisotropic factor A for compounds.

Material	C₁₁	C₁₂	C₄₄	G	E	ν	A
CoMnZnSi	106.37	175.86	73.27	0.76	2.27	0.50	–2.11
CoMnZnGe	94.93	150.45	60.36	0.97	2.90	0.50	–2.17
CoMnZnSn	94.17	130.42	60.59	4.87	14.41	0.48	–3.34
CoMnZnPb	58.98	97.61	30.17	–1.69	–5.12	0.51	–1.56

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表 3 计算得到的温度压力均为0状态下的纵向(v_l)、横向(v_t)、平均声速 (v_m)和德拜温度(θ_D)

Table 3. Calculated longitudinal (v_l), transverse (v_t), and average (v_m) sound velocity and Debye temperature (θ_D) for compounds.

Material	v_t/ m·s^–1	v_l/ m·s^–1	v_m/ m·s^–1	θ_D/K
CoMnZnSi	3732.6	3178.9	2341	208.63
CoMnZnGe	1366	1001.9	6397.9	284.78
CoMnZnSn	3030	8999.9	2901.3	172.36
CoMnZnPb	1147	4121.8	7588.8	81.813

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表 4 每分子式总自旋磁矩M_t、间隙区磁矩M_i和各原子磁矩(M_X, M'_X, M_Y, M_Z)、自旋极化率

Table 4. Total, interstitial and local magnetic moments, calculated spin-polarization.

Material	M_t/μ_B	M_i/μ_B	M_X/μ_B	M'_X/μ_B	M_Y/μ_B	M_Z/μ_B	Spin polarization ratio/%
CoMnZnSi	4.00	0.0872	0.91	3.01	0.01	–0.02	100
CoMnZnGe	4.00	0.0005	0.81	3.20	0.02	–0.03	100
CoMnZnSn	4.00	–0.0321	0.74	3.34	–0.01	–0.04	100
CoMnZnPb	4.34	–0.0181	0.87	3.49	–0.02	–0.01	47

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map

[1]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[2]	Galanakis I, Dederichs P H, Papanikolaou N 2002 Phys. Rev. B 66 174429 Google Scholar
[3]	Skaftouros S, Ozdogan K, Sasioglu E, Galanakis I 2013 Phys. Rev. B 87 024420 Google Scholar
[4]	Luo H, Meng F, Liu H, Li J, Liu E, Wu G, Zhu X, Jiang C 2012 J. Magn. Magn. Mater. 324 2127 Google Scholar
[5]	Luo H, Liu G, Meng F, Wang L, Liu E, Wu G, Zhu X, Jiang C 2011 Computat. Mater. Sci. 50 3119 Google Scholar
[6]	Gao Q, Li L, Lei G, Deng J B, Hun X R 2015 J. Magn. Magn. Mater. 379 288 Google Scholar
[7]	Bainsla L, Mallick A I, Coelho A A, Nigam A K, Varaprasad B, Takahashi Y K, Alam A, Suresh K G, Hono K 2015 J. Magn. Magn. Mater. 394 82 Google Scholar
[8]	Berri S, Maouche D, Ibrir M, Zerarga F 2014 J. Magn. Magn. Mater. 354 65 Google Scholar
[9]	Ozdogan K, Sasioglu E, Galanakis I 2013 J. Appl. Phys. 113 193903 5
[10]	Halder M, Mukadam M D, Suresh K G, Yusuf S M 2015 J. Magn. Magn. Mater. 377 220 Google Scholar
[11]	Venkateswara E Y, Gupta S, Varma M R, Singh P, Suresh K G, Alam A 2015 Phys. Rev. B 92 224413
[12]	Bainsla L, Yadav A K, Venkateswara Y, Jha S N, Bhattacharyya D, Suresh K G 2015 J. Alloys Compounds 651 509 Google Scholar
[13]	Al-zyadi J M K, Gao G Y, Yao K L 2015 J. Magn. Magn. Mater. 378 1 Google Scholar
[14]	姚仲瑜, 孙丽, 潘孟美, 孙书娟, 刘汉军 2018 67 217501 Google Scholar Yao Z Y, Sun L, Pan M M, Sun S J, Liu H J 2018 Acta Phys. Sin. 67 217501 Google Scholar
[15]	黄海深, 孙剑, 吴波, 杨秀德, 李平 2018 材料导报 32 2124 Google Scholar Huang H S, Sun J, Wu B, Yang X D, Li P 2018 Mater. Reports 32 2124 Google Scholar
[16]	Alijani V, Ouardi S, Fecher G H, Winterlik J, Naghavi S S, Kozina X, Stryganyuk G, Felser C, Ikenaga E, Yamashita Y, Ueda S, Kobayashi K 2011 Phys. Rev. B 84 224416 Google Scholar
[17]	Klaer P, Balke B, Alijani V, Winterlik J, Fecher G H, Felser C, Elmers H J 2011 Phys. Rev. B 84 144413 Google Scholar
[18]	Vajiheh A, Juergen W, Gerhard H F, Naghavi S S, Stanislav C, Thomas G, Claudia F 2012 J. Phys.: Condens. Matter 24 046001 Google Scholar
[19]	Benkabou M, Rached H, Abdellaoui A, Rached D, Khenata R, Elahmar M H, Abidri B, Benkhettou N, Bin-Omran S 2015 J. Alloys Compd. 647 276 Google Scholar
[20]	Jia L Y, Xu J L, Zhao R B, Pan H, Shen J L, Yuan L Y, Li G K, Ma L, Zhen C M, Hou D L 2018 J. Supercond. Nov. Magn. 31 1067 Google Scholar
[21]	辛月朋, 马悦兴, 郝红月, 孟凡斌, 刘何燕, 罗鸿志 2016 65 147102 Google Scholar Xin Y P, Ma Y X, Hao H Y, Meng F B, Liu H Y, Luo H Z 2016 Acta Phys. Sin. 65 147102 Google Scholar
[22]	Murnaghan F 1944 Proc. Nat. Acad. Sci. USA 50 697
[23]	Rached H, Rached D, Khenata R, Reshak A H, Rabah M 2009 Phys. Status Solidi (b) 246 1580 Google Scholar
[24]	Rached H, Rached D, Rabah M, Khenata R, Reshak A H 2010 Physica B: Condens. Matter 405 3515 Google Scholar
[25]	Pettifor D G 1992 Mater. Sci. Technol. 8 345 Google Scholar
[26]	Kanchana V, Vaitheeswaran G, Ma Y, Xie Y, Svane A, Eriksson O 2009 Phys. Rev. B 80 125108 Google Scholar
[27]	Pugh S F 1954 The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 45 823 Google Scholar
[28]	Haines J, Leger J, Bocquillon G 2001 Ann. Rev. Mater. Res. 31 1 Google Scholar
[29]	Biskri Z E, Rached H, Bouchear M, Rached D 2014 J. Mech. Behav. Biomed. Mater. 32 345 Google Scholar
[30]	Anderson O L 1963 J. Phys. Chem. Solids 24 909 Google Scholar

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Structure and half-metallic ferromagnetism of quaternary Heusler compounds CoMnZnZ

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Corresponding author: Jia Li-Yun, jliyun@126.com

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Structure and half-metallic ferromagnetism of quaternary Heusler compounds CoMnZnZ

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Corresponding author: Jia Li-Yun, jliyun@126.com

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