First-principles calculations of magnetic and optical properties of Ga<sub>1–x</sub>Cr<sub>x</sub>Sb (x = 0.25, 0.50, 0.75)

Wang Chuang; Zhao Yong-Hong; Liu Yong

doi:10.7498/aps.68.20182305

Abstract

As the demand for electronic devices increases continually, the spintronic materials have played an important role in materials science and electronics. Spintronic devices have excellent properties such as non-volatility, low power consumption, and high integration compared with conventional semiconductor devices. In this paper, we investigate the electronic structure, magnetic and optical properties of the semiconductor GaSb doped with 3d transition metal Cr, based on first-principles calculations. The compounds are constructed by replacing some Ga atoms with Cr in zinc-blende GaSb semiconductor, where the concentrations of the Ga atoms replaced are 0, 0.25, 0.50, and 0.75. We adopt the projected plane wave method and the electronic exchange correlation functional PBE in the generalized gradient approximation. Band gap is modified by Heyd-Scuseria-Ernzerhof (HSE06) functional. We study the equilibrium lattice constants of Cr-doped GaSb in zinc-blende structure at different concentrations. The energy of nonmagnetic, ferromagnetic and antiferromagnetic states at the equilibrium lattice constants are compared to identify the ground state. For Ga_1–xCr_xSb (x = 0.25, 0.50, 0.75), we find that the most stable state is ferromagnetic state. In the electronic structure of the ground state, the spin-up bands pass through the Fermi level while the spin-down bands each have a direct band gap. The Ga_1–xCr_xSb exhibit ferromagnetic half-metallic properties. The magnetic properties at different lattice constants under different concentrations are studied. Our analysis indicates that the Ga_1–xCr_xSb have integer Bohr magnetic moments of 3.0, 6.0, 9.0 μ_B for x = 0.25, 0.50 and 0.75, respectively. We find that when the lattice changes fom –5% to 20%, the total magnetic moment for each of Ga_1–xCr_xSb still remains the integer Bohr magnetic moment, and the magnetic moment of the Cr increases with the lattice constant increasing. We also find that the ferromagnetisms of Ga_1–xCr_xSb have Curie temperatures above room temperature, estimated by mean-field method. The p-d electron hybridization occurs in Cr-3d orbital and Sb-5p orbital, and the electron state density distribution of Cr-3d is transferred, that is, the electron orbital hybridization makes the total electron state density of crystal material redistributed, which is the main reason why Ga_1–xCr_xSb (x = 0.25, 0.50, 0.75) present ferromagnetic half-metallic properties. Additionally, the Ga_1–xCr_xSb have good absorption ability in the infrared region, compatible with zinc-blende semiconductors such as GaSb, which makes Ga_1–xCr_xSb have promising potential applications in both spintronic devices and infrared optoelectronic devices.

Keywords:

Authors and contacts

1.
Key Laboratory for Microstructural Material Physics of Hebei Province, State Key Laboratory of Metastable Materials Science and Technology, School of Science, Yanshan University, Qinhuangdao 066004, China
2.
College of Physics and Electronic Engineering, Center for Computational Sciences, Sichuan Normal University, Chengdu 610068, China

Corresponding author: Liu Yong, yongliu@ysu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11874273) and the Natural Science Foundation of the Hebei Higher Education Institutions of China (Grant No. ZD2018015).

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References

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[2]	Ohno H, Munekata H, Penney T, von Molnar S, Chang L L 1992 Phys. Rev. Lett. 68 2664 Google Scholar
[3]	Groot R A D, Mueller F M, Engen P G V, Buschow K H J 1983 Phys. Rev. Lett. 50 2024 Google Scholar
[4]	Chen S, Ren Z 2013 Mater. Today 16 387 Google Scholar
[5]	Watts S M, Wirth S, Von Molnár S, Barry A, Coey J M D 2000 Phys. Rev. B 61 9621 Google Scholar
[6]	Xie W H, Liu B G 2004 J. Appl. Phys. 96 3559 Google Scholar
[7]	Doumi B, Mokaddem A, Temimi L, Beldjoudi N, Elkeurti M, Dahmane F, Sayede A, Tadjer A, Ishak-Boushaki M 2015 Eur. Phys. J. B 88 93
[8]	Pickett W E, Moodera J S 2001 Phys. Today 54 39 Google Scholar
[9]	Osborne Ian S 2001 Science 294 1483 Google Scholar
[10]	Zutic I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323
[11]	Katsnelson M I, Irkhin V Y, Chioncel L, Lichtenstein A I, de Groot R A 2008 Rev. Mod. Phys. 80 315 Google Scholar
[12]	Chadov S, Graf T, Chadova K, Casper F, Fecher G H, Dai X F, Felser C 2011 Phys. Rev. Lett. 107 047202 Google Scholar
[13]	Alijani V, Winterlik J, Fecher G H, Naghavi S S, Felser C 2011 Phys. Rev. B 83 184428 Google Scholar
[14]	Liu H, Zhang J M 2017 Phys. Status Solidi B 254 1700098 Google Scholar
[15]	Lin H F, Lau W M, Zhao J 2017 Sci. Rep. 7 45869 Google Scholar
[16]	Coey J M D 2005 Solid State Sci. 7 660 Google Scholar
[17]	Yang K, Wu R, Shen L, Feng Y P, Dai Y, Huang B 2010 Phys. Rev. B 81 125211 Google Scholar
[18]	Katayama-Yoshida H, Sato K 2003 Physica B 327 337 Google Scholar
[19]	Tu N T, Hai P N, Anh L D, Tanaka M 2016 Appl. Phys. Lett. 108 192401 Google Scholar
[20]	Anh L D, Kaneko D, Hai P N, Tanaka M 2015 Appl. Phys. Lett. 107 232405 Google Scholar
[21]	Ahmad I, Amin B 2013 Comput. Mater. Sci. 68 55 Google Scholar
[22]	黄保瑞, 张富春, 王海洋 2016 电子元件与材料 35 34 Huang B R, Zhang F C, Wang H Y 2016 Electronic Components and Materials 35 34
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[24]	Hass M, Henvis B W 1962 J. Phys. Chem. Solids 23 1099 Google Scholar
[25]	Ehrenreich H 1961 J. Appl. Phys. 32 2155 Google Scholar
[26]	Liu Y, Liu B G 2007 J. Phys. D-Appl. Phys. 40 6791 Google Scholar
[27]	Noor N A, Ali S, Shaukat A 2011 J. Phys. Chem. Solids 72 836 Google Scholar
[28]	Rahman G, Cho S, Hong S C 2007 Phys. Status Solidi B 244 4435
[29]	Shinya H, Fukushima T, Masago A, Sato K, Katayama-Yoshida H 2018 J. Appl. Phys. 124 103902 Google Scholar
[30]	Luo K W, Xu L, Wang L L, Li Q, Wang Z 2016 Comput. Mater. Sci. 117 300 Google Scholar
[31]	Abe E, Sato K, Matsukura F, Zhao J H, Ohno Y, Ohno H 2004 J. Supercond. Nov. Magn. 17 349 Google Scholar
[32]	Seña N, Dussan A, Mesa F, Castaño E, González-Hernández R 2016 J. Appl. Phys. 120 051704 Google Scholar
[33]	Milnes A G, Polyakov A Y 1993 Solid-State Electron. 36 803 Google Scholar
[34]	Zhang H I, Callaway J 1969 Phys. Rev. 181 1163 Google Scholar
[35]	Ahmed R, Hashemifar S J, Rashid H, Akbarzadeh H 2009 Commun. Theor. Phys. 52 527 Google Scholar
[36]	Schottky W F, Bever M B 1958 Acta Metall. 6 320 Google Scholar
[37]	Bennett B R, Soref R A 1987 IEEE J. Quantum Electron. 23 2159 Google Scholar
[38]	Aspnes D E, Studna A A 1983 Phys. Rev. B 27 985 Google Scholar
[39]	Wei Y, Gin A, Razeghi M, Brown G J 2002 Appl. Phys. Lett. 81 3675 Google Scholar
[40]	Rothmayr F, Pfenning A, Kistner C, Koeth J, Knebl G, Schade A, Höfling S 2018 Appl. Phys. Lett. 112 161107 Google Scholar
[41]	Lin X, Pan F 2018 Mater. Res. Express 6 015901 Google Scholar
[42]	Liu L H, Yu L H 2015 Intermetallics 57 139 Google Scholar
[43]	Varshney D, Joshi G, Varshney M, Shriya S 2010 Physica B 405 1663 Google Scholar
[44]	Amin B, Arif S, Ahmad I, Maqbool M, Ahmad R, Goumri-Said S, Prisbrey K 2011 J. Electron. Mater. 40 1428 Google Scholar
[45]	Dresselhaus G 1955 Phys. Rev. 100 580 Google Scholar
[46]	Cohen M L, Bergstresser T K 1966 Phys. Rev. 141 789 Google Scholar
[47]	Zerouali A, Mokaddem A, Doumi B, Dahmane F, Elkeurti M, Sayede A, Tadjer A 2016 J. Comput. Electron. 15 1255 Google Scholar
[48]	Liu X, Fan H Q 2018 Chin. Phys. B 27 86104 Google Scholar
[49]	Peng G W, Gan X P, Li Z, Zhou K C 2018 Chin. Phys. B 27 86302 Google Scholar
[50]	Kresse G, Hafner J 1993 Phys. Rev. B 48 13115 Google Scholar
[51]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[52]	Kresse G 1999 Phys. Rev. B 59 1758
[53]	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
[54]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[55]	Batista E R, Heyd J, Hennig R G, Uberuaga B P, Martin R L, Scuseria G E, Wilkins J W 2006 Phys. Rev. B 74 121102 Google Scholar
[56]	Heyd J, Scuseria G E, Ernzerhof M 2003 J. Chem. Phys. 118 8207 Google Scholar
[57]	Cang Y P, Lian S B, Yang H M, Chen D 2016 Chin. Phys. Lett. 33 66301 Google Scholar
[58]	Zhu Z Y, Wang S Q, Fu Y M 2016 Chin. Phys. Lett. 33 26302 Google Scholar
[59]	Wu J H, Liu C X 2016 Chin. Phys. Lett. 33 36202 Google Scholar
[60]	原野, 田博博, 段纯刚 2018 67 157511 Google Scholar Yuan Y, Tian B B, Duan C G 2018 Acta Phys. Sin. 67 157511 Google Scholar
[61]	Shirai M 2003 J. Appl. Phys. 93 6844 Google Scholar
[62]	Cheng Y C, Zhu Z Y, Mi W B, Guo Z B, Schwingenschlögl U 2013 Phys. Rev. B 87 100401
[63]	Fukushima T, Sato K, Katayama-Yoshida H, Dederichs P H 2004 Jpn. J. Appl. Phys. 43 L1416 Google Scholar
[64]	Şaşıoğlu E, Sandratskii L M, Bruno P 2004 Phys. Rev. B 70 024427 Google Scholar
[65]	Liu B G 2003 Phys. Rev. B 67 172411
[66]	Kim Y S, Marsman M, Kresse G, Tran F, Blaha P 2010 Phys. Rev. B 82 205212 Google Scholar
[67]	Guo S D, Liu B G 2011 EPL 93 47006 Google Scholar
[68]	Zheng F, Zhou G, Liu Z, Wu J, Duan W, Gu B L, Zhang S B 2008 Phys. Rev. B 78 205415 Google Scholar
[69]	De Paiva R, Nogueira R A, Alves J L A 2004 J. Appl. Phys. 96 6565 Google Scholar
[70]	Chen Z Y, Xu B, Gao G Y 2013 J. Magn. Magn. Mater. 347 14 Google Scholar
[71]	Arif S, Ahmad I, Amin B 2012 Int. J. Quantum Chem. 112 882 Google Scholar
[72]	Nabi A, Akhtar Z, Iqbal T, Ali A, Javid M A 2017 J. Semicond. 38 073001
[73]	王逸飞, 李晓薇 2018 67 116301 Google Scholar Wang Y F, Li X W 2018 Acta Phys. Sin. 67 116301 Google Scholar

Cited By

图 1 闪锌矿结构GaSb　(a)结构图; (b)能带图

Figure 1. (a) Zinc-blende structure and (b) band structure of GaSb.

DownLoad: Full-Size Img PowerPoint

图 2 晶体Ga_1–xCr_xSb (x = 0.25, 0.50, 0.75)结构优化的能量-体积关系图　(a) Ga_0.75Cr_0.25Sb; (b) Ga_0.5Cr_0.5Sb; (c) Ga_0.25Cr_0.75Sb; (d) Ga_0.25Cr_0.75Sb的铁磁态及两种反铁磁性磁序分布

Figure 2. The energy-volume curve of Ga_1–xCr_xSb (x = 0.25, 0.50, 0.75): (a) Ga_0.75Cr_0.25Sb; (b) Ga_0.5Cr_0.5Sb; (c) Ga_0.25Cr_0.75Sb; (d) the FM is ferromagnetic state and AFM stands for two types of antiferromagnetic state for Ga_0.25Cr_0.75Sb.

DownLoad: Full-Size Img PowerPoint

图 3 Ga_1–xCr_xSb单胞总磁矩及Cr-d轨道和Sb-p轨道贡献磁矩随晶格变化图　同一颜色的表示是同一浓度材料, 线上的方块、三角、圆形分别表示总磁矩、Cr原子d轨道贡献磁矩和Sb原子p轨道贡献磁矩

Figure 3. The total magnetic moment per formula and the contribution of magnetic moment from Cr-d and Sb-p orbits as a function of the relative change of lattice constant of Ga_1–xCr_xSb. The same color represents the same concentration. The square, triangle and circle on the line represent the total magnetic moment, the contribution magnetic moment of the Cr atom d-orbit, and the magnetic moment of the Sb atom p-orbit, respectively.

DownLoad: Full-Size Img PowerPoint

图 4 自旋能带结构图　(a) Ga_0.75Cr_0.25Sb; (b) Ga_0.5Cr_0.5Sb; (c) Ga_0.75Cr_0.25Sb; (d) CrSb

Figure 4. The spin-dependent band structure: (a) Ga_0.75Cr_0.25Sb; (b) Ga_0.5Cr_0.5Sb; (c) Ga_0.25Cr_0.75Sb; (d) CrSb.

DownLoad: Full-Size Img PowerPoint

图 5 晶体电子态密度图　(a) GaSb; (b) Ga_0.75Cr_0.25Sb

Figure 5. Total electron density states of (a) GaSb; (b) Ga_0.75Cr_0.25Sb.

DownLoad: Full-Size Img PowerPoint

图 6 Ga_1–xCr_xSb (x = 0, 0.25, 0.50, 0.75)的光学性质图谱对比　(a)折射系数; (b)反射率; (c)吸收系数

Figure 6. Comparison of optical properties of Ga_1–xCr_xSb (x = 0, 0.25, 0.50, 0.75): (a) The calculated optical refractive index; (b) the calculated optical reflectivity; (c) the calculated optical absorption coefficient.

DownLoad: Full-Size Img PowerPoint

表 1 Ga_1–xCr_xSb (x = 0, 0.25, 0.50, 0.75, 1.00)总磁矩M_tot/N_Cr, Cr原子d轨道磁矩M_Cr, Sb原子p轨道磁矩M_Sb, 居里温度, 其中SM表示半导体, HMF表示半金属铁磁体

Table 1. Ga_1–xCr_xSb (x = 0, 0.25, 0.50, 0.75, 1.00) magnetic moment M_tot/N_Cr, Cr atom d-orbit magnetic moment M_Cr, Sb atom p-orbit magnetic moment M_Sb, Curie temperature, SM and HMF represent semiconductor and half-metal ferromagnetic, respectively.

	M_tot/N_Cr/μ_B	M_Cr/μ_B	M_Sb/μ_B	居里温度/K	基态性质	材料性质
GaSb	0	—	—	—	NF	SM
Ga_0.75Cr_0.25Sb	3.00	3.266	–0.124	872	FM	HMF
Ga_0.5Cr_0.5Sb	3.00	3.113	–0.143	1104	FM	HMF
Ga_0.25Cr_0.75Sb	3.00	3.224	–0.176	1372	FM	HMF
CrSb	3.00	3.154	–0.152	1600^[61]	FM	HMF

DownLoad: CSV

表 2 Ga_1–xCr_xSb (x = 0, 0.25, 0.50, 0.75, 1.00)系列晶体各项性质, a₀表示平衡晶格常数, L_CS表示Cr—Sb键长, L_GS表示Ga—Sb键长, HM_HSE表示用HSE方法得到的半金属能隙(eV), HM_PBE表示用PBE方法得到的半金属能隙(eV), SM_HSE表示用HSE方法得到的半导体能隙(eV), SM_PBE表示用PBE方法得到的半导体能隙(eV)

Table 2. Crystals Properties of Ga_1–xCr_xSb (x = 0, 0.25, 0.50, 0.75, 1.00), the equilibrium lattice constant a₀, Cr—Sb bond length L_CS, Ga—Sb bond length L_GS, the half-metal gap (eV) calculated by HSE HM_HSE, denotes the half-metal gap (eV) calculated by PBE HM_PBE, the semiconductor gap (eV) calculated by HSE SM_HSE, and the semiconductor gap (eV) calculated by PBE SM_PBE.

	a₀/Å	L_CS/Å	L_GS/Å	HM_HSE	HM_PBE	SM_HSE	SM_PBE
GaSb	6.095	—	2.638	—	—	0.526	0.083
						0.720^[66]	0.110^[66]
Ga_0.75Cr_0.25Sb	6.210	2.652	2.702	0.137	0.121	1.275	0.637
Ga_0.5Cr_0.5Sb	6.181	2.653	2.713	0.403	—	1.281	0.653
Ga_0.25Cr_0.75Sb	6.159	2.654	2.725	0.613	—	1.305	0.664
CrSb	6.128	2.654	—	0.657	0.750	2.327	1.52
					0.774^[65]		1.646^[65]
					0.751^[67]		1.650^[67]

DownLoad: CSV

map

[1]	Prinz G A 1998 Science 282 1660 Google Scholar
[2]	Ohno H, Munekata H, Penney T, von Molnar S, Chang L L 1992 Phys. Rev. Lett. 68 2664 Google Scholar
[3]	Groot R A D, Mueller F M, Engen P G V, Buschow K H J 1983 Phys. Rev. Lett. 50 2024 Google Scholar
[4]	Chen S, Ren Z 2013 Mater. Today 16 387 Google Scholar
[5]	Watts S M, Wirth S, Von Molnár S, Barry A, Coey J M D 2000 Phys. Rev. B 61 9621 Google Scholar
[6]	Xie W H, Liu B G 2004 J. Appl. Phys. 96 3559 Google Scholar
[7]	Doumi B, Mokaddem A, Temimi L, Beldjoudi N, Elkeurti M, Dahmane F, Sayede A, Tadjer A, Ishak-Boushaki M 2015 Eur. Phys. J. B 88 93
[8]	Pickett W E, Moodera J S 2001 Phys. Today 54 39 Google Scholar
[9]	Osborne Ian S 2001 Science 294 1483 Google Scholar
[10]	Zutic I, Fabian J, Sarma S D 2004 Rev. Mod. Phys. 76 323
[11]	Katsnelson M I, Irkhin V Y, Chioncel L, Lichtenstein A I, de Groot R A 2008 Rev. Mod. Phys. 80 315 Google Scholar
[12]	Chadov S, Graf T, Chadova K, Casper F, Fecher G H, Dai X F, Felser C 2011 Phys. Rev. Lett. 107 047202 Google Scholar
[13]	Alijani V, Winterlik J, Fecher G H, Naghavi S S, Felser C 2011 Phys. Rev. B 83 184428 Google Scholar
[14]	Liu H, Zhang J M 2017 Phys. Status Solidi B 254 1700098 Google Scholar
[15]	Lin H F, Lau W M, Zhao J 2017 Sci. Rep. 7 45869 Google Scholar
[16]	Coey J M D 2005 Solid State Sci. 7 660 Google Scholar
[17]	Yang K, Wu R, Shen L, Feng Y P, Dai Y, Huang B 2010 Phys. Rev. B 81 125211 Google Scholar
[18]	Katayama-Yoshida H, Sato K 2003 Physica B 327 337 Google Scholar
[19]	Tu N T, Hai P N, Anh L D, Tanaka M 2016 Appl. Phys. Lett. 108 192401 Google Scholar
[20]	Anh L D, Kaneko D, Hai P N, Tanaka M 2015 Appl. Phys. Lett. 107 232405 Google Scholar
[21]	Ahmad I, Amin B 2013 Comput. Mater. Sci. 68 55 Google Scholar
[22]	黄保瑞, 张富春, 王海洋 2016 电子元件与材料 35 34 Huang B R, Zhang F C, Wang H Y 2016 Electronic Components and Materials 35 34
[23]	Shirai M 2001 Physica E 10 143 Google Scholar
[24]	Hass M, Henvis B W 1962 J. Phys. Chem. Solids 23 1099 Google Scholar
[25]	Ehrenreich H 1961 J. Appl. Phys. 32 2155 Google Scholar
[26]	Liu Y, Liu B G 2007 J. Phys. D-Appl. Phys. 40 6791 Google Scholar
[27]	Noor N A, Ali S, Shaukat A 2011 J. Phys. Chem. Solids 72 836 Google Scholar
[28]	Rahman G, Cho S, Hong S C 2007 Phys. Status Solidi B 244 4435
[29]	Shinya H, Fukushima T, Masago A, Sato K, Katayama-Yoshida H 2018 J. Appl. Phys. 124 103902 Google Scholar
[30]	Luo K W, Xu L, Wang L L, Li Q, Wang Z 2016 Comput. Mater. Sci. 117 300 Google Scholar
[31]	Abe E, Sato K, Matsukura F, Zhao J H, Ohno Y, Ohno H 2004 J. Supercond. Nov. Magn. 17 349 Google Scholar
[32]	Seña N, Dussan A, Mesa F, Castaño E, González-Hernández R 2016 J. Appl. Phys. 120 051704 Google Scholar
[33]	Milnes A G, Polyakov A Y 1993 Solid-State Electron. 36 803 Google Scholar
[34]	Zhang H I, Callaway J 1969 Phys. Rev. 181 1163 Google Scholar
[35]	Ahmed R, Hashemifar S J, Rashid H, Akbarzadeh H 2009 Commun. Theor. Phys. 52 527 Google Scholar
[36]	Schottky W F, Bever M B 1958 Acta Metall. 6 320 Google Scholar
[37]	Bennett B R, Soref R A 1987 IEEE J. Quantum Electron. 23 2159 Google Scholar
[38]	Aspnes D E, Studna A A 1983 Phys. Rev. B 27 985 Google Scholar
[39]	Wei Y, Gin A, Razeghi M, Brown G J 2002 Appl. Phys. Lett. 81 3675 Google Scholar
[40]	Rothmayr F, Pfenning A, Kistner C, Koeth J, Knebl G, Schade A, Höfling S 2018 Appl. Phys. Lett. 112 161107 Google Scholar
[41]	Lin X, Pan F 2018 Mater. Res. Express 6 015901 Google Scholar
[42]	Liu L H, Yu L H 2015 Intermetallics 57 139 Google Scholar
[43]	Varshney D, Joshi G, Varshney M, Shriya S 2010 Physica B 405 1663 Google Scholar
[44]	Amin B, Arif S, Ahmad I, Maqbool M, Ahmad R, Goumri-Said S, Prisbrey K 2011 J. Electron. Mater. 40 1428 Google Scholar
[45]	Dresselhaus G 1955 Phys. Rev. 100 580 Google Scholar
[46]	Cohen M L, Bergstresser T K 1966 Phys. Rev. 141 789 Google Scholar
[47]	Zerouali A, Mokaddem A, Doumi B, Dahmane F, Elkeurti M, Sayede A, Tadjer A 2016 J. Comput. Electron. 15 1255 Google Scholar
[48]	Liu X, Fan H Q 2018 Chin. Phys. B 27 86104 Google Scholar
[49]	Peng G W, Gan X P, Li Z, Zhou K C 2018 Chin. Phys. B 27 86302 Google Scholar
[50]	Kresse G, Hafner J 1993 Phys. Rev. B 48 13115 Google Scholar
[51]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[52]	Kresse G 1999 Phys. Rev. B 59 1758
[53]	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
[54]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[55]	Batista E R, Heyd J, Hennig R G, Uberuaga B P, Martin R L, Scuseria G E, Wilkins J W 2006 Phys. Rev. B 74 121102 Google Scholar
[56]	Heyd J, Scuseria G E, Ernzerhof M 2003 J. Chem. Phys. 118 8207 Google Scholar
[57]	Cang Y P, Lian S B, Yang H M, Chen D 2016 Chin. Phys. Lett. 33 66301 Google Scholar
[58]	Zhu Z Y, Wang S Q, Fu Y M 2016 Chin. Phys. Lett. 33 26302 Google Scholar
[59]	Wu J H, Liu C X 2016 Chin. Phys. Lett. 33 36202 Google Scholar
[60]	原野, 田博博, 段纯刚 2018 67 157511 Google Scholar Yuan Y, Tian B B, Duan C G 2018 Acta Phys. Sin. 67 157511 Google Scholar
[61]	Shirai M 2003 J. Appl. Phys. 93 6844 Google Scholar
[62]	Cheng Y C, Zhu Z Y, Mi W B, Guo Z B, Schwingenschlögl U 2013 Phys. Rev. B 87 100401
[63]	Fukushima T, Sato K, Katayama-Yoshida H, Dederichs P H 2004 Jpn. J. Appl. Phys. 43 L1416 Google Scholar
[64]	Şaşıoğlu E, Sandratskii L M, Bruno P 2004 Phys. Rev. B 70 024427 Google Scholar
[65]	Liu B G 2003 Phys. Rev. B 67 172411
[66]	Kim Y S, Marsman M, Kresse G, Tran F, Blaha P 2010 Phys. Rev. B 82 205212 Google Scholar
[67]	Guo S D, Liu B G 2011 EPL 93 47006 Google Scholar
[68]	Zheng F, Zhou G, Liu Z, Wu J, Duan W, Gu B L, Zhang S B 2008 Phys. Rev. B 78 205415 Google Scholar
[69]	De Paiva R, Nogueira R A, Alves J L A 2004 J. Appl. Phys. 96 6565 Google Scholar
[70]	Chen Z Y, Xu B, Gao G Y 2013 J. Magn. Magn. Mater. 347 14 Google Scholar
[71]	Arif S, Ahmad I, Amin B 2012 Int. J. Quantum Chem. 112 882 Google Scholar
[72]	Nabi A, Akhtar Z, Iqbal T, Ali A, Javid M A 2017 J. Semicond. 38 073001
[73]	王逸飞, 李晓薇 2018 67 116301 Google Scholar Wang Y F, Li X W 2018 Acta Phys. Sin. 67 116301 Google Scholar

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Vol. 68, Issue 17 - 2019-09-05

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First-principles calculations of magnetic and optical properties of Ga_1–xCr_xSb (x = 0.25, 0.50, 0.75)

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First-principles calculations of magnetic and optical properties of Ga1–xCrxSb (x = 0.25, 0.50, 0.75)

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Corresponding author: Liu Yong, yongliu@ysu.edu.cn

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First-principles calculations of magnetic and optical properties of Ga_1–xCr_xSb (x = 0.25, 0.50, 0.75)