[1] G. F. Nataf, M. Guennou, J. M. Gregg, D. Meier, J. Hlinka, E. K. H. Salje, J. Kreisel. Domain-wall engineering and topological defects in ferroelectric and ferroelastic materials. Nat. Rev. Phys., 2, 634(2020).
[2] M. Höfling, X. Zhou, L. M. Riemer, E. Bruder, B. Liu, L. Zhou, P. B. Groszewicz, F. Zhuo, B. X. Xu, K. Durst. Control of polarization in bulk ferroelectrics by mechanical dislocation imprint. Science, 372, 961(2021).
[3] G. Dong, S. Li, M. Yao, Z. Zhou, Y. Q. Zhang, X. Han, Z. Luo, J. Yao, B. Peng, Z. Hu. Super-elastic ferroelectric single-crystal membrane with continuous electric dipole rotation. Science, 366, 475(2019).
[4] M. Wu. 100 years of ferroelectricity. Nat. Rev. Phys., 3, 726(2021).
[5] S. Das, Z. Hong, V. A. Stoica, M. A. P. Gonçalves, Y. T. Shao, E. Parsonnet, E. J. Marksz, S. Saremi, M. R. McCarter, A. Reynoso, C. J. Long, A. M. Hagerstrom, D. Meyers, V. Ravi, B. Prasad, H. Zhou, Z. Zhang, H. Wen, F. Gómez-Ortiz, P. García-Fernández, J. Bokor, J. Íñiguez, J. W. Freeland, N. D. Orloff, J. Junquera, L. Q. Chen, S. Salahuddin, D. A. Muller, L. W. Martin, R. Ramesh. Local negative permittivity and topological phase transition in polar skyrmions. Nat. Mater., 20, 194(2021).
[6] Y. J. Wang, Y. P. Feng, Y. L. Zhu, Y. L. Tang, L. X. Yang, M. J. Zou, W. R. Geng, M. J. Han, X. W. Guo, B. Wu, X. L. Ma. Polar meron lattice in strained oxide ferroelectrics. Nat. Mater., 19, 881(2020).
[7] F. H. Gong, Y. L. Tang, Y. L. Zhu, H. Zhang, Y. J. Wang, Y. T. Chen, Y. P. Feng, M. J. Zou, B. Wu, W. R. Geng. Atomic mapping of periodic dipole waves in ferroelectric oxide. Sci. Adv., 7, eabg5503(2021).
[8] II. Naumov, L. Bellaiche, H. Fu. Unusual phase transitions in ferroelectric nanodisks and nanorods. Nature, 432, 737(2004).
[9] I. Naumov, H. X. Fu. Vortex-to-polarization phase transformation path in ferroelectric Pb(ZrTi)O3 nanoparticles. Phys. Rev. Lett., 98, 77603(2007).
[10] A. K. Yadav, C. T. Nelson, S. L. Hsu, Z. Hong, J. D. Clarkson, C. M. Schleputz, A. R. Damodaran, P. Shafer, E. Arenholz, L. R. Dedon, D. Chen, A. Vishwanath, A. M. Minor, L. Q. Chen, J. F. Scott, L. W. Martin, R. Ramesh. Observation of polar vortices in oxide superlattices. Nature, 530, 198(2016).
[11] M. G. Stachiotti, M. Sepliarsky. Toroidal ferroelectricity in PbTiO3 nanoparticles. Phys. Rev. Lett., 106, 137601(2011).
[12] S. Velten, R. Streubel, A. Farhan, N. Kent, M. Y. Im, A. Scholl, S. Dhuey, C. Behncke, G. Meier, P. Fischer. Vortex circulation patterns in planar microdisk arrays. Appl. Phys. Lett., 110, 262406(2017).
[13] Z. Hong, S. Das, C. Nelson, A. Yadav, Y. Wu, J. Junquera, L. Q. Chen, L. W. Martin, R. Ramesh. Vortex Domain Walls in Ferroelectrics. Nano. Lett., 21, 3533(2021).
[14] S. Prosandeev, I. Ponomareva, I. Naumov, I. Kornev, L. Bellaiche. Original properties of dipole vortices in zero-dimensional ferroelectrics. J. Phys-Condens. Mat., 20, 193201(2008).
[15] R. G. McQuaid, L. J. McGilly, P. Sharma, A. Gruverman, J. M. Gregg. Mesoscale flux-closure domain formation in single-crystal BaTiO3. Nat. Commun., 2, 1(2011).
[16] A. Gruverman, D. Wu, H. J. Fan, I. Vrejoiu, M. Alexe, R. J. Harrison, J. F. Scott. Vortex ferroelectric domains. J. Phys-Condens. Mat., 20, 342201(2008).
[17] Z. Hong, A. R. Damodaran, F. Xue, S. L. Hsu, J. Britson, A. K. Yadav, C. T. Nelson, J. J. Wang, J. F. Scott, L. W. Martin, R. Ramesh, L. Q. Chen. Stability of Polar Vortex Lattice in Ferroelectric Superlattices. Nano. Lett., 17, 2246(2017).
[18] F. T. Huang, S. W. Cheong. Aperiodic topological order in the domain configurations of functional materials. Nat. Rev. Mater., 2, 17004(2017).
[19] L. L. Tao, T. R. Paudel, A. A. Kovalev, E. Y. Tsymbal. Reversible spin texture in ferroelectric HfO2. Phys. Rev. B, 95, 245141(2017).
[20] J. W. Hong, G. Catalan, D. N. Fang, E. Artacho, J. F. Scott. Topology of the polarization field in ferroelectric nanowires from first principles. Phys. Rev. B, 81, 172101(2010).
[21] R. K. Vasudevan, Y. C. Chen, H. H. Tai, N. Balke, P. Wu, S. Bhattacharya, L. Q. Chen, Y. H. Chu, I. N. Lin, S. V. Kalinin, V. Nagarajan. Exploring topological defects in epitaxial BiFeO3 thin films. ACS. Nano., 5, 879(2011).
[22] S. Li, Y. J. Wang, Y. L. Zhu, Y. L. Tang, Y. Liu, J. Y. Ma, M. J. Han, B. Wu, X. L. Ma. Evolution of flux-closure domain arrays in oxide multilayers with misfit strain. Acta. Mater., 171, 176(2019).
[23] D. Karpov, Z. Liu, T. D. S. Rolo, R. Harder, P. V. Balachandran, D. Xue, T. Lookman, E. Fohtung. Three-dimensional imaging of vortex structure in a ferroelectric nanoparticle driven by an electric field. Nat. Commun., 8, 280(2017).
[24] Y. L. Tang, Y. L. Zhu, X. L. Ma, A. Y. Borisevich, A. N. Morozovska, E. A. Eliseev, W. Y. Wang, Y. J. Wang, Y. B. Xu, Z. D. Zhang, S. J. Pennycook. Observation of a periodic array of flux-closure quadrants in strained ferroelectric PbTiO3 films. Science, 348, 547(2015).
[25] S. L. Hsu, M. R. McCarter, C. Dai, Z. Hong, L. Q. Chen, C. T. Nelson, L. W. Martin, R. Ramesh. Emergence of the Vortex State in Confined Ferroelectric Heterostructures. Adv. Mater., 31, 1901014(2019).
[26] S. Yuan, W. J. Chen, L. L. Ma, Y. Ji, W. M. Xiong, J. Y. Liu, Y. L. Liu, B. Wang, Y. Zheng. Defect-mediated vortex multiplication and annihilation in ferroelectrics and the feasibility of vortex switching by stress. Acta. Mater., 148, 330(2018).
[27] S. C. Chae, N. Lee, Y. Horibe, M. Tanimura, S. Mori, B. Gao, S. Carr, S. W. Cheong. Direct observation of the proliferation of ferroelectric loop domains and vortex-antivortex pairs. Phys. Rev. Lett., 108, 167603(2012).
[28] A. Hierro-Rodriguez, C. Quiros, A. Sorrentino, R. Valcarcel, I. Estebanez, L. M. Alvarez-Prado, J. I. Martin, J. M. Alameda, E. Pereiro, M. Velez, S. Ferrer. Deterministic propagation of vortex-antivortex pairs in magnetic trilayers. Appl. Phys. Lett., 110, 262402(2017).
[29] A. V. Kimmel, O. T. Gindele, D. M. Duffy, R. E. Cohen. Giant electrocaloric effect at the antiferroelectric-to-ferroelectric phase boundary in Pb(ZrxTi1−x)O3. Appl. Phys. Lett., 115, 023902(2019).
[30] W. L. Shu, J. Wang, T. Y. Zhang. Effect of grain boundary on the electromechanical response of ferroelectric polycrystals. J. Appl. Phys., 112, 064108(2012).
[31] X. B. Tian, X. H. Yang, P. Wang, D. Peng. Motion, collision and annihilation of polarization vortex pair in single crystalline BaTiO3 thin film. Appl. Phys. Lett., 103, 242905(2013).
[32] S. Mantri, J. Oddershede, D. Damjanovic, J. E. Daniels. Ferroelectric domain continuity over grain boundaries. Acta. Mater., 128, 400(2017).
[33] H. Rohm, T. Leonhard, A. D. Schulz, S. Wagner, M. J. Hoffmann, A. Colsmann. Ferroelectric properties of perovskite thin films and their implications for solar energy conversion. Adv. Mater., 31, 1806661(2019).
[34] Y. Su, H. Kang, Y. Wang, J. Li, G. J. Weng. Intrinsic versus extrinsic effects of the grain boundary on the properties of ferroelectric nanoceramics. Phys. Rev. B, 95, 054121(2017).
[35] J. Wang, W. Shu, T. Shimada, T. Kitamura, T. Y. Zhang. Role of grain orientation distribution in the ferroelectric and ferroelastic domain switching of ferroelectric polycrystals. Acta. Mater., 61, 6037(2013).
[36] L. Zhang, J. Chen, L. Fan, O. Dieguez, J. Cao, Z. Pan, Y. Wang, J. Wang, M. Kim, S. Deng, J. Wang, H. Wang, J. Deng, R. Yu, J. F. Scott, X. Xing. Giant polarization in super-tetragonal thin films through interphase strain. Science, 361, 494(2018).
[37] L. Xie, L. Li, C. A. Heikes, Y. Zhang, Z. Hong, P. Gao, C. T. Nelson, F. Xue, E. Kioupakis, L. Chen, D. G. Schlom, P. Wang, X. Pan. Giant ferroelectric polarization in ultrathin ferroelectrics via boundary-condition engineering. Adv. Mater., 29, 1701475(2017).
[38] Y. Zhang, J. Hong, B. Liu, D. Fang. Strain effect on ferroelectric behaviors of BaTiO3 nanowires: A molecular dynamics study. Nanotechnology, 21, 015701(2010).
[39] I. T. Todorov, W. Smith, K. Trachenko, M. T. Dove. DL_POLY_3: New dimensions in molecular dynamics simulations via massive parallelism. J. Mater. Chem., 16, 1911(2006).
[40] Y. L. Sang, B. Liu, D. N. Fang. The size and strain effects on the electric-field-induced domain evolution and hysteresis loop in ferroelectric BaTiO3 nanofilms. Comput. Mater. Sci., 44, 404(2008).
[41] Y. Ivry, D. P. Chu, J. F. Scott, C. Durkan. Domains beyond the grain boundary. Adv. Funct. Mater., 21, 1827(2011).
[42] Y. Ivry, D. P. Chu, J. F. Scott, C. Durkan. Flux closure vortexlike domain structures in ferroelectric thin films. Phys. Rev. Lett., 104, 207602(2010).
[43] D. M. Marincel, H. R. Zhang, S. Jesse, A. Belianinov, M. B. Okatan, S. V. Kalinin, W. M. Rainforth, I. M. Reaney, C. A. Randall, S. Trolier-McKinstry. Domain wall motion across various grain boundaries in ferroelectric thin films. J. Am. Ceram. Soc., 98, 1848(2015).