First-principles study of structure, electronic structure and thermoelectric properties for Co2-based Heusler alloys Co2FeAl1–xSix (x = 0.25, x = 0.5, x = 0.75)

Yang Yan-Min; Li Jia; Ma Hong-Ran; Yang Guang; Mao Xiu-Juan; Li Cong-Cong

doi:10.7498/aps.68.20181641

Abstract

In the recent decades, the half-metallic materials have become a research hotspot because of their unique electronic structure. The 100% spin polarization at the Fermi level makes them widely used in spintronic devices. The Co-based Heusler alloys belong to an important class of magnetic material, and Co₂FeAl and Co₂FeSi have been experimentally confirmed to be half-metallic materials with 100% spin polarization at the Fermi level, and the Co₂FeSi has a high Curie temperature of 1100 K and a large magnetic moment of 6.0 ${{\text{μ}}{\rm{B}}}$, which is a good candidate for spintronic devices. We here choose and substitute Al atoms in Co₂FeAl with Si atoms, and then carry out the theoretical predictions of Co₂FeAl_1–xSi_x (x = 0.25, 0.5, 0.75) for both bulk and film . In this paper, using the first principles calculations based on the density functional theory (DFT) we study the electronic structure, tetragonal distortion, elastic constants, phonon spectrum and thermoelectric properties of Co₂FeAl_1–xSi_x (x = 0.25, 0.5, 0.75) series alloys. The calculation results show that the electronic structure of Co₂FeAl_1–xSi_x (x = 0.25, 0.5, 0.75) series alloys are all half-metallic with 100% spin polarization, and the down spin states (semiconducting character) all exhibit good thermoelectric properties, and the power factor increases with the substitution concentration of Si atoms increasing. The calculated phonon spectrum does not have virtual frequency, indicating its dynamic stability, and all cubic phases fulfill the mechanical stability criteria, i.e. Born criteria: C₁₁ > 0, C₄₄ > 0, C₁₁–C₁₂ > 0, C₁₁ + 2C₁₂ > 0, and C₁₂ < B < C₁₁. With the variation of lattice constant ratio c/a, the lowest energy point of the structure for Co₂FeAl_1–xSi_x (x = 0.25, 0.5, 0.75) series alloys are all at c/a = 1, showing that the stability of the structure does not change with the variation of distortion c/a, and further the martensitic transformation cannot occur. For the Co₂FeAl_1–xSi_x (x = 0.25, 0.5, 0.75) series alloy thin films, the calculated electronic structures all show a high spin polarization, and it reaches 100% at x = 0.75, and for x = 0.75, the lowest energy point of the structure is at c/a = 1.2, suggesting the martensitic transformation in this structure. With the variation of the tetragonal distortion, the total magnetic moment also changes and it is mainly determined by the changes of atomic magnetic moment of transition-metals Fe and Co.

Keywords:

Authors and contacts

School of Science, Hebei University of Technology, Tianjin 300401, China

Corresponding author: Li Jia, jiali@hebut.edu.cn

Funds: Project supported by the National Natural Science Foundation (Grant No. 61671199), the China Postdoctoral Foundation (Grant No. 61671199), Hebei Provincial Postdoctoral Special Foundation (Grant No. 2016M601243), and the National Chunhui Plan (Grant No. Z2017024).

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References

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[3]	Donni A, Fischer P, Fauth F, Convert P, Aoki Y, Sugawara H, Sato H 1999 Physica B 259 705
[4]	Wu G H, Yu C H, Meng L Q, Chen J L, Yang F M, Qi S R, Zhan W S 1999 Appl. Phys. Lett. 75 2990 Google Scholar
[5]	Saha B, Shakouri A, Sands T D 2018 Appl. Phys. Rev. 5 021101 Google Scholar
[6]	Webster P J 1971 J. Phys. Chem. Solids 32 1221 Google Scholar
[7]	Kübler J, William A R, Sommers C B 1983 Phys. Rev. B 28 1745 Google Scholar
[8]	de Groot R A, Müller F M, van Engen P G, Buschow K H J 1983 Phys. Rev. Lett. 50 2024 Google Scholar
[9]	Comtesse D, Geisler B, Entel P, Kratzer P, Szunyogh L 2014 Phys. Rev. B 89 094410 Google Scholar
[10]	Fecher G H, Felser C 2007 J. Phys. D: Appl. Phys. 40 1582 Google Scholar
[11]	Li X M, Li T, Chen Z F, Hui F, Li X S, Wang X R, Xu J B, Zhu H W 2017 Appl. Phys. Rev. 4 021306 Google Scholar
[12]	Balli M, Jandl S, Fournier P, Kedous-Lebouc A 2017 Appl. Phys. Rev. 4 021305 Google Scholar
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[30]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[31]	Kandpal H C, Fecher G H, Felser C 2007 J. Phys. D: Appl. Phys. 40 1507 Google Scholar
[32]	Madsen G K H, Singh D J 2006 Comput. Phys. Commum. 175 67 Google Scholar
[33]	Galanakis I, Mavropoulos P, Dederichs P H 2006 J. Phys. D: Appl. Phys. 39 765 Google Scholar
[34]	Sargolzaei M, Richter M, Koepernik K, Opahle I, Eschrig H, Chaplygin I 2006 Phys. Rev. B 74 224410 Google Scholar
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[37]	Li J, Yang G, Yang Y M, Ma H R, Zhang Q, Zhang Z D, Fang W, Yin F X, Li J 2017 J. Magn. Magn. Mater. 442 371 Google Scholar
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[48]	Huang X F, Dai Z W, Huang L, Lu G D, Liu M, Piao H G, Kim D H, Yu S C, Pan L Q 2016 J. Phys.: Condens. Matter 284 76006

Cited By

图 1 (a) Co₂FeAl₁_－xSi_x (x = 0.25)的L2₁结构; (b) Co₂FeAl_0.75Si_0.25的薄膜结构

Figure 1. (a) L2₁ structure of Co₂FeAl_1－_xSi_x (x = 0.25); (b)thin film structure of Co₂FeAl_0.75Si_0.25.

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图 2 Co₂FeAl_1－_xSi_x合金在铁磁态(FM)和反铁磁态(AFM)下的晶格常数优化曲线 (a) x = 0.25; (b) x = 0.5; (c) x = 0.75

Figure 2. Optimization curves of lattice constant for Co₂FeAl_1－_xSi_x alloy under ferromagnetic and antiferromagnetic magnetic order.

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图 3 (a) Co₂FeAl_0.75Si_0.25, (b) Co₂FeAl_0.5Si_0.5和(c) Co₂FeAl_0.25Si_0.75的能带结构

Figure 3. Energy band structure of (a) Co₂FeAl_0.75Si_0.25, (b) Co₂FeAl_0.5Si_0.5 and (c) Co₂FeAl_0.25Si_0.75.

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图 4 (a) Co₂FeAl_0.75Si_0.25,(b) Co₂FeAl_0.5Si_0.5和(c) Co₂FeAl_0.25Si_0.75的总态密度和分态密度

Figure 4. Thetotaland atom-projected density of states for Heusler alloys Co₂FeAl₁_－xSi_x (x = 0.25, 0.5, 0.75） film in (a), (b) and (c).

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图 5 Co₂FeAl_0.75Si_0.25向下自旋态的(a)Seebeck系数, (b)电导, (c)热导和(d)功率因子随化学势的变化; Co₂FeAl_0.5Si_0.5向下自旋态的(e) Seebeck系数, (f)电导, (g)热导和(h) 功率因子随化学势的变化; Co₂FeAl_0.25Si_0.75向下自旋态的(i)Seebeck系数, (j)电导, (k)热导和(l)功率因子随化学势的变化

Figure 5. The transport properties with variation of chemical potential $\mu $ for Co₂FeAl_1－_xSi_x(x = 0.25, 0.5 and 0.75). The case of x = 0.25 corresponds to (a), (b), (c) and (d), and the case of x = 0.5 corresponds to (e), (f), (g) and (h), and the case of x = 0.75 corresponds to (i), (j), (k) and (l). The four columns from left to right correspond to the Seebeck coefficients S, electrical conductivity $\sigma $, electronic thermal conductivity ${\kappa _{\rm{e}}}$ and PF (${S^2}\sigma $), respectively.

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图 6 Co₂FeAl₁_－xSi_x合金在x = 0.25, 0.5, 0.75时的声子谱及比热容 (a) Co₂FeAl₁_－xSi_x (x = 0.25), (b) Co₂FeAl₁_－xSi_x (x = 0.5)和(c) Co₂FeAl₁_－xSi_x (x = 0.75)的声子谱; (d) Co₂FeAl₁_{－ x}Si_x (x = 0.25, 0.5, 0.75)的比热容随温度的变化

Figure 6. Full phonon spectra of Co₂FeAl₁_－xSi_x (x = 0.25, 0.5 and 0.75) alloys in (a), (b) and (c). The temperature dependent heat capacity C_v with an inset graph showing the temperaturefrom 180 K to 250 K in (d).

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图 7 (a) Co₂FeAl_0.75Si_0.25, (b) Co₂FeAl_0.5Si_0.5和(c) Co₂FeAl_0.25Si_0.75薄膜的总态密度和原子分态密度

Figure 7. Thetotaland atom-projected density of states for Co₂FeAl₁_－xSi_x (x = 0.25, 0.5 and 0.75) film in (a), (b) and (c).

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图 8 (a) x = 0.25,(b) x = 0.5和(c) x = 0.75替代浓度下Co₂FeAl₁_－xSi_x合金体相的总能量差$\Delta E$与畸变度c/a的关系; (d) x = 0.25, (e) x = 0.5和(f) x = 0.75替代浓度下Co₂FeAl_1－_xSi_x薄膜的驱动力$\Delta E$与畸变度c/a的关系

Figure 8. Calculated total energies as a function of the c/a ratio for Co₂FeAl₁_－xSi_x (x = 0.25, 0.5 and 0.75) Heusler alloys in (a), (b) and (c) andfilm materials in (d), (e) and (f).

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图 9 (a) x = 0.25,(b) x = 0.5和(c) x = 0.75替代浓度下Co₂FeAl_1－_xSi_x合金薄膜的总磁矩及各原子总磁矩随畸变度的变化

Figure 9. The total magnetic moment and the magnetic moment of each atom of Co₂FeAl_1－_xSi_x film change with distortion at x = 0.25, x = 0.5 and x = 0.75 in (a), (b) and (c).

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表 1 Co₂FeAl₁_－xSi_x合金在x = 0.25, 0.5, 0.75时的晶格参数及磁矩

Table 1. Lattice parameters and magnetic moments of Co₂FeAl₁_－xSi_x alloys at x = 0.25, 0.5 and 0.75.

	a/Å	m_Al/${{\text{μ}}_{\rm{B}}}$	m_Si/${{\text{μ}}_{\rm{B}}}$	m_Fe/${{\text{μ}}_{\rm{B}}}$	m_Co/${{\text{μ}}_{\rm{B}}}$	M_t/${{\text{μ}}_{\rm{B}}}$
Co₂FeAl_0.75Si_0.25	5.6520	–0.053	–0.039	2.998	1.262	5.473
Co₂FeAl_0.5Si_0.5	5.6607	–0.046	–0.028	3.037	1.337	5.688
Co₂FeAl_0.25Si_0.75	5.6406	–0.038	–0.012	3.094	1.400	5.891

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表 2 计算的Co₂FeAl₁_－xSi_x (x = 0.25, x = 0.5, x = 0.75)合金的弹性常数、体模量及剪切模量

Table 2. The calculated cubic elastic constant C₁₁, C₁₂, C₄₄, shear modulus G_v, G_R and G_H in GPa.

	C₁₁/GPa	C₁₂/GPa	C₄₄/GPa	B/GPa	G_V/GPa	G_R/GPa	G_H/GPa
Co₂FeAl_0.75Si_0.25	247.38	166.97	142.33	193.77	101.48	70.60	86.04
Co₂FeAl_0.5Si_0.5	266.15	143.57	141.73	184.43	109.55	92.94	101.25
Co₂FeAl_0.25Si_0.75	176.46	51.042	137.67	92.85	107.69	93.14	100.42

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[1]	Heusler F 1903 Deut. Phys. Ges. 5 219
[2]	Murray S J, Marioni M, Allen S M, O’Handley R C 2000 Appl. Phys. Lett. 77 886 Google Scholar
[3]	Donni A, Fischer P, Fauth F, Convert P, Aoki Y, Sugawara H, Sato H 1999 Physica B 259 705
[4]	Wu G H, Yu C H, Meng L Q, Chen J L, Yang F M, Qi S R, Zhan W S 1999 Appl. Phys. Lett. 75 2990 Google Scholar
[5]	Saha B, Shakouri A, Sands T D 2018 Appl. Phys. Rev. 5 021101 Google Scholar
[6]	Webster P J 1971 J. Phys. Chem. Solids 32 1221 Google Scholar
[7]	Kübler J, William A R, Sommers C B 1983 Phys. Rev. B 28 1745 Google Scholar
[8]	de Groot R A, Müller F M, van Engen P G, Buschow K H J 1983 Phys. Rev. Lett. 50 2024 Google Scholar
[9]	Comtesse D, Geisler B, Entel P, Kratzer P, Szunyogh L 2014 Phys. Rev. B 89 094410 Google Scholar
[10]	Fecher G H, Felser C 2007 J. Phys. D: Appl. Phys. 40 1582 Google Scholar
[11]	Li X M, Li T, Chen Z F, Hui F, Li X S, Wang X R, Xu J B, Zhu H W 2017 Appl. Phys. Rev. 4 021306 Google Scholar
[12]	Balli M, Jandl S, Fournier P, Kedous-Lebouc A 2017 Appl. Phys. Rev. 4 021305 Google Scholar
[13]	Kainuma R, Imano Y, Ito W, Sutou Y, Morito H, Okamoto S, Kitakami O, Oikawa K, Fujita A, Kanomata T, Ishida K 2006 Nature 439957
[14]	Yu S Y, Liu Z H, Liu G D, Chen J L, Cao Z X, Wu G H, Zhang B, Zhang X X 2006 Appl. Phys. Lett. 89 162503 Google Scholar
[15]	Dubenko I, Pathak A K, Stadler S, Ali N, Kovarskii Y, Prudnikov V N, Perov N S, Granovsky A B 2009 Phys. Rev. B 80 092408 Google Scholar
[16]	Karaca H E, Karaman I, Basaran B, Ren Y, Chumlyakov Y I, Maier H J 2009 Adv. Funct. Mater. 19 983 Google Scholar
[17]	Chmielus M, Zhang X X, Witherspoon C, Dunand D C, Mullner P 2009 Nat. Mater. 8 863 Google Scholar
[18]	Sarawate N, Dapino M 2006 Appl. Phys. Lett. 88 121923 Google Scholar
[19]	Mañosa L, González-Alonso D, Planes A, Bonnot E, Barrio M, Tamarit J L, Aksoy S, Acet M 2010 Nat. Mater. 9 478 Google Scholar
[20]	Barman S R, Chakrabarti A, Singh S, Banik S, Bhardwaj S, Paulose P L, Chalke B A, Panda A K, Mitra A, Awasthi A M 2008 Phys. Rev. B 78 134406 Google Scholar
[21]	Zayak A T, Entel P, Rabe K M, Adeagbo W A, Acet M 2005 Phys. Rev. B 72 054113 Google Scholar
[22]	罗礼进, 仲崇贵, 董正超, 方靖淮, 周朋霞, 江学范 2010 物理学报 59 8037 Google Scholar Luo L J, Zhong C G, Dong Z C, Fang J H, Zhou P X, Jiang X F 2010 Acta Phys. Sin. 59 8037 Google Scholar
[23]	罗礼进, 仲崇贵, 江学范, 方靖淮, 蒋青 2010 物理学报 59 521 Google Scholar Luo L J, Zhong C G, Jiang X F, Fang J H, Jiang Q 2010 Acta Phys. Sin. 59 521 Google Scholar
[24]	罗礼进, 仲崇贵, 赵永林, 方靖淮, 周朋霞, 江学范 2011 物理学报 60 127502 Google Scholar Luo L J, Zhong C G, Zhao Y L, Fang J H, Zhou P X, Jiang X F 2011 Acta Phys. Sin. 60 127502 Google Scholar
[25]	罗礼进, 仲崇贵, 董正超, 方靖淮, 周朋霞, 江学范 2012 物理学报 61 207503 Google Scholar Luo L J, Zhong C G, Dong Z C, Fang J H, Zhou P X, Jiang X F 2012 Acta Phys. Sin. 61 207503 Google Scholar
[26]	Luo H Z, Jia P Z, Liu G D, Meng F B, Liu H Y, Liu E K, Wang W H, Wu G H, 2013 Solid State Commun. 17044
[27]	Luo H Z, Meng F B, Liu G D, Liu H Y, Jia P Z, Liu E K, Wang W H, Wu G H 2013 Intermetallics 38 139 Google Scholar
[28]	Kress G, Hafner J 1993 Phys. Rev. B 47 558 Google Scholar
[29]	Perdew J P, Chevary J A, Vosko S H, Jackson K A, Pederson M R, Singh D J, Fiolhais C 1992 Phys. Rev. B 46 6671 Google Scholar
[30]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[31]	Kandpal H C, Fecher G H, Felser C 2007 J. Phys. D: Appl. Phys. 40 1507 Google Scholar
[32]	Madsen G K H, Singh D J 2006 Comput. Phys. Commum. 175 67 Google Scholar
[33]	Galanakis I, Mavropoulos P, Dederichs P H 2006 J. Phys. D: Appl. Phys. 39 765 Google Scholar
[34]	Sargolzaei M, Richter M, Koepernik K, Opahle I, Eschrig H, Chaplygin I 2006 Phys. Rev. B 74 224410 Google Scholar
[35]	Jansen H J F, Freeman A J 1984 Phys. Rev. B 30 561 Google Scholar
[36]	Li J, Li J, Zhang Q, Zhang Z D, Yang G, Ma H R, Lu Z M, Fang W, Xie H X, Liang C Y, Yin F X 2016 Comp. Mater. Sci. 125 183 Google Scholar
[37]	Li J, Yang G, Yang Y M, Ma H R, Zhang Q, Zhang Z D, Fang W, Yin F X, Li J 2017 J. Magn. Magn. Mater. 442 371 Google Scholar
[38]	Kourov N I, Marchenkov V V, Perevozchikova Y A, Weber H W 2017 Phys. Solid State 59 898 Google Scholar
[39]	Bilc D I, Mahanti S D, Kanatzidis M G 2006 Phys. Rev. B 74 125202 Google Scholar
[40]	Al S, Arikan N, Demir S, Iyig€or A 2018 Physica B 531 16 Google Scholar
[41]	Li J, Zhang Z D, Sun Y B, Zhang J, Zhou G X, Luo H Z, Liu G D 2013 Physica B 409 35 Google Scholar
[42]	Okamura S, Miyazaki A, Sugimoto S 2005 Appl. Phys. Lett. 86 232503 Google Scholar
[43]	Zhu W H, Wu D, Zhao B C, Zhu Z D, Yang X D, Zhang Z Z, Jin Q Y 2017 Phys. Rev. Appl. 8 034012
[44]	Hazra B K, Raja M M, Srinath S 2016 J. Phys. D: Appl. Phys. 49 065007 Google Scholar
[45]	Xu Z, Zhang Z, Hu F, Liu E, Xu F 2016 Mater. Res. Express 3 116103 Google Scholar
[46]	Yadav A, Chaudhary S 2015 J. Appl. Phys. 118 193902 Google Scholar
[47]	Chen J, Sakuraba Y, Masuda K, Miura Y, Li S, Kasai S, Furubayashi T, Hono K 2017 Appl. Phys. Lett. 110 242401 Google Scholar
[48]	Huang X F, Dai Z W, Huang L, Lu G D, Liu M, Piao H G, Kim D H, Yu S C, Pan L Q 2016 J. Phys.: Condens. Matter 284 76006

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Vol. 68, Issue 4 - 2019-02-20

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First-principles study of structure, electronic structure and thermoelectric properties for Co₂-based Heusler alloys Co₂FeAl_1–xSi_x (x = 0.25, x = 0.5, x = 0.75)

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Corresponding author: Li Jia, jiali@hebut.edu.cn

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