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Co2-基Heusler合金Co2FeAl1–xSix(x = 0.25, x = 0.5, x = 0.75)的结构、电子结构及热电特性的第一性原理研究

杨艳敏 李佳 马洪然 杨广 毛秀娟 李聪聪

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Co2-基Heusler合金Co2FeAl1–xSix(x = 0.25, x = 0.5, x = 0.75)的结构、电子结构及热电特性的第一性原理研究

杨艳敏, 李佳, 马洪然, 杨广, 毛秀娟, 李聪聪

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
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  • 运用基于密度泛函理论的第一性原理方法, 对Co2FeAl1–xSix(x = 0.25, 0.5, 0.75)系列Heusler合金的电子结构、四方畸变、弹性常数, 声子谱以及热电特性进行了计算研究. 结果显示, Co2FeAl1–xSix系列合金的电子结构均为半金属特性, 向下自旋态(半导体性)均呈现良好的热电特性, 并且随着硅原子浓度的增加功率因子随之增加. 计算的声子谱不存在虚频, 均满足动力学稳定性条件, 弹性常数均满足玻恩稳定性条件, 机械稳定性均良好. 随着晶格常数c/a的比值变化, 体系的能量最低点均出现在c/a = 1处, 即结构稳定性不随畸变度c/a的变化而变化, 说明不存在马氏体相变. 此系列合金薄膜的电子结构呈现较高的自旋极化率, 在替代浓度x = 0.75时自旋极化率达到100%, 且当x = 0.75时薄膜在畸变度c/a = 1.2时存在马氏体相变. 随着晶格畸变度的改变, 总磁矩也发生变化, 且主要由Fe和Co两种过渡金属原子的磁矩变化所决定.
    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.
      通信作者: 李佳, jiali@hebut.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 61671199)、中国博士后基金(批准号: 61671199)、河北省博士后特别资助(批准号: 2016M601243)和国家春晖计划(批准号: Z2017024)资助的课题.
      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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    Murray S J, Marioni M, Allen S M, O’Handley R C 2000 Appl. Phys. Lett. 77 886Google Scholar

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    Donni A, Fischer P, Fauth F, Convert P, Aoki Y, Sugawara H, Sato H 1999 Physica B 259 705

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    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 2990Google Scholar

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    Saha B, Shakouri A, Sands T D 2018 Appl. Phys. Rev. 5 021101Google Scholar

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    Kübler J, William A R, Sommers C B 1983 Phys. Rev. B 28 1745Google Scholar

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    de Groot R A, Müller F M, van Engen P G, Buschow K H J 1983 Phys. Rev. Lett. 50 2024Google Scholar

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    Comtesse D, Geisler B, Entel P, Kratzer P, Szunyogh L 2014 Phys. Rev. B 89 094410Google Scholar

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    Fecher G H, Felser C 2007 J. Phys. D: Appl. Phys. 40 1582Google Scholar

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    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 021306Google Scholar

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    Balli M, Jandl S, Fournier P, Kedous-Lebouc A 2017 Appl. Phys. Rev. 4 021305Google Scholar

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    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 092408Google Scholar

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    Karaca H E, Karaman I, Basaran B, Ren Y, Chumlyakov Y I, Maier H J 2009 Adv. Funct. Mater. 19 983Google Scholar

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    Chmielus M, Zhang X X, Witherspoon C, Dunand D C, Mullner P 2009 Nat. Mater. 8 863Google Scholar

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    Sarawate N, Dapino M 2006 Appl. Phys. Lett. 88 121923Google Scholar

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    Mañosa L, González-Alonso D, Planes A, Bonnot E, Barrio M, Tamarit J L, Aksoy S, Acet M 2010 Nat. Mater. 9 478Google Scholar

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    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 134406Google Scholar

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    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

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    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 139Google Scholar

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  • 图 1  (a) Co2FeAl1xSix (x = 0.25)的L21结构; (b) Co2FeAl0.75Si0.25的薄膜结构

    Fig. 1.  (a) L21 structure of Co2FeAl1-xSix (x = 0.25); (b)thin film structure of Co2FeAl0.75Si0.25.

    图 2  Co2FeAl1-xSix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

    Fig. 2.  Optimization curves of lattice constant for Co2FeAl1-xSix alloy under ferromagnetic and antiferromagnetic magnetic order.

    图 3  (a) Co2FeAl0.75Si0.25, (b) Co2FeAl0.5Si0.5和(c) Co2FeAl0.25Si0.75的能带结构

    Fig. 3.  Energy band structure of (a) Co2FeAl0.75Si0.25, (b) Co2FeAl0.5Si0.5 and (c) Co2FeAl0.25Si0.75.

    图 4  (a) Co2FeAl0.75Si0.25,(b) Co2FeAl0.5Si0.5和(c) Co2FeAl0.25Si0.75的总态密度和分态密度

    Fig. 4.  Thetotaland atom-projected density of states for Heusler alloys Co2FeAl1-xSix (x = 0.25, 0.5, 0.75) film in (a), (b) and (c).

    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

    Fig. 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  Co2FeAl1xSix合金在x = 0.25, 0.5, 0.75时的声子谱及比热容 (a) Co2FeAl1xSix (x = 0.25), (b) Co2FeAl1xSi x (x = 0.5)和(c) Co2FeAl1xSi 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

    Fig. 6.  Full phonon spectra of Co2FeAl1xSix (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 7  (a) Co2FeAl0.75Si0.25, (b) Co2FeAl0.5Si0.5和(c) Co2FeAl0.25Si0.75薄膜的总态密度和原子分态密度

    Fig. 7.  Thetotaland atom-projected density of states for Co2FeAl1xSix (x = 0.25, 0.5 and 0.75) film in (a), (b) and (c).

    图 8  (a) x = 0.25,(b) x = 0.5和(c) x = 0.75替代浓度下Co2FeAl1xSix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

    Fig. 8.  Calculated total energies as a function of the c/a ratio for Co2FeAl1xSix (x = 0.25, 0.5 and 0.75) Heusler alloys in (a), (b) and (c) andfilm materials in (d), (e) and (f).

    图 9  (a) x = 0.25,(b) x = 0.5和(c) x = 0.75替代浓度下Co2FeAl1-xSix合金薄膜的总磁矩及各原子总磁矩随畸变度的变化

    Fig. 9.  The total magnetic moment and the magnetic moment of each atom of Co2FeAl1-xSix film change with distortion at x = 0.25, x = 0.5 and x = 0.75 in (a), (b) and (c).

    表 1  Co2FeAl1xSix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 Co2FeAl1xSix alloys at x = 0.25, 0.5 and 0.75.

    amAl/${{\text{μ}}_{\rm{B}}}$mSi/${{\text{μ}}_{\rm{B}}}$mFe/${{\text{μ}}_{\rm{B}}}$mCo/${{\text{μ}}_{\rm{B}}}$Mt/${{\text{μ}}_{\rm{B}}}$
    Co2FeAl0.75Si0.255.6520–0.053–0.0392.9981.2625.473
    Co2FeAl0.5Si0.55.6607–0.046–0.0283.0371.3375.688
    Co2FeAl0.25Si0.755.6406–0.038–0.0123.0941.4005.891
    下载: 导出CSV

    表 2  计算的Co2FeAl1xSix (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/GPaC12/GPaC44/GPaB/GPaGV/GPaGR/GPaGH/GPa
    Co2FeAl0.75Si0.25247.38166.97142.33193.77101.4870.6086.04
    Co2FeAl0.5Si0.5266.15143.57141.73184.43109.5592.94101.25
    Co2FeAl0.25Si0.75176.4651.042137.6792.85107.6993.14100.42
    下载: 导出CSV
  • [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 886Google 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 2990Google Scholar

    [5]

    Saha B, Shakouri A, Sands T D 2018 Appl. Phys. Rev. 5 021101Google Scholar

    [6]

    Webster P J 1971 J. Phys. Chem. Solids 32 1221Google Scholar

    [7]

    Kübler J, William A R, Sommers C B 1983 Phys. Rev. B 28 1745Google Scholar

    [8]

    de Groot R A, Müller F M, van Engen P G, Buschow K H J 1983 Phys. Rev. Lett. 50 2024Google Scholar

    [9]

    Comtesse D, Geisler B, Entel P, Kratzer P, Szunyogh L 2014 Phys. Rev. B 89 094410Google Scholar

    [10]

    Fecher G H, Felser C 2007 J. Phys. D: Appl. Phys. 40 1582Google 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 021306Google Scholar

    [12]

    Balli M, Jandl S, Fournier P, Kedous-Lebouc A 2017 Appl. Phys. Rev. 4 021305Google 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 162503Google 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 092408Google Scholar

    [16]

    Karaca H E, Karaman I, Basaran B, Ren Y, Chumlyakov Y I, Maier H J 2009 Adv. Funct. Mater. 19 983Google Scholar

    [17]

    Chmielus M, Zhang X X, Witherspoon C, Dunand D C, Mullner P 2009 Nat. Mater. 8 863Google Scholar

    [18]

    Sarawate N, Dapino M 2006 Appl. Phys. Lett. 88 121923Google Scholar

    [19]

    Mañosa L, González-Alonso D, Planes A, Bonnot E, Barrio M, Tamarit J L, Aksoy S, Acet M 2010 Nat. Mater. 9 478Google 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 134406Google Scholar

    [21]

    Zayak A T, Entel P, Rabe K M, Adeagbo W A, Acet M 2005 Phys. Rev. B 72 054113Google 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 8037Google Scholar

    Luo L J, Zhong C G, Dong Z C, Fang J H, Zhou P X, Jiang X F 2010 Acta Phys. Sin. 59 8037Google Scholar

    [23]

    罗礼进, 仲崇贵, 江学范, 方靖淮, 蒋青 2010 物理学报 59 521Google Scholar

    Luo L J, Zhong C G, Jiang X F, Fang J H, Jiang Q 2010 Acta Phys. Sin. 59 521Google 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 127502Google Scholar

    Luo L J, Zhong C G, Zhao Y L, Fang J H, Zhou P X, Jiang X F 2011 Acta Phys. Sin. 60 127502Google 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 207503Google Scholar

    Luo L J, Zhong C G, Dong Z C, Fang J H, Zhou P X, Jiang X F 2012 Acta Phys. Sin. 61 207503Google 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 139Google Scholar

    [28]

    Kress G, Hafner J 1993 Phys. Rev. B 47 558Google 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 6671Google Scholar

    [30]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [31]

    Kandpal H C, Fecher G H, Felser C 2007 J. Phys. D: Appl. Phys. 40 1507Google Scholar

    [32]

    Madsen G K H, Singh D J 2006 Comput. Phys. Commum. 175 67Google Scholar

    [33]

    Galanakis I, Mavropoulos P, Dederichs P H 2006 J. Phys. D: Appl. Phys. 39 765Google Scholar

    [34]

    Sargolzaei M, Richter M, Koepernik K, Opahle I, Eschrig H, Chaplygin I 2006 Phys. Rev. B 74 224410Google Scholar

    [35]

    Jansen H J F, Freeman A J 1984 Phys. Rev. B 30 561Google 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 183Google 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 371Google Scholar

    [38]

    Kourov N I, Marchenkov V V, Perevozchikova Y A, Weber H W 2017 Phys. Solid State 59 898Google Scholar

    [39]

    Bilc D I, Mahanti S D, Kanatzidis M G 2006 Phys. Rev. B 74 125202Google Scholar

    [40]

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出版历程
  • 收稿日期:  2018-09-03
  • 修回日期:  2018-12-24
  • 上网日期:  2019-02-01
  • 刊出日期:  2019-02-20

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