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BaTiO3 (BTO) is a typical studying object both in ferroelectrics and in material science. By the GW method, optical property of BTO is investigated, and its volume effect under the case of iso-strain is also studied. It is found that the results of excited states are closer to the experimental results with the consideration of electron-hole interaction in the framework of GW method. Considering the volume effect, we obtain that the red shift of the peaks of optical absorption occurs under the expansion of volume, and the blue shift appears when the BTO is compressed. At the same time, the polarization and the hybridization between d orbital of Ti atom and p orbital of O atom are enhanced for the case of volume expansion, however, things will be opposite under the compression of volume. Furthermore, the volume effect in the iso-strain case is less dramatic than in the iso-stress case.
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Keywords:
- BaTiO3 /
- optical property /
- volume effect /
- GW method
[1] 钟维烈 1998 铁电体物理学(北京: 科学出版社)
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图 1 BTO块材自发极化随体积的变化曲线
Figure 1. Spontaneous polarization of bulk BTO versus its volume
图 2 体积变化对Ti原子d轨道分波态密度的影响
Figure 2. Projected DOS of
${\rm d}_{xy}$ and${\rm d}_{xz}$ of Ti atom for different volume
图 3 体积改变对BTO能带的影响
Figure 3. Energy bands of BTO for selected volumes.
图 4 不同体积BTO的介电常数虚部谱(
$\epsilon_2^{\bot}$ 为垂直于极化方向即xy平面内的介电常数虚部,$\epsilon_2^{^{_{/\!/}}}$ 为z方向的介电常数虚部)Figure 4. Spectrum of imagine part of dielectric constant for selected BTO volumes, where
$\epsilon_2^{\bot}$ corresponds the direction perpendicular to the polarization, and$\epsilon_2^{^{_{/\!/}}}$ stands for the direction parallel to the polarization
图 5 不同体积下BTO块材的光学吸收谱(
$\alpha^{\bot}$ 为垂直于极化方向即xy平面内的光学吸收系数,$\alpha^{^{_{/\!/}}}$ 为z方向的吸收系数)Figure 5. Spectrum of optical absorption of BTO for selected volumes, where
$\alpha^{\bot}$ corresponds the direction perpendicular to the polarization, and$\alpha^{^{_{/\!/}}}$ stands for the direction parallel to the polarization表 1 不同体积下计算得到的BTO块材的能隙(单位：eV)
Table 1. Energy gaps (in eV) for selected BTO volumes and different theoretical method
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[1] 钟维烈 1998 铁电体物理学(北京: 科学出版社)
Zhong W L 1998 Ferroelectric Physics (Beijing: Science Press) (in Chinese)
[2] Cohen R E 1992 Nature 358 136
Google Scholar
[3] Ma C, Jin K J, Ge C, Yang G Z 2018 Phys. Rev. B 97 115103
Google Scholar
[4] Zhuravlev M Y, Sabirianov R F, Jaswal S S, Tsymbal E Y 2005 Phys. Rev. Lett. 94 246802
Google Scholar
[5] Yu Z L, Ma Q R, Zhao Y Q, Liu B, Cai M Q 2018 J. Phys. Chem. C 122 9275
[6] Khenata R, Sahnoun M, Baltache H, Rerat M, Rashek A H, Illes N, Bouhafs B 2005 Solid State Commun. 136 120
Google Scholar
[7] Hosseini S M, Movlarooy T, Kompany A 2005 Euro. Phys. J B 46 463
Google Scholar
[8] Gupta G, Nautiyal T, Auluck S 2004 Phys. Rev. B 69 052101
[9] Saha S, Sinha T P, Mookerjee A 2000 Phys. Rev. B 62 8828
Google Scholar
[10] Liu Q J, Zhang N C, Liu F S, Wang H Y, Liu Z T 2013 Opt. Mater. 35 2629
Google Scholar
[11] Wemple S H 1970 Phys. Rev. B 2 2679
Google Scholar
[12] Piskunov S, Heifets E, Eglitis R I, Borstel G 2004 Comp. Mater. Sci. 29 165
Google Scholar
[13] Hybertsen M S, Louie S G 1986 Phy. Rev. B 34 5390
Google Scholar
[14] Rohlfing M, Louie S G 2000 Phy. Rev. B 62 4927
[15] Deslippe J, Samsonidze, Strubbe D A, Jain M, Cohen M L, Louie S G 2012 Comp. Mater. Sci. 183 1269
[16] Sanna S, Thierfelder C, Wippermann S, Sinha T P, Schmidt W G 2011 Phys. Rev. B 83 054112
Google Scholar
[17] Kornev I A, Bellaiche L, Bouvier P, Janolin P E, Dkhil B, Kreisel J 2005 Phys. Rev. Lett. 95 196804
Google Scholar
[18] Moriwake H, Koyama Y, Matsunaga K, Hirayama T, Tanaka I 2008 J Phys.: Condens. Mat. 20 345207
Google Scholar
[19] Wang X X, Wang C L 2003 Chin. J. Chem. 21 1130
[20] Nguyen M D, Dekkers M, Houwman E, Steenwelle R, Wan X, Roelofs A, Schmitz-Kempen T, Rijnders G 2011 Appl. Phys. Lett. 99 252904
Google Scholar
[21] Wen Z, Qiu X B, Li C, Zheng C Y, Ge X Y, Li A D, Wu D 2014 Appl. Phys. Lett. 104 042907
Google Scholar
[22] Li W, Weng G J 2001 J. Appl. Phys. 90 2484
Google Scholar
[23] Dieguez O, Tinte S, Antons A, Bungaro C, Neaton J B, Rabe K M, Vanderbilt D 2004 Phys. Rev. B 69 212101
Google Scholar
[24] Zhao R, Li W W, Lee J H, Choi E M, Liang Y, Zhang W, Tang R J, Wang H Y, Jia Q X, MacManus-Driscoll J L, Yang H 2014 Adv. Funct. Mater. 24 5240
Google Scholar
[25] Van Helvoort A T J, Da H L, Soleim B G, Holmestad R, Tybell T 2005 Appl. Phys. Lett. 86 092907
Google Scholar
[26] Chen A, Hu J M, Lu P, Yang T N, Zhang W R, Li L G, Ahmed T, Enriquez E, Weigand W, Su Q, Wang H Y, Zhu J Y, MacManus-Driscoll J L, Chen L Q, Yarotski D, Jia Q X 2016 Sci. Adv. 2 e1600245
Google Scholar
[27] Kohn W, Sham L J 1965 Phys. Rev. 140 A1133
Google Scholar
[28] Perdew J P, Yue W 1986 Phys. Rev. B 33 8820
[29] Gao S Y, Yang L 2017 Phys. Rev. B 96 155410
Google Scholar
[30] Ehrenreich H, Cohen M H 1959 Phys. Rev. 115 1786
[31] Bilc D I, Orlando R, Shaltaf R, Rignanese G M, Íñiguez J, Ghosez P 2008 Phys. Rev. B 77 165107
Google Scholar
[32] Wang F G, Grinberg I, Rappe A M 2014 Appl. Phys. Lett. 104 152903
Google Scholar
[33] Dong H F, Wu Z G, Wang S Y, Duan W H, Li J B 2013 Appl. Phys. Lett. 102 072905
Google Scholar
[34] Chernova E, Pacherova O, Chvostova D, Dejneka A, Kocourek T, Jelinek M, Tyunina M 2015 Appl. Phys. Lett. 106 192903
Google Scholar
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