铁电材料中的电畴: 形成、结构、动性及相关性能

吕笑梅; 黄凤珍; 朱劲松

doi:10.7498/aps.69.20200312

摘要

铁电材料的研究有近百年的历史, 而铁电畴的存在是铁电材料最基本的微观结构特征. 随着材料制备和表征技术的发展, 铁电畴的排列组合方式对材料性能的影响越来越凸显. 而近年来的研究显示, 铁电畴及畴壁甚至能够作为各种微纳电子器件的独立功能单元, 在信息存储、能量转换、机电驱动、量子计算等领域有着广泛的应用潜力. 本文从铁电畴结构的群论推导开始, 介绍了铁电畴的形成、结构到宏观力学谱和电学性能, 以及利用压电力显微镜研究铁电开关、铁电畴微观特征的相关历程及现状.

关键词:

畴结构 /
铁电材料 /
开关现象 /
内耗

Abstract

Ferroelectric materials with domains being the basic microstructures, have been investigated for about 100 years. With the development of the material fabrication method and the characterization technique, the important influence of domain configuration on the physical properties of ferroelectrics becomes more and more prominent. Recent researches even reveal that the domains and domain walls can act as individual functional units of micro-nano electronic devices, possessing wide potentials in the areas of information storage, energy transformation, electro-mechanical drive, quantum computation, etc. In this paper, starting from group theory analysis of domain structures, we introduce first the formation and the structures of ferroelectric domains, and then the macroscopic mechanical spectra as well as the electrical properties of the ferroelectric materials. Finally, the recent research progress of polarization switching and domain characterization by piezoresponse force microscopy are also reviewed.

Keywords:

作者及机构信息

南京大学物理学院, 固体微结构物理国家重点实验室, 人工微结构科学与技术协同创新中心, 南京　210093

通信作者: 朱劲松, jszhu@nju.edu.cn

Authors and contacts

National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, School of Physics, Nanjing University, Nanjing 210093, China

Corresponding author: Zhu Jin-Song, jszhu@nju.edu.cn

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参考文献

[1]	Lines M E, Glass A M 2001 Principles and Applications of Ferroelectrics and Related Materials (Oxford: Oxford University Press) pp87–126
[2]	Tagantsev A K, Cross L E, Fousek J 2010 Domains in Ferroic Crystals and Thin Films (Springer: New York Dordrecht Heidelberg London) pp11–100
[3]	Catalan G, Seidel J, Ramesh R, Scott J F 2012 Rev. Mod. Phys. 84 119 Google Scholar
[4]	丁勇 2000 博士学位论文 (南京: 南京大学) Ding Y 2000 Ph. D. Dissertation (Nanjing: Nanjing University) (in Chinese)
[5]	王仁卉, 郭可信 1990 晶体学中的对称群 (北京: 科学出版社) 第十章 Wang R H, Guo K X 1990 Crystallographic Symmetry Group (Beijing: Science Press) Chap.10 (in Chinese)
[6]	Tendeloo V G, Amelinckx S 1974 Acta. Crystallogr. A 30 431 Google Scholar
[7]	刘建设 1998 博士后研究工作报告 (南京: 南京大学) Liu J S 1998 Research Report for Post Doctor (Nanjing: Nanjing University) (in Chinese)
[8]	Guymont M 1978 Phys. Rev. B 18 5385 Google Scholar
[9]	Guymont M, Gratias D, Portier R, Fayard M 1976 Phys. Status Solidi A 38 629 Google Scholar
[10]	Chen X J, Liu J S, Zhu J S, Wang Y N 2000 J. Phys. Condens. Mater 12 3745 Google Scholar
[11]	Ding Y, Liu J S, Wang Y N 2000 Appl. Phys. Lett. 76 103 Google Scholar
[12]	Ding Y, Liu J S, Qin H X, Zhu J S, Wang Y N 2001 Appl. Phys. Lett. 78 4175 Google Scholar
[13]	Zheludev I S 1971 Solid State Phys. 26 429 Google Scholar
[14]	Sun W Y, Shen H M, Wang Y N, Lu B S 1985 J. Phys. (Paris) Collog 46 C10-609
[15]	Wang Y N, Sun W Y, Chen X H, Shen H M, Lu B S 1987 Phys. Status Solidi A 102 279 Google Scholar
[16]	Wang Y N, Huang Y N, Shen H M, Zhang Z F 1996 J. Phys. Ⅳ 6 C8-505 Google Scholar
[17]	Li W, Ma J, Chen K, Su D, Zhu J S 2005 Europhys. Lett. 72 131 Google Scholar
[18]	Su D, Zhu J S, Wang Y N, Xu Q Y, Liu J S 2003 J. Appl. Phys. 93 4784 Google Scholar
[19]	Su D, Ding Y, Zhu J S, Yao Y Y, Bao P, Liu J S, Wang Y N 2004 J. Phys. Condens. Matter 16 4549 Google Scholar
[20]	Ren S B, Lu C J, Liu J S, Shen H M, Wang Y N 1996 Phys. Rev. B 54 R14337 Google Scholar
[21]	Ren S B, Lu C J, Shen H M, Wang Y N 1997 Phys. Rev. B 55 3485 Google Scholar
[22]	Lu X M, Zhu J S, Zhang X S, Liu Z G, Wang Y N, Chen X B 2002 Appl. Phys. Lett. 80 2961 Google Scholar
[23]	Lu X M, Zhu J S, Zhang W Y, Ma G Q, Wang Y N 1996 Thin Solid Films 274 165 Google Scholar
[24]	Zhu J S, Lu X M, Jiang W, Tian W, Zhu M, Zhang M S, Chen X B, Liu X, Wang Y N 1997 J. Appl. Phys. 81 1392 Google Scholar
[25]	Zhu J S, Zhang X B, Zhu Y F, Desu S B 1998 J. Appl. Phys. 83 1610 Google Scholar
[26]	Lu X M, Zhu J S, Li X L, Zhang Z G, Zhang X S, Wu D, Yan F, Ding Y, Wang Y N 2000 Appl. Phys. Lett. 76 3103 Google Scholar
[27]	Wu X M, Lu X M, Chen A P, Yin Y, Ma J, Li W, Kan Y, Qian D, Zhu J S 2005 Appl. Phys. Lett. 86 092904 Google Scholar
[28]	Wu X M, Lu X M, Kan Y, Huang F Z, Ma J, Zhu J S 2006 Appl. Phys. Lett. 89 122910 Google Scholar
[29]	Lu X M, Wu X M, Li L B, Qian D, Li W, Ye Y D, Wu X S, Zhu J S 2005 Phys. Rev. B 72 212103 Google Scholar
[30]	Liu Y F, Kan Y, Lu X M, Cai W, Wu X B, Wu X M, Wang X F, Bo H F, Huang F Z, Zhu J S 2010 Appl. Phys. Lett. 96 072902 Google Scholar
[31]	Xu T T, Kan Y, Jin Y M, Sun H, Du Y C, Wu X M, Bo H F, Cai W, Huang F Z, Lu X M, Zhu J S 2013 J. Appl. Phys. 113 187204 Google Scholar
[32]	Kan Y, Liu Y F, Mieth O, Bo H F, Wu X M, Lu X M, Eng L M, Zhu J S 2009 Phys. Lett. A 374 360 Google Scholar
[33]	Shin J, Goyal A, Jesse S, Heatherly L 2011 Appl. Phys. Express 4 021501 Google Scholar
[34]	Yan F, Zhu T J, Lai M O, Lu L 2011 J. Appl. Phys. 110 084102 Google Scholar
[35]	Shvartsman V V, Kleemann W, Haumont R, Kreisel J 2007 Appl. Phys. Lett. 90 172115 Google Scholar
[36]	Wang Y, Nan C W 2008 J. Appl. Phys. 103 114104 Google Scholar
[37]	Jin Y M, Lu X M, Zhang J T, Kan Y, Bo H F, Huang F Z, Xu T T, Du Y C, Xiao S Y, Zhu J S 2015 Sci. Rep. 5 12237 Google Scholar
[38]	Rodriguez B J, Nemanich R J, Kingon A, Gruverman A, Kalinin S V, Terabe K, Liu X Y, Kitamura K 2005 Appl. Phys. Lett. 86 012906 Google Scholar
[39]	Kan Y, Lu X M, Bo H F, Huang F Z, Wu X B, Zhu J S 2007 Appl. Phys. Lett. 91 132902 Google Scholar
[40]	Kan Y, Bo H F, Lu X M, Xu T T, Jin Y M, Wu X B, Huang F Z, Zhu J S 2010 Appl. Phys. Lett. 97 202903 Google Scholar
[41]	Bo H F, Jin Y M, Xu T T, Du Y C, Kan Y, Lu X M, Zhu J S 2013 Appl. Phys. Lett. 103 252903 Google Scholar
[42]	Du Y C, Bo H F, Kan Y, Jin Y M, Lu X M, Xu T T, Xiao S Y, Yue C, Huang F Z, Zhu J S 2014 J. Appl. Phys. 116 066814 Google Scholar
[43]	Scott J F 2000 Ferroelectric Memories (Berlin: Springer-Verlag) p121
[44]	Gruverman A, Kholkin A 2006 Rep. Prog. Phys. 69 2443 Google Scholar
[45]	Hashimoto S, Orihara H, Ishibashi Y 1994 J. Phys. Soc. Jpn. 63 1601 Google Scholar
[46]	Gruverman A, Rodriguez B J, Dehoff C, Waldrep J D, Kingon A I, Nemanich R J, Cross J S 2005 Appl. Phys. Lett. 87 082902 Google Scholar
[47]	Ganpule C S, Nagarajan V, Ogale S B, Roytburd A L, Williams E D, Ramesh R 2000 Appl. Phys. Lett. 77 3275 Google Scholar
[48]	Merz W J 1954 Phys. Rev. 95 690 Google Scholar
[49]	Guo E J, Roth R, Herklotz A, Hesse D, Dorr K 2015 Adv. Mater. 27 1615 Google Scholar
[50]	Ganpule C S, Roytburd A L, Nagarajan V, Hill B K, Ogale S B, Williams E D, Ramesh R, Scott J F 2001 Phys. Rev. B 65 014101 Google Scholar
[51]	Molotskii M, Agronin A, Urenski P, Shvebelman M, Rosenman G, Rosenwaks Y 2003 Phys. Rev. Lett. 90 107601 Google Scholar
[52]	Kan Y, Lu X M, Wu X M, Zhu J S 2006 Appl. Phys. Lett. 89 262907 Google Scholar
[53]	Abplanalp M, Fousek J, Günter P 2001 Phys. Rev. Lett. 86 5799 Google Scholar
[54]	Morita T, Cho Y 2004 Appl. Phys. Lett. 84 257 Google Scholar
[55]	Dahan D, Molotskii M, Rosenman G, Rosenwaks Y 2006 Appl. Phys. Lett. 89 152902 Google Scholar
[56]	Bühlmann S, Colla E, Muralt P 2005 Phys. Rev. B 72 214120 Google Scholar
[57]	Kan Y, Bo H F, Lu X M, Cai W, Liu Y F, Zhu J S 2008 Appl. Phys. Lett. 92 172910 Google Scholar
[58]	Balke N, Choudhury S, Jesse S, Huijben M, Chu Y H, Baddorf A P, Chen L Q, Ramesh R, Kalinin S V 2009 Nat. Nanotechnol. 4 868 Google Scholar
[59]	Chae S C, Horibe Y, Jeong D Y, Lee N, Iida K, Tanimura M, Cheong S W 2013 Phys. Rev. Lett. 110 167601 Google Scholar
[60]	Choi T, Horibe Y, Yi H T, Choi Y J, Wu W, Cheong S W 2010 Nat. Mater. 9 253 Google Scholar
[61]	Han M G, Zhu Y M, Wu L J, Aoki T, Volkov V, Wang X Y, Chae S C, Oh Y S, Cheong S W 2013 Adv. Mater. 25 2415 Google Scholar
[62]	Balke N, Winchester B, Ren W, Chu Y H, Morozovska A N, Eliseev E A, Huijben M, Vasudevan R K, Maksymovych P, Britson J, Jesse S, Kornev I, Ramesh R, Bellaiche L, Chen L Q, Kalinin S V 2012 Nat. Phys. 8 81 Google Scholar
[63]	Cheng S B, Li J, Han M G, Deng S Q, Tan G T, Zhang X X, Zhu J, Zhu Y M 2017 Phys. Rev. Lett. 118 145501 Google Scholar
[64]	Kim K E, Jeong S, Chu K, Lee J H, Kim G Y, Xue F, Koo T Y, Chen L Q, Choi S Y, Ramesh R, Yang C H 2018 Nat. Commun. 9 403 Google Scholar
[65]	Li Z W, Wang Y J, Tian G, Li P L, Zhao L N, Zhang F Y, Yao J X, Fan H, Song X, Chen D Y, Fan Z, Qin M H, Zeng M, Zhang Z, Lü X B, Hu S J, Lei C H, Zhu Q F, Li J Y, Gao X S, Liu J M 2017 Sci. Adv. 3 e1700919 Google Scholar
[66]	Ma J, Zhang Q H, Peng R C, Wang J, Liu C, Wang M, Li N, Chen M F, Cheng X X, Gao P, Gu L, Chen L Q, Yu P, Zhang J X, Nan C W 2018 Nat. Nanotechnol. 13 947 Google Scholar
[67]	Yadav A K, Nguyen K X, Hong Z J, Pablo G, Pablo A P, Nelson C T, Das S, Prasad B, Kwon D, Cheema S, Khan A I, Hu C M, Íñiguez J, Junquera J, Chen L Q, Muller D A, Ramesh R, Salahuddin S 2019 Nature 565 468 Google Scholar
[68]	Li Y, Jin Y M, Lu X M, Yang J C, Chu Y M, Huang F Z, Zhu J S, Cheong S W 2017 NPJ Quantum Mater. 2 43 Google Scholar
[69]	Gaĭnutdinov R V, Belugina N V, Tolstikhina A L, Lysova O A 2007 Crystallogr. Rep. 52 332 Google Scholar
[70]	Stolichnov I, Iwanowska M, Colla E, Ziegler B, Gaponenko I, Paruch P, Huijben M, Rijnders G, Setter N 2014 Appl. Phys. Lett. 104 132902 Google Scholar
[71]	Chiu Y P, Chen Y T, Huang B C, Shih M C, Yang J C, He Q, Liang C W, Seidel J, Chen Y C, Ramash R, Chu Y H 2011 Adv. Mater. 23 1530 Google Scholar
[72]	Seidel J, Martin L W, He Q, Zhan Q, Chu Y H, Rother A, Hawkridge M E, Maksymovych P, Yu P, Gajek M, Balke N, Kalinin S V, Gemming S, Wang F, Catalan G, Scott J F, Spaldin N A, Orenstein J, Ramesh R 2009 Nat. Mater. 8 229 Google Scholar
[73]	Farokhipoor S, Noheda B 2011 Phys. Rev. Lett. 107 127601 Google Scholar
[74]	Maksymovych P, Seidel J, Chu Y H, Wu P P, Baddorf A P, Chen L Q, Kalinin S V, Ramesh R 2011 Nano Lett. 11 1906 Google Scholar
[75]	Vasudevan R K, Cao Y, Laanait N, Ievlev A, Li L L, Yang J C, Chu Y H, Chen L Q, Kalinin S V, Maksymovych P 2017 Nat. Commun. 8 1318 Google Scholar
[76]	Schröder M, Haußmann A, Thiessen A, Soergel E, Woike T, Eng L M 2012 Adv. Funct. Mater. 22 3936 Google Scholar
[77]	Godau C, Kämpfe T. Thiessen A, Eng L M, Haußmann A 2017 ACS Nano 11 4816 Google Scholar
[78]	Guyonnet J, Gaponenko I, Gariglio S, Paruch P 2011 Adv. Mater. 23 5377 Google Scholar
[79]	Kim D J, Connell J G, Seo S S, Gruverman A 2016 Nanotechnology 27 155705 Google Scholar
[80]	Mundy J A, Schaab J, Kumagai Y, Cano A, Stengel M, Krug I P, Gottlob D M, Doğanay H, Holtz M E, Held R, Yan Z, Bourret E, Schneider C M, Schlom D G, Muller D A, Ramesh R, Spaldin N A, Meier D 2017 Nat. Mater. 16 622 Google Scholar
[81]	Vasudevan R K, Morozovska A N, Eliseev E A, Britson J, Yang J C, Chu Y H, Maksymovych P, Chen L Q, Nagarajan V, Kalinin S V 2012 Nano Lett. 12 5524 Google Scholar
[82]	Meier D, Seidel J, Cano A, Delaney K, Kumagi Y, Mostovoy M, Spaldin N A, Ramesh R, Fiebig M 2012 Nat. Mater. 11 284 Google Scholar
[83]	Wu W D, Horibe Y, Lee N, Cheong S W, Guest J R 2012 Phys. Rev. Lett. 108 077203 Google Scholar
[84]	Sluka T, Tagantsev A K, Bednyakov P, Setter N 2013 Nat. Commun. 4 1808 Google Scholar
[85]	Jin Y M, Xiao S Y, Yang J C, Zhang J T, Lu X M, Chu Y H, Cheong S W, Li J Y, Kan Y, Yue C, Li Y, Ju C C, Huang F Z, Zhu J S 2018 Appl. Phys. Lett. 113 082904 Google Scholar
[86]	Xiao S Y, Kämpfe T, Jin Y M, Haußmann A, Lu X M, Eng L M 2018 Phys. Rev. Appl. 10 034002 Google Scholar
[87]	Xiao S Y, Jin Y M, Lu X M, Cheong S W, Li J Y, Li Y, Huang F Z, Zhu J S 2020 Natl. Sci. Rev. 7 278 Google Scholar
[88]	Yang S Y, Seidel J, Byrnes S J, Shafer P, Yang C H, Rossell M D, Yu P, Chu Y H, Scott J F, Ager J W, Martin L W, Ramesh R 2010 Nat. Nanotechnol. 5 143 Google Scholar
[89]	Ju C C, Yang J C, Luo C, Shafer P, Liu H J, Huang Y L, Kuo H H, Xue F, Luo C W, He Q, Yu P, Arenholz E, Chen L Q, Zhu J S, Lu X M, Chu Y H 2016 Adv. Mater. 28 876 Google Scholar
[90]	Yang C B, Xiao S Y, Yang J C, Lu X M, Chu Y H, Zhou M, Huang F Z, Zhu J S 2018 Appl. Surf. Sci. 457 797 Google Scholar

施引文献

图 1 SBT中五种不同的畴组态示意图^[10]　(a) 原始极化态; (b) 反相畴; (c) 180°畴; (d) 90°畴; (e) 180°反相畴; (f) 90°反相畴

Fig. 1. Schematic domain configurations in SBT^[10]: (a) Original; (b) the translational domain pair; (c) the 180° (rotational) domain pair; (d) the 90° domain pair; (e) the translational –180° domain pair; (f) the translational –90° domain pair.

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图 2 TEM下SBT中的电畴结构^[4,11]　(a), (b) 不同时间相同衍射条件的TEM暗场像; (c), (d) 标出了(a), (b)图中各畴区的极化方向; 红线、蓝线、黑线分别表示反相畴、180°畴界、90°畴界

Fig. 2. TEM observation of the domain structure in SBT^[4,11]: (a), (b) TEM dark field images at different time; (c) and (d) the depicted domain patterns of panels (a) and (b) respectively, with arrows showing the polarization directions. The red, blue and black lines are the antiphase boundary, 180^o domain wall and 90° domain wall in SBT, respectively.

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图 3 铁电陶瓷中与氧空位缺陷相关的内耗峰^[17]　(a) BiT和BNT陶瓷的内耗与温度关系; (b) BNT陶瓷在电场极化前后的内耗谱

Fig. 3. Internal friction related with oxygen vacancies in ferroelectric ceramics^[17]: (a) Internal friction of BiT and BNT ceramics with temperature; (b) internal friction of BNT ceramics before and after poling.

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图 4 BLT薄膜的应力效应^[28,31,32]　(a)不同晶粒尺寸薄膜中张应力(正值)和压应力(负值)对剩余极化的影响; (b)应力对疲劳特性的影响; (c)应力下电畴重新取向示意图; (d)张应力诱导电畴取向的PFM原位观察

Fig. 4. Stress effect in BLT films^[28,31,32]: (a) Normalized remnant polarization with stress for films with different grain sizes; (b) fatigue properties under stress; (c) schematic diagram of stress-induced-polarization-reorientation; (d) in-situ PFM observation of stress-induced-polarization-reorientation.

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图 5 多晶BFO薄膜中的极化开关^[37]　(a)面外z方向的压电位移面; (b)三种不同角度翻转的PFM相位图和翻转晶格示意图

Fig. 5. Polarization switching in polycrystalline BFO films^[37]: (a) Displacement along z direction; (b) examples for 71°, 109° and 180° domain switching.

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图 6 LN晶体中的电畴生长^[39,42]　(a)点状畴的半径衰减过程; (b)临界稳定半径与晶片厚度的关系; (c)两种方向条形畴的PFM相位; (d)宽度及不规则度随扫描电压的变化

Fig. 6. Domain growth in LN crystals^[39,42]: (a) Decay process of domains with various initial radii; (b) critical initial domain radius as a function of sample thickness; (c) PFM phase images of linear domains along different directions; (d) poling voltage dependence of domain width and irregularity of linear domains.

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图 7 LN晶体中的极化弛豫^[52], 80 V极性扫描后(a) 17 min以及(b) 68 min的PFM相位图; (c)最终稳定翻转畴面积比例随极化电压的变化; (d)回转畴成核时间和生长维度随极化电压的变化

Fig. 7. Polarization relaxation in LN single crystals^[52]: PFM phase images in (a) 17 min and (b) 68 min after poling with 80 V; (c) final fraction of switched domains with poling voltage; (d) nucleation time and dimension of domain growth with voltage.

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图 8 LN晶体中的电畴异常翻转^[57]　(a)不同定点脉冲电压条件下异常翻转畴区的压电力显微镜图像; (b)异常翻转畴区半径随脉冲电压和时间的变化; (c)翻转畴区的弛豫; (d)异常翻转畴区寿命随脉冲偏压强度和宽度的变化

Fig. 8. Abnormally switched domains in LN crystals^[57]: (a) Piezoresponse phase images after poling with various pulse voltages; (b) internal radius as a function of pulse magnitude; (c) decay process after poling; (d) lifetime of internal domains with poling conditions.

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图 9 铁电拓扑畴^[68]　(a)正、反涡旋示意图; (b) BFO薄膜中原71°畴壁附近定点极化形成的3对涡旋畴

Fig. 9. Ferroelectric topological domains^[68]: (a) Schematic of vortex and antivortex structures; (b) three pairs of vortex-antivortex formed near the BFO 71° domain wall.

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图 10 BFO薄膜中的畴壁电导^[85]　(a) c-AFM图像和畴结构示意图; (b)模拟模型示意图和针尖-样品势垒对电流的影响; (c)模拟电势和电流图像

Fig. 10. Conductive domain walls in BFO films^[85]: (a) c-AFM image and domain pattern; (b) schematic of domain configuration in the dipole-tunneling model and effect of tip-surface barrier on the simulated current; (c) simulated potential and current images.

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图 11 LN晶体中的畴壁电导^[86]　(a)实验二次谐波图像、c-AFM图像和电流截线图; (b)畴壁粗糙度示意图、粗糙畴壁电流模拟图和截线图

Fig. 11. Conductive domain walls in LN crystals^[86]: (a) Cross section obtained by 3D Cherenkov second-harmonic-generation microscopy, c-AFM image, and cross section of the c-AFM image; (b) sketches for domain walls with different roughness, simulated current distribution for the rough domain walls, and cross section of the simulated current.

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图 12 71° BFO条形畴衬底上LSMO薄膜的(a)电输运各向异性和(b)磁电阻各向异性; 109°条形畴衬底上(c)异质结示意图和(d) LSMO (30 nm)/BFO (30 nm)样品的电输运各向异性^[89]

Fig. 12. LSMO/BFO heterostructure^[89]: Anisotropic (a) transport and (b) magnetoresistance of LSMO/BFO heterostructure with 71° domain structure; (c) Schematics and (d) anisotropic transport of LSMO (30 nm)/BFO (30 nm) heterostructure with 109° domain pattern.

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表 1 群G = Pm$\bar 3$m对其子群H = P4mm的陪集展开^[4,13]

Table 1. Decompose G = Pm$\bar 3$m into left cosets of subgroup H = P4mm^[4,13].

序号	畴类型	陪集	陪集中的基本对称操作
1	V[001]	H = P4mm	1, 4⁺[001], 2[001], m[100], m[010], m[110], m[$1\bar 10$]
2	V[100]	3^–[$1{\bar 1}1$]H	3^–[$1{\bar 1}1$], 4⁺[010], 2[101], 3⁺[111], 3^–[$\bar 1\bar 11$], 3^–[$\bar 1\bar 11$], m[$\bar 1 01$], $\bar 4$^–[010]
3	V[010]	2[011]H	2[011], 3^–[111], 3⁺[$\bar 111$], 4^–[100], m[$0{\bar 1}1$], $\bar 4$⁺[100], 3⁺[$1{\bar 1}1$], 3^–[$\bar1{\bar 1}1$]
4	V[$\bar 100$]	2[${\bar 1}01$]H	2[${\bar 1}01$], 3^–[${\bar 1}11$], 3⁺[${\bar 1}{\bar 1}1$], 4^–[010], $\bar 4$⁺[010], m[101], 3^–[$1{\bar 1}1$], 3⁺[111]
5	V[$0{\bar 1}0$]	3⁺[$1{\bar 1}1$]H	3⁺[$1{\bar 1}1$], 2[$0{\bar 1}1$], 4⁺[100], 3^–[${\bar 1}{\bar 1}1$], 3^–[111], 3⁺[$\bar 1 11$], m[011]
6	V[$00\bar 1$]	2[110]H	2[110], 2[100], 2[010], 2[$\bar 1 10$], 4⁺[001], 4^–[001], $\bar 1$, m[001]

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[1]	Lines M E, Glass A M 2001 Principles and Applications of Ferroelectrics and Related Materials (Oxford: Oxford University Press) pp87–126
[2]	Tagantsev A K, Cross L E, Fousek J 2010 Domains in Ferroic Crystals and Thin Films (Springer: New York Dordrecht Heidelberg London) pp11–100
[3]	Catalan G, Seidel J, Ramesh R, Scott J F 2012 Rev. Mod. Phys. 84 119 Google Scholar
[4]	丁勇 2000 博士学位论文 (南京: 南京大学) Ding Y 2000 Ph. D. Dissertation (Nanjing: Nanjing University) (in Chinese)
[5]	王仁卉, 郭可信 1990 晶体学中的对称群 (北京: 科学出版社) 第十章 Wang R H, Guo K X 1990 Crystallographic Symmetry Group (Beijing: Science Press) Chap.10 (in Chinese)
[6]	Tendeloo V G, Amelinckx S 1974 Acta. Crystallogr. A 30 431 Google Scholar
[7]	刘建设 1998 博士后研究工作报告 (南京: 南京大学) Liu J S 1998 Research Report for Post Doctor (Nanjing: Nanjing University) (in Chinese)
[8]	Guymont M 1978 Phys. Rev. B 18 5385 Google Scholar
[9]	Guymont M, Gratias D, Portier R, Fayard M 1976 Phys. Status Solidi A 38 629 Google Scholar
[10]	Chen X J, Liu J S, Zhu J S, Wang Y N 2000 J. Phys. Condens. Mater 12 3745 Google Scholar
[11]	Ding Y, Liu J S, Wang Y N 2000 Appl. Phys. Lett. 76 103 Google Scholar
[12]	Ding Y, Liu J S, Qin H X, Zhu J S, Wang Y N 2001 Appl. Phys. Lett. 78 4175 Google Scholar
[13]	Zheludev I S 1971 Solid State Phys. 26 429 Google Scholar
[14]	Sun W Y, Shen H M, Wang Y N, Lu B S 1985 J. Phys. (Paris) Collog 46 C10-609
[15]	Wang Y N, Sun W Y, Chen X H, Shen H M, Lu B S 1987 Phys. Status Solidi A 102 279 Google Scholar
[16]	Wang Y N, Huang Y N, Shen H M, Zhang Z F 1996 J. Phys. Ⅳ 6 C8-505 Google Scholar
[17]	Li W, Ma J, Chen K, Su D, Zhu J S 2005 Europhys. Lett. 72 131 Google Scholar
[18]	Su D, Zhu J S, Wang Y N, Xu Q Y, Liu J S 2003 J. Appl. Phys. 93 4784 Google Scholar
[19]	Su D, Ding Y, Zhu J S, Yao Y Y, Bao P, Liu J S, Wang Y N 2004 J. Phys. Condens. Matter 16 4549 Google Scholar
[20]	Ren S B, Lu C J, Liu J S, Shen H M, Wang Y N 1996 Phys. Rev. B 54 R14337 Google Scholar
[21]	Ren S B, Lu C J, Shen H M, Wang Y N 1997 Phys. Rev. B 55 3485 Google Scholar
[22]	Lu X M, Zhu J S, Zhang X S, Liu Z G, Wang Y N, Chen X B 2002 Appl. Phys. Lett. 80 2961 Google Scholar
[23]	Lu X M, Zhu J S, Zhang W Y, Ma G Q, Wang Y N 1996 Thin Solid Films 274 165 Google Scholar
[24]	Zhu J S, Lu X M, Jiang W, Tian W, Zhu M, Zhang M S, Chen X B, Liu X, Wang Y N 1997 J. Appl. Phys. 81 1392 Google Scholar
[25]	Zhu J S, Zhang X B, Zhu Y F, Desu S B 1998 J. Appl. Phys. 83 1610 Google Scholar
[26]	Lu X M, Zhu J S, Li X L, Zhang Z G, Zhang X S, Wu D, Yan F, Ding Y, Wang Y N 2000 Appl. Phys. Lett. 76 3103 Google Scholar
[27]	Wu X M, Lu X M, Chen A P, Yin Y, Ma J, Li W, Kan Y, Qian D, Zhu J S 2005 Appl. Phys. Lett. 86 092904 Google Scholar
[28]	Wu X M, Lu X M, Kan Y, Huang F Z, Ma J, Zhu J S 2006 Appl. Phys. Lett. 89 122910 Google Scholar
[29]	Lu X M, Wu X M, Li L B, Qian D, Li W, Ye Y D, Wu X S, Zhu J S 2005 Phys. Rev. B 72 212103 Google Scholar
[30]	Liu Y F, Kan Y, Lu X M, Cai W, Wu X B, Wu X M, Wang X F, Bo H F, Huang F Z, Zhu J S 2010 Appl. Phys. Lett. 96 072902 Google Scholar
[31]	Xu T T, Kan Y, Jin Y M, Sun H, Du Y C, Wu X M, Bo H F, Cai W, Huang F Z, Lu X M, Zhu J S 2013 J. Appl. Phys. 113 187204 Google Scholar
[32]	Kan Y, Liu Y F, Mieth O, Bo H F, Wu X M, Lu X M, Eng L M, Zhu J S 2009 Phys. Lett. A 374 360 Google Scholar
[33]	Shin J, Goyal A, Jesse S, Heatherly L 2011 Appl. Phys. Express 4 021501 Google Scholar
[34]	Yan F, Zhu T J, Lai M O, Lu L 2011 J. Appl. Phys. 110 084102 Google Scholar
[35]	Shvartsman V V, Kleemann W, Haumont R, Kreisel J 2007 Appl. Phys. Lett. 90 172115 Google Scholar
[36]	Wang Y, Nan C W 2008 J. Appl. Phys. 103 114104 Google Scholar
[37]	Jin Y M, Lu X M, Zhang J T, Kan Y, Bo H F, Huang F Z, Xu T T, Du Y C, Xiao S Y, Zhu J S 2015 Sci. Rep. 5 12237 Google Scholar
[38]	Rodriguez B J, Nemanich R J, Kingon A, Gruverman A, Kalinin S V, Terabe K, Liu X Y, Kitamura K 2005 Appl. Phys. Lett. 86 012906 Google Scholar
[39]	Kan Y, Lu X M, Bo H F, Huang F Z, Wu X B, Zhu J S 2007 Appl. Phys. Lett. 91 132902 Google Scholar
[40]	Kan Y, Bo H F, Lu X M, Xu T T, Jin Y M, Wu X B, Huang F Z, Zhu J S 2010 Appl. Phys. Lett. 97 202903 Google Scholar
[41]	Bo H F, Jin Y M, Xu T T, Du Y C, Kan Y, Lu X M, Zhu J S 2013 Appl. Phys. Lett. 103 252903 Google Scholar
[42]	Du Y C, Bo H F, Kan Y, Jin Y M, Lu X M, Xu T T, Xiao S Y, Yue C, Huang F Z, Zhu J S 2014 J. Appl. Phys. 116 066814 Google Scholar
[43]	Scott J F 2000 Ferroelectric Memories (Berlin: Springer-Verlag) p121
[44]	Gruverman A, Kholkin A 2006 Rep. Prog. Phys. 69 2443 Google Scholar
[45]	Hashimoto S, Orihara H, Ishibashi Y 1994 J. Phys. Soc. Jpn. 63 1601 Google Scholar
[46]	Gruverman A, Rodriguez B J, Dehoff C, Waldrep J D, Kingon A I, Nemanich R J, Cross J S 2005 Appl. Phys. Lett. 87 082902 Google Scholar
[47]	Ganpule C S, Nagarajan V, Ogale S B, Roytburd A L, Williams E D, Ramesh R 2000 Appl. Phys. Lett. 77 3275 Google Scholar
[48]	Merz W J 1954 Phys. Rev. 95 690 Google Scholar
[49]	Guo E J, Roth R, Herklotz A, Hesse D, Dorr K 2015 Adv. Mater. 27 1615 Google Scholar
[50]	Ganpule C S, Roytburd A L, Nagarajan V, Hill B K, Ogale S B, Williams E D, Ramesh R, Scott J F 2001 Phys. Rev. B 65 014101 Google Scholar
[51]	Molotskii M, Agronin A, Urenski P, Shvebelman M, Rosenman G, Rosenwaks Y 2003 Phys. Rev. Lett. 90 107601 Google Scholar
[52]	Kan Y, Lu X M, Wu X M, Zhu J S 2006 Appl. Phys. Lett. 89 262907 Google Scholar
[53]	Abplanalp M, Fousek J, Günter P 2001 Phys. Rev. Lett. 86 5799 Google Scholar
[54]	Morita T, Cho Y 2004 Appl. Phys. Lett. 84 257 Google Scholar
[55]	Dahan D, Molotskii M, Rosenman G, Rosenwaks Y 2006 Appl. Phys. Lett. 89 152902 Google Scholar
[56]	Bühlmann S, Colla E, Muralt P 2005 Phys. Rev. B 72 214120 Google Scholar
[57]	Kan Y, Bo H F, Lu X M, Cai W, Liu Y F, Zhu J S 2008 Appl. Phys. Lett. 92 172910 Google Scholar
[58]	Balke N, Choudhury S, Jesse S, Huijben M, Chu Y H, Baddorf A P, Chen L Q, Ramesh R, Kalinin S V 2009 Nat. Nanotechnol. 4 868 Google Scholar
[59]	Chae S C, Horibe Y, Jeong D Y, Lee N, Iida K, Tanimura M, Cheong S W 2013 Phys. Rev. Lett. 110 167601 Google Scholar
[60]	Choi T, Horibe Y, Yi H T, Choi Y J, Wu W, Cheong S W 2010 Nat. Mater. 9 253 Google Scholar
[61]	Han M G, Zhu Y M, Wu L J, Aoki T, Volkov V, Wang X Y, Chae S C, Oh Y S, Cheong S W 2013 Adv. Mater. 25 2415 Google Scholar
[62]	Balke N, Winchester B, Ren W, Chu Y H, Morozovska A N, Eliseev E A, Huijben M, Vasudevan R K, Maksymovych P, Britson J, Jesse S, Kornev I, Ramesh R, Bellaiche L, Chen L Q, Kalinin S V 2012 Nat. Phys. 8 81 Google Scholar
[63]	Cheng S B, Li J, Han M G, Deng S Q, Tan G T, Zhang X X, Zhu J, Zhu Y M 2017 Phys. Rev. Lett. 118 145501 Google Scholar
[64]	Kim K E, Jeong S, Chu K, Lee J H, Kim G Y, Xue F, Koo T Y, Chen L Q, Choi S Y, Ramesh R, Yang C H 2018 Nat. Commun. 9 403 Google Scholar
[65]	Li Z W, Wang Y J, Tian G, Li P L, Zhao L N, Zhang F Y, Yao J X, Fan H, Song X, Chen D Y, Fan Z, Qin M H, Zeng M, Zhang Z, Lü X B, Hu S J, Lei C H, Zhu Q F, Li J Y, Gao X S, Liu J M 2017 Sci. Adv. 3 e1700919 Google Scholar
[66]	Ma J, Zhang Q H, Peng R C, Wang J, Liu C, Wang M, Li N, Chen M F, Cheng X X, Gao P, Gu L, Chen L Q, Yu P, Zhang J X, Nan C W 2018 Nat. Nanotechnol. 13 947 Google Scholar
[67]	Yadav A K, Nguyen K X, Hong Z J, Pablo G, Pablo A P, Nelson C T, Das S, Prasad B, Kwon D, Cheema S, Khan A I, Hu C M, Íñiguez J, Junquera J, Chen L Q, Muller D A, Ramesh R, Salahuddin S 2019 Nature 565 468 Google Scholar
[68]	Li Y, Jin Y M, Lu X M, Yang J C, Chu Y M, Huang F Z, Zhu J S, Cheong S W 2017 NPJ Quantum Mater. 2 43 Google Scholar
[69]	Gaĭnutdinov R V, Belugina N V, Tolstikhina A L, Lysova O A 2007 Crystallogr. Rep. 52 332 Google Scholar
[70]	Stolichnov I, Iwanowska M, Colla E, Ziegler B, Gaponenko I, Paruch P, Huijben M, Rijnders G, Setter N 2014 Appl. Phys. Lett. 104 132902 Google Scholar
[71]	Chiu Y P, Chen Y T, Huang B C, Shih M C, Yang J C, He Q, Liang C W, Seidel J, Chen Y C, Ramash R, Chu Y H 2011 Adv. Mater. 23 1530 Google Scholar
[72]	Seidel J, Martin L W, He Q, Zhan Q, Chu Y H, Rother A, Hawkridge M E, Maksymovych P, Yu P, Gajek M, Balke N, Kalinin S V, Gemming S, Wang F, Catalan G, Scott J F, Spaldin N A, Orenstein J, Ramesh R 2009 Nat. Mater. 8 229 Google Scholar
[73]	Farokhipoor S, Noheda B 2011 Phys. Rev. Lett. 107 127601 Google Scholar
[74]	Maksymovych P, Seidel J, Chu Y H, Wu P P, Baddorf A P, Chen L Q, Kalinin S V, Ramesh R 2011 Nano Lett. 11 1906 Google Scholar
[75]	Vasudevan R K, Cao Y, Laanait N, Ievlev A, Li L L, Yang J C, Chu Y H, Chen L Q, Kalinin S V, Maksymovych P 2017 Nat. Commun. 8 1318 Google Scholar
[76]	Schröder M, Haußmann A, Thiessen A, Soergel E, Woike T, Eng L M 2012 Adv. Funct. Mater. 22 3936 Google Scholar
[77]	Godau C, Kämpfe T. Thiessen A, Eng L M, Haußmann A 2017 ACS Nano 11 4816 Google Scholar
[78]	Guyonnet J, Gaponenko I, Gariglio S, Paruch P 2011 Adv. Mater. 23 5377 Google Scholar
[79]	Kim D J, Connell J G, Seo S S, Gruverman A 2016 Nanotechnology 27 155705 Google Scholar
[80]	Mundy J A, Schaab J, Kumagai Y, Cano A, Stengel M, Krug I P, Gottlob D M, Doğanay H, Holtz M E, Held R, Yan Z, Bourret E, Schneider C M, Schlom D G, Muller D A, Ramesh R, Spaldin N A, Meier D 2017 Nat. Mater. 16 622 Google Scholar
[81]	Vasudevan R K, Morozovska A N, Eliseev E A, Britson J, Yang J C, Chu Y H, Maksymovych P, Chen L Q, Nagarajan V, Kalinin S V 2012 Nano Lett. 12 5524 Google Scholar
[82]	Meier D, Seidel J, Cano A, Delaney K, Kumagi Y, Mostovoy M, Spaldin N A, Ramesh R, Fiebig M 2012 Nat. Mater. 11 284 Google Scholar
[83]	Wu W D, Horibe Y, Lee N, Cheong S W, Guest J R 2012 Phys. Rev. Lett. 108 077203 Google Scholar
[84]	Sluka T, Tagantsev A K, Bednyakov P, Setter N 2013 Nat. Commun. 4 1808 Google Scholar
[85]	Jin Y M, Xiao S Y, Yang J C, Zhang J T, Lu X M, Chu Y H, Cheong S W, Li J Y, Kan Y, Yue C, Li Y, Ju C C, Huang F Z, Zhu J S 2018 Appl. Phys. Lett. 113 082904 Google Scholar
[86]	Xiao S Y, Kämpfe T, Jin Y M, Haußmann A, Lu X M, Eng L M 2018 Phys. Rev. Appl. 10 034002 Google Scholar
[87]	Xiao S Y, Jin Y M, Lu X M, Cheong S W, Li J Y, Li Y, Huang F Z, Zhu J S 2020 Natl. Sci. Rev. 7 278 Google Scholar
[88]	Yang S Y, Seidel J, Byrnes S J, Shafer P, Yang C H, Rossell M D, Yu P, Chu Y H, Scott J F, Ager J W, Martin L W, Ramesh R 2010 Nat. Nanotechnol. 5 143 Google Scholar
[89]	Ju C C, Yang J C, Luo C, Shafer P, Liu H J, Huang Y L, Kuo H H, Xue F, Luo C W, He Q, Yu P, Arenholz E, Chen L Q, Zhu J S, Lu X M, Chu Y H 2016 Adv. Mater. 28 876 Google Scholar
[90]	Yang C B, Xiao S Y, Yang J C, Lu X M, Chu Y H, Zhou M, Huang F Z, Zhu J S 2018 Appl. Surf. Sci. 457 797 Google Scholar

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