-
随着高性能电子器件需求的日益增加, 自旋电子学材料在材料研究和电子元件中具有重要地位, 因为自旋电子学器件相比于传统半导体电子元件具有非易失性, 低功耗和高集成度的优点. 本文研究了Cr离子注入GaSb的电子性质、磁学和光学性质, 采用基于密度泛函理论框架下的缀加投影平面波方法, 利用广义梯度近似下电子交换关联泛函, 考虑了Heyd-Scuseria-Ernzerhof (HSE06)杂化泛函计算进行电子能带带隙修正, 首先对不同浓度Cr离子注入下的闪锌矿结构半导体GaSb形成的Ga1–xCrxSb (x = 0.25, 0.50, 0.75)进行结构优化, 计算了无磁、铁磁及反铁磁的基态能量, 对比发现它们的基态均为铁磁态. 对电子能带结构图分析发现, 它们自旋向上的电子能带穿过费米面, 而自旋向下的电子能带存在直接带隙, 呈现铁磁半金属性质. 同时在平衡晶格常数下具有整数倍玻尔磁矩, 并在一定晶格变化范围内保持磁矩不变. 同时发现它们在红外波段具有良好的吸收能力, 这使得Ga1–xCrxSb在自旋电子学器件和红外光电器件中拥有潜在的应用前景.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 Ga1–xCrxSb (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 Ga1–xCrxSb exhibit ferromagnetic half-metallic properties. The magnetic properties at different lattice constants under different concentrations are studied. Our analysis indicates that the Ga1–xCrxSb have integer Bohr magnetic moments of 3.0, 6.0, 9.0 μB 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 Ga1–xCrxSb 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 Ga1–xCrxSb 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 Ga1–xCrxSb (x = 0.25, 0.50, 0.75) present ferromagnetic half-metallic properties. Additionally, the Ga1–xCrxSb have good absorption ability in the infrared region, compatible with zinc-blende semiconductors such as GaSb, which makes Ga1–xCrxSb have promising potential applications in both spintronic devices and infrared optoelectronic devices.
-
Keywords:
- first-principles /
- Cr ion implantation /
- electronics structure /
- optical properties
[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 物理学报 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 物理学报 67 116301
Google Scholar
Wang Y F, Li X W 2018 Acta Phys. Sin. 67 116301
Google Scholar
-
图 1 闪锌矿结构GaSb (a)结构图; (b)能带图
Fig. 1. (a) Zinc-blende structure and (b) band structure of GaSb.
图 2 晶体Ga1–xCrxSb (x = 0.25, 0.50, 0.75)结构优化的能量-体积关系图 (a) Ga0.75Cr0.25Sb; (b) Ga0.5Cr0.5Sb; (c) Ga0.25Cr0.75Sb; (d) Ga0.25Cr0.75Sb的铁磁态及两种反铁磁性磁序分布
Fig. 2. The energy-volume curve of Ga1–xCrxSb (x = 0.25, 0.50, 0.75): (a) Ga0.75Cr0.25Sb; (b) Ga0.5Cr0.5Sb; (c) Ga0.25Cr0.75Sb; (d) the FM is ferromagnetic state and AFM stands for two types of antiferromagnetic state for Ga0.25Cr0.75Sb.
图 3 Ga1–xCrxSb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
Fig. 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 Ga1–xCrxSb. 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.
图 4 自旋能带结构图 (a) Ga0.75Cr0.25Sb; (b) Ga0.5Cr0.5Sb; (c) Ga0.75Cr0.25Sb; (d) CrSb
Fig. 4. The spin-dependent band structure: (a) Ga0.75Cr0.25Sb; (b) Ga0.5Cr0.5Sb; (c) Ga0.25Cr0.75Sb; (d) CrSb.
图 5 晶体电子态密度图 (a) GaSb; (b) Ga0.75Cr0.25Sb
Fig. 5. Total electron density states of (a) GaSb; (b) Ga0.75Cr0.25Sb.
图 6 Ga1–xCrxSb (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
Fig. 6. Comparison of optical properties of Ga1–xCrxSb (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.
表 1 Ga1–xCrxSb (x = 0, 0.25, 0.50, 0.75, 1.00)总磁矩Mtot/NCr, Cr原子d轨道磁矩MCr, Sb原子p轨道磁矩MSb, 居里温度, 其中SM表示半导体, HMF表示半金属铁磁体
Table 1. Ga1–xCrxSb (x = 0, 0.25, 0.50, 0.75, 1.00) magnetic moment Mtot/NCr, Cr atom d-orbit magnetic moment MCr, Sb atom p-orbit magnetic moment MSb, Curie temperature, SM and HMF represent semiconductor and half-metal ferromagnetic, respectively.
Mtot/NCr/μB MCr/μB MSb/μB 居里温度/K 基态性质 材料性质 GaSb 0 — — — NF SM Ga0.75Cr0.25Sb 3.00 3.266 –0.124 872 FM HMF Ga0.5Cr0.5Sb 3.00 3.113 –0.143 1104 FM HMF Ga0.25Cr0.75Sb 3.00 3.224 –0.176 1372 FM HMF CrSb 3.00 3.154 –0.152 1600[61] FM HMF 
下载: 导出CSV
表 2 Ga1–xCrxSb (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, LCS表示Cr—Sb键长, LGS表示Ga—Sb键长, HMHSE表示用HSE方法得到的半金属能隙(eV), HMPBE表示用PBE方法得到的半金属能隙(eV), SMHSE表示用HSE方法得到的半导体能隙(eV), SMPBE表示用PBE方法得到的半导体能隙(eV)
Table 2. Crystals Properties of Ga1–xCrxSb (x = 0, 0.25, 0.50, 0.75, 1.00), the equilibrium lattice constant a0, Cr—Sb bond length LCS, Ga—Sb bond length LGS, the half-metal gap (eV) calculated by HSE HMHSE, denotes the half-metal gap (eV) calculated by PBE HMPBE, the semiconductor gap (eV) calculated by HSE SMHSE, and the semiconductor gap (eV) calculated by PBE SMPBE.
a0/Å LCS/Å LGS/Å HMHSE HMPBE SMHSE SMPBE GaSb 6.095 — 2.638 — — 0.526 0.083 0.720[66] 0.110[66] Ga0.75Cr0.25Sb 6.210 2.652 2.702 0.137 0.121 1.275 0.637 Ga0.5Cr0.5Sb 6.181 2.653 2.713 0.403 — 1.281 0.653 Ga0.25Cr0.75Sb 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]
下载: 导出CSV
-
[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 物理学报 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 物理学报 67 116301
Google Scholar
Wang Y F, Li X W 2018 Acta Phys. Sin. 67 116301
Google Scholar
下载:
计量
- 文章访问数: 9542
- PDF下载量: 99
- 被引次数: 0
