Co_(2~-)基Heusler合金Co_2FeAl_(1–x)Si_x(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
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摘要
运用基于密度泛函理论的第一性原理方法,对Co_2FeAl_(1–x)Si_x(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, Co_2FeAl_(1–x)Si_x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 Co_2 Fe Al and Co_2 Fe Si have been experimentally confirmed to be half-metallic materials with 100% spin polarization at the Fermi level, and the Co_2 Fe Si has a high Curie temperature of 1100 K and a large magnetic moment of 6.0 μB,which is a good candidate for spintronic devices. We here choose and substitute Al atoms in Co_2 Fe Al with Si atoms, and then carry out the theoretical predictions of Co_2 Fe Al_(1–x) Si_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 Co_2 Fe Al_(1–x) Si_x(x = 0.25, 0.5, 0.75) series alloys. The calculation results show that the electronic structure of Co_2 Fe Al_(1–x) Si_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: C_(11) > 0, C_(44) > 0, C_(11)–C_(12)> 0, C_(11) + 2 C_(12) > 0, and C_(12) < B < C_(11). With the variation of lattice constant ratio c/a, the lowest energy point of the structure for Co_2 Fe Al_(1–x) Si_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 Co_2 Fe Al_(1–x) Si_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.
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 Co_2 Fe Al and Co_2 Fe Si have been experimentally confirmed to be half-metallic materials with 100% spin polarization at the Fermi level, and the Co_2 Fe Si has a high Curie temperature of 1100 K and a large magnetic moment of 6.0 μB,which is a good candidate for spintronic devices. We here choose and substitute Al atoms in Co_2 Fe Al with Si atoms, and then carry out the theoretical predictions of Co_2 Fe Al_(1–x) Si_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 Co_2 Fe Al_(1–x) Si_x(x = 0.25, 0.5, 0.75) series alloys. The calculation results show that the electronic structure of Co_2 Fe Al_(1–x) Si_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: C_(11) > 0, C_(44) > 0, C_(11)–C_(12)> 0, C_(11) + 2 C_(12) > 0, and C_(12) < B < C_(11). With the variation of lattice constant ratio c/a, the lowest energy point of the structure for Co_2 Fe Al_(1–x) Si_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 Co_2 Fe Al_(1–x) Si_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.
引文
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[31]Kandpal H C, Fecher G H, Felser C 2007 J. Phys. D:Appl.Phys. 40 1507
[32]Madsen G K H, Singh D J 2006 Comput. Phys. Commum.175 67
[33]Galanakis I, Mavropoulos P, Dederichs P H 2006 J. Phys. D:Appl. Phys. 39 765
[34]Sargolzaei M, Richter M, Koepernik K, Opahle I, Eschrig H,Chaplygin I 2006 Phys. Rev. B 74 224410
[35] Jansen H J F, Freeman A J 1984 Phys. Rev. B 30 561
[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
[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
[38]Kourov N I, Marchenkov V V, Perevozchikova Y A, Weber H W 2017 Phys. Solid State 59 898
[39]Bilc D I, Mahanti S D, Kanatzidis M G 2006 Phys. Rev. B74 125202
[40] Al S, Arikan N, Demir S, Iyig€or A 2018 Physica B 531 16
[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
[42]Okamura S, Miyazaki A, Sugimoto S 2005 Appl. Phys. Lett.86 232503
[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]HazraBK,RajaMM,SrinathS2016J. Phys. D:Appl.Phys. 49 065007
[45]Xu Z, Zhang Z, Hu F, Liu E, Xu F 2016 Mater. Res. Express3 116103
[46] Yadav A, Chaudhary S 2015 J. Appl. Phys. 118 193902
[47]ChenJ,SakurabaY,MasudaK,MiuraY,LiS,KasaiS,Furubayashi T, Hono K 2017 Appl. Phys. Lett. 110 242401
[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. Matter284 76006
[2]MurraySJ,MarioniM,AllenSM,O’ HandleyRC2000Appl. Phys. Lett. 77 886
[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
[5]SahaB,ShakouriA,SandsTD2018Appl. Phys. Rev.5021101
[6] Webster P J 1971 J. Phys. Chem. Solids 32 1221
[7]Kübler J, William A R, Sommers C B 1983 Phys. Rev. B 281745
[8]de Groot R A, Müller F M, van Engen P G, Buschow K H J1983 Phys. Rev. Lett. 50 2024
[9]Comtesse D, Geisler B, Entel P, Kratzer P, Szunyogh L 2014Phys. Rev. B 89 094410
[10] Fecher G H, Felser C 2007 J. Phys. D:Appl. Phys. 40 1582
[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
[12]Balli M, Jandl S, Fournier P, Kedous-Lebouc A 2017 Appl.Phys. Rev. 4 021305
[13]Kainuma R, Imano Y, Ito W, Sutou Y, Morito H, Okamoto S, Kitakami O, Oikawa K, Fujita A, Kanomata T, Ishida K2006 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
[15]DubenkoI,PathakAK,StadlerS,AliN,KovarskiiY,Prudnikov V N, Perov N S, Granovsky A B 2009 Phys. Rev.B 80 092408
[16]Karaca H E, Karaman I, Basaran B, Ren Y, Chumlyakov Y I, Maier H J 2009 Adv. Funct. Mater. 19 983
[17]ChmielusM,ZhangXX,WitherspoonC,DunandDC,Mullner P 2009 Nat. Mater. 8 863
[18] Sarawate N, Dapino M 2006 Appl. Phys. Lett. 88 121923
[19]Ma?osa L, González-Alonso D, Planes A, Bonnot E, Barrio M, Tamarit J L, Aksoy S, Acet M 2010 Nat. Mater. 9 478
[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
[21]Zayak A T, Entel P, Rabe K M, Adeagbo W A, Acet M 2005Phys. Rev. B 72 054113
[22]Luo L J, Zhong C G, Dong Z C, Fang J H, Zhou P X, Jiang X F 2010 Acta Phys. Sin. 59 8037(in Chinese)[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]
[23]Luo L J, Zhong C G, Jiang X F, Fang J H, Jiang Q 2010Acta Phys. Sin. 59 521(in Chinese)[罗礼进,仲崇贵,江学范,方靖淮,蒋青2010物理学报59 521]
[24]Luo L J, Zhong C G, Zhao Y L, Fang J H, Zhou P X, Jiang X F 2011 Acta Phys. Sin. 60 127502(in Chinese)[罗礼进,仲崇贵,赵永林,方靖淮,周朋霞,江学范2011物理学报60127502]
[25]Luo L J, Zhong C G, Dong Z C, Fang J H, Zhou P X, Jiang X F 2012 Acta Phys. Sin. 61 207503(in Chinese)[罗礼进,仲崇贵,董正超,方靖淮,周朋霞,江学范2012物理学报61207503]
[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
[28] Kress G, Hafner J 1993 Phys. Rev. B 47 558
[29]PerdewJP,ChevaryJA,VoskoSH,JacksonKA,Pederson M R, Singh D J, Fiolhais C 1992 Phys. Rev. B 466671
[30]Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 773865
[31]Kandpal H C, Fecher G H, Felser C 2007 J. Phys. D:Appl.Phys. 40 1507
[32]Madsen G K H, Singh D J 2006 Comput. Phys. Commum.175 67
[33]Galanakis I, Mavropoulos P, Dederichs P H 2006 J. Phys. D:Appl. Phys. 39 765
[34]Sargolzaei M, Richter M, Koepernik K, Opahle I, Eschrig H,Chaplygin I 2006 Phys. Rev. B 74 224410
[35] Jansen H J F, Freeman A J 1984 Phys. Rev. B 30 561
[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
[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
[38]Kourov N I, Marchenkov V V, Perevozchikova Y A, Weber H W 2017 Phys. Solid State 59 898
[39]Bilc D I, Mahanti S D, Kanatzidis M G 2006 Phys. Rev. B74 125202
[40] Al S, Arikan N, Demir S, Iyig€or A 2018 Physica B 531 16
[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
[42]Okamura S, Miyazaki A, Sugimoto S 2005 Appl. Phys. Lett.86 232503
[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]HazraBK,RajaMM,SrinathS2016J. Phys. D:Appl.Phys. 49 065007
[45]Xu Z, Zhang Z, Hu F, Liu E, Xu F 2016 Mater. Res. Express3 116103
[46] Yadav A, Chaudhary S 2015 J. Appl. Phys. 118 193902
[47]ChenJ,SakurabaY,MasudaK,MiuraY,LiS,KasaiS,Furubayashi T, Hono K 2017 Appl. Phys. Lett. 110 242401
[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. Matter284 76006