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The flexoelectric effect describes the coupling of polarization to strain gradient, which has increasingly attracted interest in perovskite oxide materials. The perovskite oxide superlattice containing epitaxial relaxation or intrinsic surface tension or curvature, together with its high dielectric constant, is a highly desirable candidate for high flexoelectricity. In this work, the flexoelectric coefficients of 1SrTiO3/1BaTiO3 superlattice, which is composed of alternating single atomic layers of SrTiO3 and BaTiO3, are systematically investigated with first principle density functional theory calculations. Various supercell sizes are used to minimize the discrepancy between the gradient values of the fixed atoms and relaxed atoms. It is found that the strain gradients of the constrained A-site atoms and the relaxed B-site atoms are almost the same when the supercell sizes are 1×1×24 for longitudinal flexoelectric coefficient, 7×1×16 for transverse flexoelectric coefficient and 3×1×28 for shear flexoelectric coefficient. Calculation results demonstrate that the transverse flexoelectric coefficient and shear flexoelectric coefficient of 1SrTiO3/1BaTiO3 superlattice are about one order of magnitude larger than its longitudinal flexoelectric coefficient. Even though its longitudinal flexoelectric coefficient decreases slightly compared with its constituent compounds, both transverse coefficient and shear flexoelectric coefficient are about several times higher than the counterparts of its constituent compounds, respectively. Hence, the overall flexoelectric coefficient of 1SrTiO3/1BaTiO3 superlattice is enhanced several times in magnitude. There exist a large number of interfaces inside the perovskite oxide superlattice with alternating single atomic layers of SrTiO3 and BaTiO3, which potentially stimulate the redistribution of charge carriers, orbitals and spins of the atoms at the interface and promote the interfacial strain gradient. The stacking order of the superlattice atoms has a profound influence on the flexoelectric properties. These studies present an alternative approach to fabricating better flexoelectric materials for the applications of electromechanical equipment.
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Keywords:
- flexoelectricity /
- first principles /
- perovskite superlattice
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图 1 1×1×N纵向挠曲电超晶胞模型 (a) 无应变; (b) 施加纵向应变
Figure 1. 1×1×N supercell model for longitudinal flexoelectricity: (a) Strain-free supercell; (b) supercell with longitudinal strain.
图 2 1×1×N超晶胞中A位原子和Ti, O原子Z方向的位移 (a) N = 12; (b) N = 16; (c) N = 20; (d) N = 24
Figure 2. Atomic displacement along
$ z $ direction in 1×1×N supercell: (a) N =12; (b) N = 16; (c) N = 20; (d) N = 24.
图 3 M×1×N的横向挠曲电超晶胞模型 (a) 无应变; (b) 施加横向应变
Figure 3. M×1×N supercell model for transverse flexoelectricity: (a) Strain-free supercell; (b) supercell with transverse strain.
图 4 7 ×1×N超晶胞中A位原子和O原子的Z方向位移 (a) N = 8; (b) N = 12; (c) N = 16; (d) N = 16超晶胞中的挠曲电极化分布和纵向应变分布
Figure 4. Z displacement of A-atoms and O-atoms in 7 ×1×N supercell: (a) N = 8; (b) N = 12; (c) N =16; (d) the polarization and longitudinal strain along z direction with N =16.
图 5 M×1×N的剪切超晶胞模型 (a) 无应变模型; (b) 施加剪切应变
Figure 5. M×1×N supercell mode for shear flexoelectricity: (a) Strain-free supercell; (b) supercell with shear strain.
图 6 3×1×N超晶胞中A位原子和O原子的X方向位移情况 (a) N = 12; (b) N = 16; (c) N = 28; (d) N = 28超晶胞中不同高度的X方向极化
Figure 6. X displacement of A-atoms and O-atoms in 3 ×1×N supercell: (a) N = 12; (b) N = 16; (c) N = 28; (d) X-polarization at various height inside supercell with N = 28.
表 1 结构晶格常数
Table 1. Structural lattice constant.
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[1] Narvaez J, Catalan G 2014 Appl. Phys. Lett. 104 162903
Google Scholar
[2] Ma W, Cross L E 2002 Appl. Phys. Lett. 81 3440
Google Scholar
[3] Cross L E 2006 J. Mater. Sci. 41 53
Google Scholar
[4] Zhu W Y, Fu J Y, Li N, Cross L E 2006 Appl. Phys. Lett. 89 192904
Google Scholar
[5] Shu L L, Wei X Y, Pang T, Yao X, Wang C L 2011 J. Appl. Phys. 110 104106
Google Scholar
[6] Majdoub M S, Sharma P, Cagin T 2009 Phys. Rev. B 79 119904
Google Scholar
[7] Nguyen T D, Mao S, Yeh Y W, Purohit P K, McAlpine M C 2013 Adv. Mater 25 946
Google Scholar
[8] Lu H, Bark C W, Ojos D E D I, Alcala J, Eom C B, Catalan G, Gruverman A 2012 Science 336 59
Google Scholar
[9] Wen X, Li D F, Tan K, Deng Q, Shen S P 2019 Phys. Rev. Lett. 122 148001
Google Scholar
[10] Abdollahi A, Vasquez-Sancho F, Catalan G 2018 Phys. Rev. Lett. 121 205502
Google Scholar
[11] Biancoli A, Fancher C M, Jones J L, Damjanovic D 2014 Nat. Mater 14 2
Google Scholar
[12] Stengel M 2014 Phys. Rev. B 90 201112
Google Scholar
[13] Zhang X T, Pan Q, Tian D X, Zhou W F, Chen P, Zhang H F, Chu B J 2018 Phys. Rev. Lett. 121 057602
Google Scholar
[14] Zhang F, Lv P, Zhang Y, Huang S, Wong C M, Yau H M, Chen X, Wen Z, Jiang X, Zeng C 2019 Phys. Rev. Lett. 122 257601
Google Scholar
[15] Plymill A, Xu H 2018 J. Appl. Phys. 123 144101
Google Scholar
[16] Shu L, Liang R, Rao Z, Fei L, Ke S, Wang Y 2019 J. Adv. Ceram. 8 153
Google Scholar
[17] Lee H N, Christen H M, Chisholm M F, Rouleau C M, Lowndes D H 2005 Nature 433 395
Google Scholar
[18] Hong J, Catalan G, Scott J F, Artacho E 2010 J. Phys. Condens. Matter 22 112201
Google Scholar
[19] Taib M F M, Yaakob M K, Hassan O H, Yahya M Z A 2013 Ceram. Inter. 39 S297
Google Scholar
[20] Xu T, Wang J, Shimada T, Kitamura T 2013 J. Phys. Condens. Matter 25 415901
Google Scholar
[21] Wu Z G, Cohen R E 2006 Phys. Rev. B 73 235116
Google Scholar
[22] Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169
Google Scholar
[23] Troullier N, Martins J L 1991 Phys. Rev. B 43 1993
Google Scholar
[24] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
Google Scholar
[25] Guo R, Shen L, Wang H, Lim Z, Lu W, Yang P, Ariando, Gruverman A, Venkatesan T, Feng Y P, Chen J 2016 Adv. Mater. Inter. 3 1600737
Google Scholar
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