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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 Co2FeAl1–xSix (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 Co2FeAl1–xSix (x = 0.25, 0.5, 0.75) series alloys. The calculation results show that the electronic structure of Co2FeAl1–xSix (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 Co2FeAl1–xSix (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 Co2FeAl1–xSix (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:
- half-metallic /
- first principles /
- electronic structure /
- magnetism
[1] Heusler F 1903 Deut. Phys. Ges. 5 219
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Google Scholar
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[28] Kress G, Hafner J 1993 Phys. Rev. B 47 558
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Google Scholar
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图 5 Co2FeAl0.75Si0.25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; Co2FeAl0.5Si0.5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; Co2FeAl0.25Si0.75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 Co2FeAl1-xSix(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.图 6 Co2FeAl1-xSix合金在x = 0.25, 0.5, 0.75时的声子谱及比热容 (a) Co2FeAl1-xSix (x = 0.25), (b) Co2FeAl1-xSi x (x = 0.5)和(c) Co2FeAl1-xSi x (x = 0.75)的声子谱; (d) Co2FeAl1- xSix (x = 0.25, 0.5, 0.75)的比热容随温度的变化
Figure 6. Full phonon spectra of Co2FeAl1-xSix (x = 0.25, 0.5 and 0.75) alloys in (a), (b) and (c). The temperature dependent heat capacity Cv with an inset graph showing the temperaturefrom 180 K to 250 K in (d).
图 8 (a) x = 0.25,(b) x = 0.5和(c) x = 0.75替代浓度下Co2FeAl1-xSix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Co2FeAl1-xSix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-xSix (x = 0.25, 0.5 and 0.75) Heusler alloys in (a), (b) and (c) andfilm materials in (d), (e) and (f).
表 1 Co2FeAl1-xSix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-xSix alloys at x = 0.25, 0.5 and 0.75.
a/Å mAl/${{\text{μ}}_{\rm{B}}}$ mSi/${{\text{μ}}_{\rm{B}}}$ mFe/${{\text{μ}}_{\rm{B}}}$ mCo/${{\text{μ}}_{\rm{B}}}$ Mt/${{\text{μ}}_{\rm{B}}}$ Co2FeAl0.75Si0.25 5.6520 –0.053 –0.039 2.998 1.262 5.473 Co2FeAl0.5Si0.5 5.6607 –0.046 –0.028 3.037 1.337 5.688 Co2FeAl0.25Si0.75 5.6406 –0.038 –0.012 3.094 1.400 5.891 表 2 计算的Co2FeAl1-xSix (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 Gv, GR and GH in GPa.
C11/GPa C12/GPa C44/GPa B/GPa GV/GPa GR/GPa GH/GPa Co2FeAl0.75Si0.25 247.38 166.97 142.33 193.77 101.48 70.60 86.04 Co2FeAl0.5Si0.5 266.15 143.57 141.73 184.43 109.55 92.94 101.25 Co2FeAl0.25Si0.75 176.46 51.042 137.67 92.85 107.69 93.14 100.42 -
[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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