Domain-wall engineering and topological defects in ferroelectric and ferroelastic materials

A Publisher Correction to this article was published on 28 September 2020

This article has been updated

Abstract

Ferroelectric and ferroelastic domain walls are 2D topological defects with thicknesses approaching the unit cell level. When this spatial confinement is combined with observations of emergent functional properties, such as polarity in non-polar systems or electrical conductivity in otherwise insulating materials, it becomes clear that domain walls represent new and exciting objects in matter. In this Review, we discuss the exotic polarization profiles that can arise at domain walls with multiple order parameters and the different mechanisms that lead to domain-wall polarity in non-polar ferroelastic materials. The emergence of energetically degenerate variants of the domain walls themselves suggests the existence of interesting quasi-1D topological defects within such walls. We also provide an overview of the general notions that have been postulated as fundamental mechanisms responsible for domain-wall conduction in ferroelectrics. We then discuss the prospect of combining domain walls with transition regions observed at phase boundaries, homo- and heterointerfaces, and other quasi-2D objects, enabling emergent properties beyond those available in today’s topological systems.

Key points

  • In ferroelectrics, the emergence of an additional polarization component at the wall, distinct from the bulk domain polarization, leads to analogues of magnetic Bloch and Néel walls. The stabilization of these walls opens the possibility of quasi-1D topological defects separating wall regions of opposite polarities.

  • Polar domain walls in ferroelastics rely on two mechanisms: a polarity imposed by the natural symmetry of strain-compatible domain walls, which can be described by flexoelectric coupling, and the emergence of a potentially switchable polarity when their natural symmetry is broken.

  • Several mechanisms are responsible for domain-wall conduction in ferroelectrics: extrinsic intra-bandgap defect states, intrinsic depression of the conduction band and intrinsic shift of the band structure induced by local electric fields.

  • Transition regions occurring at phase boundaries, homo- and heterointerfaces, and other quasi-2D objects probably exist at a smaller length scale near domain walls and could lead to exceptional properties and coupling phenomena.

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Fig. 1: Mechanisms leading to polar domain walls.
Fig. 2: Polar domain walls in non-polar CaTiO3.
Fig. 3: Typical mechanisms of domain-wall conduction.
Fig. 4: Conduction at 180° domain walls.
Fig. 5: Exceptional properties arising at transition regions.

Change history

  • 28 September 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.

References

  1. 1.

    Aizu, K. Possible species of ferromagnetic, ferroelectric, and ferroelastic crystals. Phys. Rev. B 2, 754–772 (1970).

    ADS  Google Scholar 

  2. 2.

    Wadhawan, V. Introduction to Ferroic Materials (Gordon and Breach, 2000).

  3. 3.

    Van Aken, B. B., Rivera, J.-P., Schmid, H. & Fiebig, M. Observation of ferrotoroidic domains. Nature 449, 702–705 (2007).

    ADS  Google Scholar 

  4. 4.

    Schmid, H. Multi-ferroic magnetoelectrics. Ferroelectrics 162, 317–338 (1994).

    Google Scholar 

  5. 5.

    Fiebig, M., Lottermoser, T., Meier, D. & Trassin, M. The evolution of multiferroics. Nat. Rev. Mater. 1, 16046 (2016).

    ADS  Google Scholar 

  6. 6.

    Gonnissen, J. et al. Direct observation of ferroelectric domain walls in LiNbO3: wall-meanders, kinks, and local electric charges. Adv. Funct. Mater. 26, 7599–7604 (2016). On the nanoscale, domain walls in LiNbO3 are not straight but exhibit meanders and kinks, which result in local head-to-head or tail-to-tail sections where bound charges accumulate.

    Google Scholar 

  7. 7.

    Jia, C.-L. et al. Atomic-scale study of electric dipoles near charged and uncharged domain walls in ferroelectric films. Nat. Mater. 7, 57–61 (2008).

    ADS  Google Scholar 

  8. 8.

    Jia, C.-L., Urban, K. W., Alexe, M., Hesse, D. & Vrejoiu, I. Direct observation of continuous electric dipole rotation in flux-closure domains in ferroelectric Pb(Zr,Ti)O3. Science 331, 1420–1423 (2011).

    ADS  Google Scholar 

  9. 9.

    Salje, E. K. H. & Scott, J. F. Ferroelectric Bloch-line switching: a paradigm for memory devices? Appl. Phys. Lett. 105, 252904 (2014).

    ADS  Google Scholar 

  10. 10.

    Stepkova, V., Marton, P. & Hlinka, J. Ising lines: natural topological defects within ferroelectric Bloch walls. Phys. Rev. B 92, 094106 (2015).

    ADS  Google Scholar 

  11. 11.

    Seidel, J. (ed.) Topological Structures in Ferroic Materials (Springer, 2016).

  12. 12.

    Stepkova, V. & Hlinka, J. On the possible internal structure of the ferroelectric Ising lines in BaTiO3. Phase Transit. 90, 11–16 (2017).

    Google Scholar 

  13. 13.

    Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. Science 320, 190–194 (2008).

    ADS  Google Scholar 

  14. 14.

    Al Bahri, M. et al. Staggered magnetic nanowire devices for effective domain-wall pinning in racetrack memory. Phys. Rev. Appl. 11, 024023 (2019).

    ADS  Google Scholar 

  15. 15.

    Harrison, R. J., Redfern, S. A. T., Buckley, A. & Salje, E. K. H. Application of real-time, stroboscopic X-ray diffraction with dynamical mechanical analysis to characterize the motion of ferroelastic domain walls. J. Appl. Phys. 95, 1706–1717 (2004).

    ADS  Google Scholar 

  16. 16.

    Schilling, A. et al. Scaling of domain periodicity with thickness measured in BaTiO3 single crystal lamellae and comparison with other ferroics. Phys. Rev. B 74, 024115 (2006).

    ADS  Google Scholar 

  17. 17.

    Yang, S. Y. et al. Above-bandgap voltages from ferroelectric photovoltaic devices. Nat. Nanotechnol. 5, 143–147 (2010).

    ADS  Google Scholar 

  18. 18.

    Vul, B. M., Guro, G. M. & Ivanchik, I. I. Encountering domains in ferroelectrics. Ferroelectrics 6, 29–31 (1973).

    Google Scholar 

  19. 19.

    Catalan, G., Seidel, J., Ramesh, R. & Scott, J. F. Domain wall nanoelectronics. Rev. Mod. Phys. 84, 119–156 (2012).

    ADS  Google Scholar 

  20. 20.

    Sharma, P., Schoenherr, P. & Seidel, J. Functional ferroic domain walls for nanoelectronics. Materials 12, 2927 (2019).

    ADS  Google Scholar 

  21. 21.

    Seidel, J. Domain walls as nanoscale functional elements. J. Phys. Chem. Lett. 3, 2905–2909 (2012).

    Google Scholar 

  22. 22.

    Salje, E. K. H. Multiferroic domain boundaries as active memory devices: trajectories towards domain boundary engineering. ChemPhysChem 11, 940–950 (2010).

    Google Scholar 

  23. 23.

    Whyte, J. R. & Gregg, J. M. A diode for ferroelectric domain-wall motion. Nat. Commun. 6, 7361 (2015).

    ADS  Google Scholar 

  24. 24.

    Sharma, P. et al. Nonvolatile ferroelectric domain wall memory. Sci. Adv. 3, e1700512 (2017).

    ADS  Google Scholar 

  25. 25.

    Sharma, P. et al. Conformational domain wall switch. Adv. Funct. Mater. 29, 1807523 (2019).

    Google Scholar 

  26. 26.

    Jiang, J. et al. Temporary formation of highly conducting domain walls for non-destructive read-out of ferroelectric domain-wall resistance switching memories. Nat. Mater. 17, 49–55 (2018).

    ADS  Google Scholar 

  27. 27.

    McConville, J. P. V. et al. Ferroelectric domain wall memristor. Adv. Funct. Mater. 30, 2000109 (2020).

    Google Scholar 

  28. 28.

    Chai, X. et al. Nonvolatile ferroelectric field-effect transistors. Nat. Commun. 11, 2811 (2020).

    ADS  Google Scholar 

  29. 29.

    Bai, Z. L. et al. Hierarchical domain structure and extremely large wall current in epitaxial BiFeO3 thin films. Adv. Funct. Mater. 28, 1801725 (2018).

    Google Scholar 

  30. 30.

    Sanchez-Santolino, G. et al. Resonant electron tunnelling assisted by charged domain walls in multiferroic tunnel junctions. Nat. Nanotechnol. 12, 655–662 (2017).

    ADS  Google Scholar 

  31. 31.

    Mundy, J. A. et al. Functional electronic inversion layers at ferroelectric domain walls. Nat. Mater. 16, 622–627 (2017).

    ADS  Google Scholar 

  32. 32.

    Schaab, J. et al. Electrical half-wave rectification at ferroelectric domain walls. Nat. Nanotechnol. 13, 1028–1034 (2018).

    ADS  Google Scholar 

  33. 33.

    Nataf, G. F. et al. Control of surface potential at polar domain walls in a nonpolar oxide. Phys. Rev. Mater. 1, 074410 (2017).

    Google Scholar 

  34. 34.

    Frenkel, Y. et al. Imaging and tuning polarity at SrTiO3 domain walls. Nat. Mater. 16, 1203–1208 (2017).

    ADS  Google Scholar 

  35. 35.

    Bednyakov, P. S., Sturman, B. I., Sluka, T., Tagantsev, A. K. & Yudin, P. V. Physics and applications of charged domain walls. NPJ Comput. Mater. 4, 65 (2018).

    ADS  Google Scholar 

  36. 36.

    Seidel, J., Vasudevan, R. K. & Valanoor, N. Topological structures in multiferroics — domain walls, skyrmions and vortices. Adv. Electron. Mater. 2, 1500292 (2016).

    Google Scholar 

  37. 37.

    Seidel, J. Nanoelectronics based on topological structures. Nat. Mater. 18, 188–190 (2019).

    Google Scholar 

  38. 38.

    Meier, D. Functional domain walls in multiferroics. J. Phys. Condens. Matter 27, 463003 (2015).

    ADS  Google Scholar 

  39. 39.

    Tagantsev, A. K., Cross, L. E. & Fousek, J. Domains in Ferroic Crystals and Thin Films (Springer, 2010).

  40. 40.

    Zhirnov, V. A. A contribution to the theory of domain walls in ferroelectrics. Sov. Phys. JETP 35, 822–825 (1959).

    MathSciNet  Google Scholar 

  41. 41.

    Lawless, W. N. & Fousek, J. Small-signal permittivity of the stationary (100)-180° domain wall in BaTiO3. J. Phys. Soc. Jpn 28, 419–424 (1970).

    ADS  Google Scholar 

  42. 42.

    Lajzerowicz, J. & Niez, J. J. Phase transition in a domain wall. J. Phys. Lett. 40, 165–169 (1979).

    Google Scholar 

  43. 43.

    Houchmandzadeh, B., Lajzerowicz, J. & Salje, E. Order parameter coupling and chirality of domain walls. J. Phys. Condens. Matter 3, 5163–5169 (1991).

    ADS  Google Scholar 

  44. 44.

    Bul’bich, A. A. & Gufan, Y. M. Inevitable symmetry lowering in a domain wall near a reordering phase transition. Zh. Eksp. Teor. Fiz. 94, 121 (1988).

    Google Scholar 

  45. 45.

    Marton, P., Rychetsky, I. & Hlinka, J. Domain walls of ferroelectric BaTiO3 within the Ginzburg–Landau–Devonshire phenomenological model. Phys. Rev. B 81, 144125 (2010).

    ADS  Google Scholar 

  46. 46.

    Hlinka, J. et al. Phase–field modelling of 180° “Bloch walls” in rhombohedral BaTiO3. Phase Transit. 84, 738–746 (2011).

    Google Scholar 

  47. 47.

    Stepkova, V., Marton, P. & Hlinka, J. Stress-induced phase transition in ferroelectric domain walls of BaTiO3. J. Phys. Condens. Matter 24, 212201 (2012).

    ADS  Google Scholar 

  48. 48.

    Marton, P., Stepkova, V. & Hlinka, J. Divergence of dielectric permittivity near phase transition within ferroelectric domain boundaries. Phase Transit. 86, 103–108 (2013).

    Google Scholar 

  49. 49.

    Wojdeł, J. C. & Íñiguez, J. Ferroelectric transitions at ferroelectric domain walls found from first principles. Phys. Rev. Lett. 112, 247603 (2014).

    ADS  Google Scholar 

  50. 50.

    Gu, Y. et al. Flexoelectricity and ferroelectric domain wall structures: phase-field modeling and DFT calculations. Phys. Rev. B 89, 174111 (2014).

    ADS  Google Scholar 

  51. 51.

    Morozovska, A. N., Kalinin, S. V. & Eliseev, E. A. in Flexoelectricity in Solids 311–336 (World Scientific, 2016).

  52. 52.

    Lee, D. et al. Mixed Bloch–Néel–Ising character of 180° ferroelectric domain walls. Phys. Rev. B 80, 060102 (2009).

    ADS  Google Scholar 

  53. 53.

    Taherinejad, M., Vanderbilt, D., Marton, P., Stepkova, V. & Hlinka, J. Bloch-type domain walls in rhombohedral BaTiO3. Phys. Rev. B 86, 155138 (2012).

    ADS  Google Scholar 

  54. 54.

    Yudin, P. V., Tagantsev, A. K. & Setter, N. Bistability of ferroelectric domain walls: morphotropic boundary and strain effects. Phys. Rev. B 88, 024102 (2013).

    ADS  Google Scholar 

  55. 55.

    Cherifi-Hertel, S. et al. Non-Ising and chiral ferroelectric domain walls revealed by nonlinear optical microscopy. Nat. Commun. 8, 15768 (2017). Observation of non-Ising components of the domain wall polarization in lithium tantalate by optical second-harmonic generation.

    ADS  Google Scholar 

  56. 56.

    Wei, X.-K. et al. Néel-like domain walls in ferroelectric Pb(Zr,Ti)O3 single crystals. Nat. Commun. 7, 12385 (2016).

    ADS  Google Scholar 

  57. 57.

    De Luca, G. et al. Domain wall architecture in tetragonal ferroelectric thin films. Adv. Mater. 29, 1605145 (2017).

    Google Scholar 

  58. 58.

    Janovec, V. A symmetry approach to domain structures. Ferroelectrics 12, 43–53 (1976).

    Google Scholar 

  59. 59.

    Janovec, V. Symmetry and structure of domain walls. Ferroelectrics 35, 105–110 (1981).

    Google Scholar 

  60. 60.

    Janovec, V. & Přívratská, J. in International Tables for Crystallography 449–505 (International Union of Crystallography, 2006).

  61. 61.

    Janovec, V. & Kopský, V. Layer groups, scanning tables and the structure of domain walls. Ferroelectrics 191, 23–28 (1997).

    Google Scholar 

  62. 62.

    Janovec, V., Schranz, W., Warhanek, H. & Zikmund, Z. Symmetry analysis of domain structure in KSCN crystals. Ferroelectrics 98, 171–189 (1989).

    Google Scholar 

  63. 63.

    Kopský, V. The scanning for layer groups and positional dependence of domain wall energy and structure. Ferroelectrics 376, 168–175 (2008).

    Google Scholar 

  64. 64.

    Janovec, V., Grocký, M., Kopský, V. & Kluiber, Z. On atomic displacements in 90° ferroelectric domain walls of tetragonal BaTiO3 crystals. Ferroelectrics 303, 65–68 (2004).

    Google Scholar 

  65. 65.

    Janovec, V. & Litvin, D. B. Symmetry-allowed atomic displacements in a ferroelastic domain wall of rhombohedral BaTiO3. Phase Transit. 84, 760–768 (2011).

    Google Scholar 

  66. 66.

    Přívratská, J. & Janovec, V. Examination of point group symmetries of non-ferroelastic domain walls. Ferroelectrics 191, 17–21 (1997).

    Google Scholar 

  67. 67.

    Přívratská, J., Janovec, V. & Machonský, L. Tensor properties discriminating domain walls from non-ferroelastic domains. Ferroelectrics 240, 1349–1358 (2000).

    Google Scholar 

  68. 68.

    Tolédano, P., Guennou, M. & Kreisel, J. Order-parameter symmetries of domain walls in ferroelectrics and ferroelastics. Phys. Rev. B 89, 134104 (2014).

    ADS  Google Scholar 

  69. 69.

    Schranz, W., Rychetsky, I. & Hlinka, J. Polarity of domain boundaries in nonpolar materials derived from order parameter and layer group symmetry. Phys. Rev. B 100, 184105 (2019).

    ADS  Google Scholar 

  70. 70.

    Janovec, V., Richterová, L. & Přívratská, J. Polar properties of compatible ferroelastic domain walls. Ferroelectrics 222, 73–76 (1999). This approach yields the remarkable result that all strain-compatible ferroelastic domain walls are non-centrosymmetric and predict possible directions for the polar axis.

    Google Scholar 

  71. 71.

    Yokota, H. et al. Direct evidence of polar nature of ferroelastic twin boundaries in CaTiO3 obtained by second harmonic generation microscope. Phys. Rev. B 89, 144109 (2014).

    ADS  Google Scholar 

  72. 72.

    Yokota, H., Matsumoto, S., Salje, E. K. H. & Uesu, Y. Symmetry and three-dimensional anisotropy of polar domain boundaries observed in ferroelastic LaAlO3 in the complete absence of ferroelectric instability. Phys. Rev. B 98, 104105 (2018).

    ADS  Google Scholar 

  73. 73.

    Yokota, H., Matsumoto, S., Salje, E. K. H. & Uesu, Y. Polar nature of domain boundaries in purely ferroelastic Pb3(PO4)2 investigated by second harmonic generation microscopy. Phys. Rev. B 100, 024101 (2019).

    ADS  Google Scholar 

  74. 74.

    Yokota, H., Matsumoto, S., Hasegawa, N., Salje, E. & Uesu, Y. Enhancement of polar nature of domain boundaries in ferroelastic Pb3(PO4)2 by doping divalent-metal ions. J. Phys. Condens. Matter 32, 345401 (2020).

    Google Scholar 

  75. 75.

    Yokota, H., Hasegawa, N., Glazer, M., Salje, E. K. H. & Uesu, Y. Direct evidence of polar ferroelastic domain boundaries in semiconductor BiVO4. Appl. Phys. Lett. 116, 232901 (2020).

    ADS  Google Scholar 

  76. 76.

    Salje, E. K. H., Li, S., Stengel, M., Gumbsch, P. & Ding, X. Flexoelectricity and the polarity of complex ferroelastic twin patterns. Phys. Rev. B 94, 024114 (2016).

    ADS  Google Scholar 

  77. 77.

    Goncalves-Ferreira, L., Redfern, S. A. T., Artacho, E. & Salje, E. K. H. Ferrielectric twin walls in CaTiO3. Phys. Rev. Lett. 101, 097602 (2008).

    ADS  Google Scholar 

  78. 78.

    Conti, S., Müller, S., Poliakovsky, A. & Salje, E. K. H. Coupling of order parameters, chirality, and interfacial structures in multiferroic materials. J. Phys. Condens. Matter 23, 142203 (2011). An additional symmetry lowering at the wall can lead to a potentially switchable polarity.

    ADS  Google Scholar 

  79. 79.

    Pöttker, H. & Salje, E. K. H. Flexoelectricity, incommensurate phases and the Lifshitz point. J. Phys. Condens. Matter 28, 075902 (2016).

    ADS  Google Scholar 

  80. 80.

    Pöttker, H. & Salje, E. K. H. Twin boundary profiles with linear–quadratic coupling between order parameters. J. Phys. Condens. Matter 26, 342201 (2014).

    ADS  Google Scholar 

  81. 81.

    Van Aert, S. et al. Direct observation of ferrielectricity at ferroelastic domain boundaries in CaTiO3 by electron microscopy. Adv. Mater. 24, 523–527 (2012).

    Google Scholar 

  82. 82.

    Salje, E. K. H., Aktas, O., Carpenter, M. A., Laguta, V. V. & Scott, J. F. Domains within domains and walls within walls: evidence for polar domains in cryogenic SrTiO3. Phys. Rev. Lett. 111, 247603 (2013).

    ADS  Google Scholar 

  83. 83.

    Zhao, Z. et al. Interaction of low-energy electrons with surface polarity near ferroelastic domain boundaries. Phys. Rev. Mater. 3, 043601 (2019).

    Google Scholar 

  84. 84.

    Casals, B. et al. Low-temperature dielectric anisotropy driven by an antiferroelectric mode in SrTiO3. Phys. Rev. Lett. 120, 217601 (2018).

    ADS  Google Scholar 

  85. 85.

    Pesquera, D., Carpenter, M. A. & Salje, E. K. H. Glasslike dynamics of polar domain walls in cryogenic SrTiO3. Phys. Rev. Lett. 121, 235701 (2018).

    ADS  Google Scholar 

  86. 86.

    Novak, J. & Salje, E. K. H. Surface structure of domain walls. J. Phys. Condens. Matter 10, L359–L366 (1998).

    ADS  Google Scholar 

  87. 87.

    Nataf, G. F. et al. Low energy electron imaging of domains and domain walls in magnesium-doped lithium niobate. Sci. Rep. 6, 33098 (2016).

    ADS  Google Scholar 

  88. 88.

    Barrett, N. et al. Full field electron spectromicroscopy applied to ferroelectric materials. J. Appl. Phys. 113, 187217 (2013).

    ADS  Google Scholar 

  89. 89.

    Lu, G., Li, S., Ding, X. & Salje, E. K. H. Piezoelectricity and electrostriction in ferroelastic materials with polar twin boundaries and domain junctions. Appl. Phys. Lett. 114, 202901 (2019).

    ADS  Google Scholar 

  90. 90.

    Lu, G., Li, S., Ding, X., Sun, J. & Salje, E. K. H. Ferroelectric switching in ferroelastic materials with rough surfaces. Sci. Rep. 9, 15834 (2019).

    ADS  Google Scholar 

  91. 91.

    Schmid, H. & Pétermann, L. A. Dielectric constant and electric resistivity of copper chlorine boracite, Cu3B7O13Cl (Cu-Cl-B). Phys. Status Solidi 41, K147–K150 (1977).

    ADS  Google Scholar 

  92. 92.

    Aird, A. & Salje, E. K. H. Sheet superconductivity in twin walls: experimental evidence of WO3−x. J. Phys. Condens. Matter 10, L377–L380 (1998).

    ADS  Google Scholar 

  93. 93.

    Kim, Y., Alexe, M. & Salje, E. K. H. Nanoscale properties of thin twin walls and surface layers in piezoelectric WO3−x. Appl. Phys. Lett. 96, 032904 (2010).

    ADS  Google Scholar 

  94. 94.

    Seidel, J. et al. Conduction at domain walls in oxide multiferroics. Nat. Mater. 8, 229–234 (2009).

    ADS  Google Scholar 

  95. 95.

    Farokhipoor, S. & Noheda, B. Local conductivity and the role of vacancies around twin walls of (001)−BiFeO3 thin films. J. Appl. Phys. 112, 052003 (2012).

    ADS  Google Scholar 

  96. 96.

    Farokhipoor, S. & Noheda, B. Conduction through 71° domain walls in BiFeO3 thin films. Phys. Rev. Lett. 107, 127601 (2011).

    ADS  Google Scholar 

  97. 97.

    Chiu, Y.-P. et al. Atomic-scale evolution of local electronic structure across multiferroic domain walls. Adv. Mater. 23, 1530–1534 (2011).

    Google Scholar 

  98. 98.

    Lubk, A., Gemming, S. & Spaldin, N. A. First-principles study of ferroelectric domain walls in multiferroic bismuth ferrite. Phys. Rev. B 80, 104110 (2009).

    ADS  Google Scholar 

  99. 99.

    Diéguez, O., Aguado-Puente, P., Junquera, J. & Íñiguez, J. Domain walls in a perovskite oxide with two primary structural order parameters: first-principles study of BiFeO3. Phys. Rev. B 87, 024102 (2013).

    ADS  Google Scholar 

  100. 100.

    Seidel, J. et al. Domain wall conductivity in La-doped BiFeO3. Phys. Rev. Lett. 105, 197603 (2010).

    ADS  Google Scholar 

  101. 101.

    Campanini, M. et al. Imaging and quantification of charged domain walls in BiFeO3. Nanoscale 12, 9186–9193 (2020).

    Google Scholar 

  102. 102.

    Maksymovych, P. et al. Dynamic conductivity of ferroelectric domain walls in BiFeO3. Nano Lett. 11, 1906–1912 (2011).

    ADS  Google Scholar 

  103. 103.

    Li, L. et al. Atomic scale structure changes induced by charged domain walls in ferroelectric materials. Nano Lett. 13, 5218–5223 (2013).

    ADS  Google Scholar 

  104. 104.

    Vasudevan, R. K. et al. Domain wall geometry controls conduction in ferroelectrics. Nano Lett. 12, 5524–5531 (2012).

    ADS  Google Scholar 

  105. 105.

    Körbel, S., Hlinka, J. & Sanvito, S. Electron trapping by neutral pristine ferroelectric domain walls in BiFeO3. Phys. Rev. B 98, 100104 (2018).

    ADS  Google Scholar 

  106. 106.

    Rojac, T. et al. Domain-wall conduction in ferroelectric BiFeO3 controlled by accumulation of charged defects. Nat. Mater. 16, 322–327 (2017).

    ADS  Google Scholar 

  107. 107.

    Lee, J. H. et al. Spintronic functionality of BiFeO3 domain walls. Adv. Mater. 26, 7078–7082 (2014).

    Google Scholar 

  108. 108.

    Stolichnov, I. et al. Persistent conductive footprints of 109° domain walls in bismuth ferrite films. Appl. Phys. Lett. 104, 132902 (2014). When conducting domain walls are moved by applied electric fields, enhanced conduction persists where the domain walls were before the field-induced movement.

    ADS  Google Scholar 

  109. 109.

    Domingo, N., Farokhipoor, S., Santiso, J., Noheda, B. & Catalan, G. Domain wall magnetoresistance in BiFeO3 thin films measured by scanning probe microscopy. J. Phys. Condens. Matter 29, 334003 (2017).

    Google Scholar 

  110. 110.

    He, Q. et al. Magnetotransport at domain walls in BiFeO3. Phys. Rev. Lett. 108, 067203 (2012).

    ADS  Google Scholar 

  111. 111.

    Yang, J. C. et al. Conduction control at ferroic domain walls via external stimuli. Nanoscale 6, 10524–10529 (2014).

    ADS  Google Scholar 

  112. 112.

    Choi, T. et al. Insulating interlocked ferroelectric and structural antiphase domain walls in multiferroic YMnO3. Nat. Mater. 9, 253–258 (2010).

    ADS  Google Scholar 

  113. 113.

    Meier, D. et al. Anisotropic conductance at improper ferroelectric domain walls. Nat. Mater. 11, 284–288 (2012).

    ADS  Google Scholar 

  114. 114.

    Wu, W., Horibe, Y., Lee, N., Cheong, S.-W. & Guest, J. R. Conduction of topologically protected charged ferroelectric domain walls. Phys. Rev. Lett. 108, 077203 (2012).

    ADS  Google Scholar 

  115. 115.

    Holtz, M. E. et al. Topological defects in hexagonal manganites: inner structure and emergent electrostatics. Nano Lett. 17, 5883–5890 (2017).

    ADS  Google Scholar 

  116. 116.

    Småbråten, D. R. et al. Charged domain walls in improper ferroelectric hexagonal manganites and gallates. Phys. Rev. Mater. 2, 114405 (2018).

    Google Scholar 

  117. 117.

    Schoenherr, P. et al. Observation of uncompensated bound charges at improper ferroelectric domain walls. Nano Lett. 19, 1659–1664 (2019).

    ADS  Google Scholar 

  118. 118.

    Turner, P. W. et al. Large carrier mobilities in ErMnO3 conducting domain walls revealed by quantitative Hall-effect measurements. Nano Lett. 18, 6381–6386 (2018). The carrier mobilities at domain walls are among the highest reported in oxide systems.

    ADS  Google Scholar 

  119. 119.

    Mosberg, A. B. et al. FIB lift-out of conducting ferroelectric domain walls in hexagonal manganites. Appl. Phys. Lett. 115, 122901 (2019).

    ADS  Google Scholar 

  120. 120.

    Kumagai, Y. & Spaldin, N. A. Structural domain walls in polar hexagonal manganites. Nat. Commun. 4, 1540 (2013).

    ADS  Google Scholar 

  121. 121.

    Du, Y. et al. Domain wall conductivity in oxygen deficient multiferroic YMnO3 single crystals. Appl. Phys. Lett. 99, 252107 (2011).

    ADS  Google Scholar 

  122. 122.

    Wu, X. et al. Low-energy structural dynamics of ferroelectric domain walls in hexagonal rare-earth manganites. Sci. Adv. 3, e1602371 (2017).

    ADS  Google Scholar 

  123. 123.

    Sluka, T., Tagantsev, A. K., Bednyakov, P. & Setter, N. Free-electron gas at charged domain walls in insulating BaTiO3. Nat. Commun. 4, 1808 (2013).

    ADS  Google Scholar 

  124. 124.

    Gureev, M. Y., Tagantsev, A. K. & Setter, N. Head-to-head and tail-to-tail 180° domain walls in an isolated ferroelectric. Phys. Rev. B 83, 184104 (2011).

    ADS  Google Scholar 

  125. 125.

    Sluka, T., Tagantsev, A. K., Damjanovic, D., Gureev, M. & Setter, N. Enhanced electromechanical response of ferroelectrics due to charged domain walls. Nat. Commun. 3, 748 (2012).

    ADS  Google Scholar 

  126. 126.

    Bednyakov, P. S., Sluka, T., Tagantsev, A. K., Damjanovic, D. & Setter, N. Formation of charged ferroelectric domain walls with controlled periodicity. Sci. Rep. 5, 15819 (2015).

    ADS  Google Scholar 

  127. 127.

    Aristov, V. V., Kokhanchik, L. S. & Voronovskii, Y. I. Voltage contrast of ferroelectric domains of lithium niobate in SEM. Phys. Status Solidi 86, 133–141 (1984).

    ADS  Google Scholar 

  128. 128.

    Schröder, M. et al. Conducting domain walls in lithium niobate single crystals. Adv. Funct. Mater. 22, 3936–3944 (2012).

    Google Scholar 

  129. 129.

    Kämpfe, T. et al. Optical three-dimensional profiling of charged domain walls in ferroelectrics by Cherenkov second-harmonic generation. Phys. Rev. B 89, 035314 (2014).

    ADS  Google Scholar 

  130. 130.

    Sheng, Y. et al. Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation. Opt. Express 18, 16539 (2010).

    ADS  Google Scholar 

  131. 131.

    Pryakhina, V. I. et al. As-grown domain structure in lithium tantalate with spatially nonuniform composition. Ferroelectrics 525, 47–53 (2018).

    Google Scholar 

  132. 132.

    Greshnyakov, E. D., Lisjikh, B. I., Pryakhina, V. I., Nebogatikov, M. S. & Shur, V. Y. Charged domain walls in lithium tantalate with compositional gradients produced by partial VTE process. IOP Conf. Ser. Mater. Sci. Eng. 699, 012015 (2019).

    Google Scholar 

  133. 133.

    Eliseev, E. A., Morozovska, A. N., Svechnikov, G. S., Gopalan, V. & Shur, V. Y. Static conductivity of charged domain walls in uniaxial ferroelectric semiconductors. Phys. Rev. B 83, 235313 (2011). Inclined domain walls lead to partial head-to-head configurations with an accumulation of free electronic carriers, leading to an intrinsic rise in conductivity.

    ADS  Google Scholar 

  134. 134.

    Lu, H. et al. Electrical tunability of domain wall conductivity in LiNbO3 thin films. Adv. Mater. 31, 1902890 (2019).

    Google Scholar 

  135. 135.

    Godau, C., Kämpfe, T., Thiessen, A., Eng, L. M. & Haußmann, A. Enhancing the domain wall conductivity in lithium niobate single crystals. ACS Nano 11, 4816–4824 (2017).

    Google Scholar 

  136. 136.

    Schröder, M. et al. Nanoscale and macroscopic electrical ac transport along conductive domain walls in lithium niobate single crystals. Mater. Res. Express 1, 035012 (2014).

    ADS  Google Scholar 

  137. 137.

    Werner, C. S. et al. Large and accessible conductivity of charged domain walls in lithium niobate. Sci. Rep. 7, 9862 (2017).

    ADS  Google Scholar 

  138. 138.

    Nataf, G. F., Guennou, M., Haußmann, A., Barrett, N. & Kreisel, J. Evolution of defect signatures at ferroelectric domain walls in Mg-doped LiNbO3. Phys. Status Solidi Rapid Res. Lett. 10, 222–226 (2016).

    ADS  Google Scholar 

  139. 139.

    Nataf, G. F., Aktas, O., Granzow, T. & Salje, E. K. H. Influence of defects and domain walls on dielectric and mechanical resonances in LiNbO3. J. Phys. Condens. Matter 28, 015901 (2016).

    ADS  Google Scholar 

  140. 140.

    Wu, X. & Vanderbilt, D. Theory of hypothetical ferroelectric superlattices incorporating head-to-head and tail-to-tail 180° domain walls. Phys. Rev. B 73, 020103 (2006).

    ADS  Google Scholar 

  141. 141.

    Rahmanizadeh, K., Wortmann, D., Bihlmayer, G. & Blügel, S. Charge and orbital order at head-to-head domain walls in PbTiO3. Phys. Rev. B 90, 115104 (2014).

    ADS  Google Scholar 

  142. 142.

    Guyonnet, J., Gaponenko, I., Gariglio, S. & Paruch, P. Conduction at domain walls in insulating Pb(Zr0.2Ti0.8)O3 thin films. Adv. Mater. 23, 5377–5382 (2011).

    Google Scholar 

  143. 143.

    Eliseev, E. A., Morozovska, A. N., Svechnikov, G. S., Maksymovych, P. & Kalinin, S. V. Domain wall conduction in multiaxial ferroelectrics. Phys. Rev. B 85, 045312 (2012).

    ADS  Google Scholar 

  144. 144.

    Sifuna, J., García-Fernández, P., Manyali, G. S., Amolo, G. & Junquera, J. First-principles study of two-dimensional electron and hole gases at the head-to-head and tail-to-tail 180° domain walls in PbTiO3 ferroelectric thin films. Phys. Rev. B 101, 174114 (2020).

    ADS  Google Scholar 

  145. 145.

    Gaponenko, I., Tückmantel, P., Karthik, J., Martin, L. W. & Paruch, P. Towards reversible control of domain wall conduction in Pb(Zr0.2Ti0.8)O3 thin films. Appl. Phys. Lett. 106, 162902 (2015).

    ADS  Google Scholar 

  146. 146.

    Tselev, A. et al. Microwave a.c. conductivity of domain walls in ferroelectric thin films. Nat. Commun. 7, 11630 (2016).

    ADS  Google Scholar 

  147. 147.

    Maksymovych, P. et al. Tunable metallic conductance in ferroelectric nanodomains. Nano Lett. 12, 209–213 (2012).

    ADS  Google Scholar 

  148. 148.

    Stolichnov, I. et al. Bent ferroelectric domain walls as reconfigurable metallic-like channels. Nano Lett. 15, 8049–8055 (2015).

    ADS  Google Scholar 

  149. 149.

    Wei, X.-K. et al. Controlled charging of ferroelastic domain walls in oxide ferroelectrics. ACS Appl. Mater. Interfaces 9, 6539–6546 (2017).

    Google Scholar 

  150. 150.

    Seidel, J. et al. Efficient photovoltaic current generation at ferroelectric domain walls. Phys. Rev. Lett. 107, 126805 (2011).

    ADS  Google Scholar 

  151. 151.

    Seidel, J., Yang, S. Y., Alarcón-Lladó, E., Ager, J. W. & Ramesh, R. Nanoscale probing of high photovoltages at 109° domain walls. Ferroelectrics 433, 123–126 (2012).

    Google Scholar 

  152. 152.

    Bhatnagar, A., Roy Chaudhuri, A., Heon Kim, Y., Hesse, D. & Alexe, M. Role of domain walls in the abnormal photovoltaic effect in BiFeO3. Nat. Commun. 4, 2835 (2013).

    ADS  Google Scholar 

  153. 153.

    Yang, M.-M., Bhatnagar, A., Luo, Z.-D. & Alexe, M. Enhancement of local photovoltaic current at ferroelectric domain walls in BiFeO3. Sci. Rep. 7, 43070 (2017).

    ADS  Google Scholar 

  154. 154.

    Nataf, G. F. & Guennou, M. Optical studies of ferroelectric and ferroelastic domain walls. J. Phys. Condens. Matter 32, 183001 (2020).

    ADS  Google Scholar 

  155. 155.

    Balcells, L. et al. Enhanced conduction and ferromagnetic order at (100)-type twin walls in La0.7Sr0.3MnO3 thin films. Phys. Rev. B 92, 075111 (2015).

    ADS  Google Scholar 

  156. 156.

    Yadav, A. K. et al. Spatially resolved steady-state negative capacitance. Nature 565, 468–471 (2019).

    ADS  Google Scholar 

  157. 157.

    Zubko, P. et al. Negative capacitance in multidomain ferroelectric superlattices. Nature 534, 524–528 (2016).

    ADS  Google Scholar 

  158. 158.

    Islam Khan, A. et al. Experimental evidence of ferroelectric negative capacitance in nanoscale heterostructures. Appl. Phys. Lett. 99, 113501 (2011).

    ADS  Google Scholar 

  159. 159.

    Salahuddin, S. & Datta, S. Use of negative capacitance to provide voltage amplification for low power nanoscale devices. Nano Lett. 8, 405–410 (2008).

    ADS  Google Scholar 

  160. 160.

    Stefani, C. et al. Ferroelectric 180 degree walls are mechanically softer than the domains they separate. Preprint at https://arxiv.org/abs/2005.04249 (2020).

  161. 161.

    Royo, M., Escorihuela-Sayalero, C., Íñiguez, J. & Rurali, R. Ferroelectric domain wall phonon polarizer. Phys. Rev. Mater. 1, 051402 (2017). Domain walls can act as phonon polarizers and filter phonons depending on their polarization.

    Google Scholar 

  162. 162.

    Farokhipoor, S. et al. Artificial chemical and magnetic structure at the domain walls of an epitaxial oxide. Nature 515, 379–383 (2014).

    ADS  Google Scholar 

  163. 163.

    Bibes, M. & Barthelemy, A. Oxide spintronics. IEEE Trans. Electron Devices 54, 1003–1023 (2007).

    ADS  Google Scholar 

  164. 164.

    Kruglyak, V. V., Demokritov, S. O. & Grundler, D. Magnonics. J. Phys. D Appl. Phys. 43, 264001 (2010).

    ADS  Google Scholar 

  165. 165.

    Becher, C. et al. Strain-induced coupling of electrical polarization and structural defects in SrMnO3 films. Nat. Nanotechnol. 10, 661–665 (2015).

    ADS  Google Scholar 

  166. 166.

    Becher, C. et al. Functional ferroic heterostructures with tunable integral symmetry. Nat. Commun. 5, 4295 (2014).

    ADS  Google Scholar 

  167. 167.

    Vopson, M. M. Fundamentals of multiferroic materials and their possible applications. Crit. Rev. Solid State Mater. Sci. 40, 223–250 (2015).

    ADS  Google Scholar 

  168. 168.

    Meisenheimer, P. B., Novakov, S., Vu, N. M. & Heron, J. T. Perspective: Magnetoelectric switching in thin film multiferroic heterostructures. J. Appl. Phys. 123, 240901 (2018).

    ADS  Google Scholar 

  169. 169.

    Huang, B.-C. et al. Atomically resolved electronic states and correlated magnetic order at termination engineered complex oxide heterointerfaces. ACS Nano 12, 1089–1095 (2018).

    Google Scholar 

  170. 170.

    Li, T. X. et al. Effect of misfit strain on multiferroic and magnetoelectric properties of epitaxial La0.7Sr0.3MnO3/BaTiO3 bilayer. J. Phys. D Appl. Phys. 45, 085002 (2012).

    ADS  Google Scholar 

  171. 171.

    Hausmann, S. et al. Atomic-scale engineering of ferroelectric–ferromagnetic interfaces of epitaxial perovskite films for functional properties. Sci. Rep. 7, 10734 (2017).

    ADS  Google Scholar 

  172. 172.

    Guo, H. et al. Interface-induced multiferroism by design in complex oxide superlattices. Proc. Natl Acad. Sci. USA 114, E5062–E5069 (2017).

    Google Scholar 

  173. 173.

    Pesquera, D. et al. Surface symmetry-breaking and strain effects on orbital occupancy in transition metal perovskite epitaxial films. Nat. Commun. 3, 1189 (2012).

    ADS  Google Scholar 

  174. 174.

    Benckiser, E. et al. Orbital reflectometry of oxide heterostructures. Nat. Mater. 10, 189–193 (2011).

    ADS  Google Scholar 

  175. 175.

    Everhardt, A. S., Matzen, S., Domingo, N., Catalan, G. & Noheda, B. Ferroelectric domain structures in low-strain BaTiO3. Adv. Electron. Mater. 2, 1500214 (2016).

    Google Scholar 

  176. 176.

    Everhardt, A. S. et al. Temperature-independent giant dielectric response in transitional BaTiO3 thin films. Appl. Phys. Rev. 7, 011402 (2020). The denomination ‘transitional’ comes from the observation of a gradual change of structure from tetragonal symmetry at the top of a thick film to orthorhombic symmetry at the bottom.

    ADS  Google Scholar 

  177. 177.

    Dong, G. et al. Super-elastic ferroelectric single-crystal membrane with continuous electric dipole rotation. Science 366, 475–479 (2019).

    ADS  Google Scholar 

  178. 178.

    Nahas, Y. et al. Inverse transition of labyrinthine domain patterns in ferroelectric thin films. Nature 577, 47–51 (2020).

    ADS  Google Scholar 

  179. 179.

    Schupper, N. & Shnerb, N. M. Inverse melting and inverse freezing: a spin model. Phys. Rev. E 72, 046107 (2005).

    ADS  Google Scholar 

  180. 180.

    Nadupalli, S., Kreisel, J. & Granzow, T. Increasing bulk photovoltaic current by strain tuning. Sci. Adv. 5, eaau9199 (2019).

    ADS  Google Scholar 

  181. 181.

    Li, D. et al. Superconductivity in an infinite-layer nickelate. Nature 572, 624–627 (2019).

    ADS  Google Scholar 

  182. 182.

    Catalano, S. et al. Rare-earth nickelates RNiO3: thin films and heterostructures. Rep. Prog. Phys. 81, 046501 (2018).

    ADS  Google Scholar 

  183. 183.

    Simons, H. et al. Long-range symmetry breaking in embedded ferroelectrics. Nat. Mater. 17, 814–819 (2018).

    ADS  Google Scholar 

  184. 184.

    Xu, X. et al. Variability and origins of grain boundary electric potential detected by electron holography and atom-probe tomography. Nat. Mater. 19, 887–893 (2020).

    Google Scholar 

  185. 185.

    Mandel, S. Research suggests a new class of ferroelectric materials. Scilight 2020, 041101 (2020).

    Google Scholar 

  186. 186.

    Mermin, N. D. The topological theory of defects in ordered media. Rev. Mod. Phys. 51, 591–648 (1979).

    ADS  MathSciNet  Google Scholar 

  187. 187.

    Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198–201 (2016).

    ADS  Google Scholar 

  188. 188.

    Das, S. et al. Observation of room-temperature polar skyrmions. Nature 568, 368–372 (2019).

    ADS  Google Scholar 

  189. 189.

    Erb, K. C. & Hlinka, J. Vector, bidirector and Bloch skyrmion phases induced by structural crystallographic symmetry breaking. Phys. Rev. B 102, 024110 (2020).

    ADS  Google Scholar 

  190. 190.

    Mühlbauer, S. et al. Skyrmion lattice in a chiral magnet. Science 323, 915–919 (2009).

    ADS  Google Scholar 

  191. 191.

    Zhao, Z., Ding, X. & Salje, E. K. H. Flicker vortex structures in multiferroic materials. Appl. Phys. Lett. 105, 112906 (2014).

    ADS  Google Scholar 

  192. 192.

    Salje, E. K. H., Li, S., Zhao, Z., Gumbsch, P. & Ding, X. Polar twin boundaries and nonconventional ferroelectric switching. Appl. Phys. Lett. 106, 212907 (2015).

    ADS  Google Scholar 

  193. 193.

    Zykova-Timan, T. & Salje, E. K. H. Highly mobile vortex structures inside polar twin boundaries in SrTiO3. Appl. Phys. Lett. 104, 082907 (2014).

    ADS  Google Scholar 

  194. 194.

    Salje, E. K. H. & Ishibashi, Y. Mesoscopic structures in ferroelastic crystals: needle twins and right-angled domains. J. Phys. Condens. Matter 8, 8477–8495 (1996).

    ADS  Google Scholar 

  195. 195.

    Pertsev, N. A., Novak, J. & Salje, E. K. H. Long-range elastic interactions and equilibrium shapes of curved ferroelastic domain walls in crystals. Phil. Mag. A 80, 2201–2213 (2000).

    ADS  Google Scholar 

  196. 196.

    Juraschek, D. M. et al. Dynamical magnetic field accompanying the motion of ferroelectric domain walls. Phys. Rev. Lett. 123, 127601 (2019).

    ADS  Google Scholar 

  197. 197.

    Christensen, D. V. et al. Strain-tunable magnetism at oxide domain walls. Nat. Phys. 15, 269–274 (2019).

    Google Scholar 

  198. 198.

    Guo, E.-J., Roth, R., Herklotz, A., Hesse, D. & Dörr, K. Ferroelectric 180° domain wall motion controlled by biaxial strain. Adv. Mater. 27, 1615–1618 (2015).

    Google Scholar 

  199. 199.

    McGilly, L. J., Sandu, C. S., Feigl, L., Damjanovic, D. & Setter, N. Nanoscale defect engineering and the resulting effects on domain wall dynamics in ferroelectric thin films. Adv. Funct. Mater. 27, 1605196 (2017).

    Google Scholar 

  200. 200.

    Xu, R. et al. Ferroelectric polarization reversal via successive ferroelastic transitions. Nat. Mater. 14, 79–86 (2015).

    ADS  Google Scholar 

  201. 201.

    Liu, S., Grinberg, I. & Rappe, A. M. Intrinsic ferroelectric switching from first principles. Nature 534, 360–363 (2016).

    ADS  Google Scholar 

  202. 202.

    Ishibashi, Y. & Takagi, Y. Note on ferroelectric domain switching. J. Phys. Soc. Jpn. 31, 506–510 (1971).

    ADS  Google Scholar 

  203. 203.

    Ishibashi, Y. & Orihara, H. A theory of D–E hysteresis loop. Integr. Ferroelectr. 9, 57–61 (1995).

    Google Scholar 

  204. 204.

    Dimmler, K. et al. Switching kinetics in KNO3 ferroelectric thin-film memories. J. Appl. Phys. 61, 5467–5470 (1987).

    ADS  Google Scholar 

  205. 205.

    Eliseev, E. A. et al. Screening and retardation effects on 180°-domain wall motion in ferroelectrics: wall velocity and nonlinear dynamics due to polarization-screening charge interactions. Phys. Rev. B 78, 245409 (2008).

    ADS  Google Scholar 

  206. 206.

    Shur, V. Y., Akhmatkhanov, A. R. & Baturin, I. S. Micro- and nano-domain engineering in lithium niobate. Appl. Phys. Rev. 2, 040604 (2015).

    ADS  Google Scholar 

  207. 207.

    Shur, V. Y. Kinetics of ferroelectric domains: application of general approach to LiNbO3 and LiTaO3. J. Mater. Sci. 41, 199–210 (2006).

    ADS  Google Scholar 

  208. 208.

    Bdikin, I. K. et al. Domain dynamics in piezoresponse force spectroscopy: quantitative deconvolution and hysteresis loop fine structure. Appl. Phys. Lett. 92, 182909 (2008).

    ADS  Google Scholar 

  209. 209.

    Rodriguez, B. J. et al. Domain growth kinetics in lithium niobate single crystals studied by piezoresponse force microscopy. Appl. Phys. Lett. 86, 012906 (2005).

    ADS  Google Scholar 

  210. 210.

    Gruverman, A., Alexe, M. & Meier, D. Piezoresponse force microscopy and nanoferroic phenomena. Nat. Commun. 10, 1661 (2019).

    ADS  Google Scholar 

  211. 211.

    Vasudevan, R. K. et al. Domain wall conduction and polarization-mediated transport in ferroelectrics. Adv. Funct. Mater. 23, 2592–2616 (2013).

    Google Scholar 

  212. 212.

    Meier, D., Seidel, J., Gregg, M. & Ramesh, R. Domain Walls: From Fundamental Properties to Nanotechnology Concepts (Oxford Univ. Press, 2020).

  213. 213.

    Salje, E. K. H., Xue, D., Ding, X., Dahmen, K. A. & Scott, J. F. Ferroelectric switching and scale invariant avalanches in BaTiO3. Phys. Rev. Mater. 3, 014415 (2019).

    Google Scholar 

  214. 214.

    Sethna, J. P., Dahmen, K. A. & Myers, C. R. Crackling noise. Nature 410, 242–250 (2001).

    ADS  Google Scholar 

  215. 215.

    Salje, E. K. H. & Dahmen, K. A. Crackling noise in disordered materials. Annu. Rev. Condens. Matter Phys. 5, 233–254 (2014).

    ADS  Google Scholar 

  216. 216.

    Březina, B., Fousek, J. & Glanc, A. Barkhausen pulses in BaTiO3 connected with 90° switching processes. Czechoslov. J. Phys. 11, 595–601 (1961).

    ADS  Google Scholar 

  217. 217.

    Miller, R. C. On the origin of Barkhausen pulses in BaTiO3. J. Phys. Chem. Solids 17, 93–100 (1960).

    ADS  Google Scholar 

  218. 218.

    Tan, C. D. et al. Electrical studies of Barkhausen switching noise in ferroelectric PZT: critical exponents and temperature dependence. Phys. Rev. Mater. 3, 034402 (2019).

    Google Scholar 

  219. 219.

    Puchberger, S. et al. The noise of many needles: jerky domain wall propagation in PbZrO3 and LaAlO3. APL Mater. 5, 046102 (2017).

    ADS  Google Scholar 

  220. 220.

    Soprunyuk, V. et al. Strain intermittency due to avalanches in ferroelastic and porous materials. J. Phys. Condens. Matter 29, 224002 (2017).

    ADS  Google Scholar 

  221. 221.

    Harrison, R. J. & Salje, E. K. H. The noise of the needle: avalanches of a single progressing needle domain in LaAlO3. Appl. Phys. Lett. 97, 021907 (2010).

    ADS  Google Scholar 

  222. 222.

    Casals, B., van Dijken, S., Herranz, G. & Salje, E. K. H. Electric-field-induced avalanches and glassiness of mobile ferroelastic twin domains in cryogenic SrTiO3. Phys. Rev. Res 1, 032025 (2019).

    Google Scholar 

  223. 223.

    Casals, B., Nataf, G. F., Pesquera, D. & Salje, E. K. H. Avalanches from charged domain wall motion in BaTiO3 during ferroelectric switching. APL Mater. 8, 011105 (2020).

    ADS  Google Scholar 

  224. 224.

    Kustov, S., Liubimova, I. & Salje, E. K. H. Domain dynamics in quantum-paraelectric SrTiO3. Phys. Rev. Lett. 124, 016801 (2020).

    ADS  Google Scholar 

  225. 225.

    Anderson, P. W., Halperin, B. I. & Varma, C. M. Anomalous low-temperature thermal properties of glasses and spin glasses. Phil. Mag. 25, 1–9 (1972).

    ADS  Google Scholar 

  226. 226.

    Kirkpatrick, S. & Sherrington, D. Infinite-ranged models of spin-glasses. Phys. Rev. B 17, 4384–4403 (1978).

    ADS  Google Scholar 

  227. 227.

    Eliseev, E. A. et al. Conductivity of twin-domain-wall/surface junctions in ferroelastics: interplay of deformation potential, octahedral rotations, improper ferroelectricity, and flexoelectric coupling. Phys. Rev. B 86, 085416 (2012).

    ADS  Google Scholar 

  228. 228.

    Eliseev, E. A. et al. Surface effect on domain wall width in ferroelectrics. J. Appl. Phys. 106, 084102 (2009).

    ADS  Google Scholar 

  229. 229.

    Morozovska, A. N. et al. Thermodynamics of nanodomain formation and breakdown in scanning probe microscopy: Landau–Ginzburg–Devonshire approach. Phys. Rev. B 80, 214110 (2009).

    ADS  Google Scholar 

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Acknowledgements

G.F.N. thanks the Royal Commission for the Exhibition of 1851 for the award of a Research Fellowship. J.K. and M.G. acknowledge financial support from the Fond National de Recherche Luxembourg through a PEARL grant (no. FNR/P12/4853155/Kreisel). J.H. acknowledges financial support from the Czech Science Foundation (project no. 19-28594X). D.M. was supported by the Research Council of Norway through its Centres of Excellence funding scheme, project number 262633, “QuSpin” and by NTNU via the Onsager Fellowship Program and the Outstanding Academic Fellows Program. E.K.H.S is grateful to EPSRC (EP/K009702/1) and the Leverhulme Foundation (RPG-2012-564).

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Glossary

Layer group

A group of symmetry operations applicable to objects possessing a lattice translation invariance along two directions only in 3D space. Planar domain walls in crystals are such objects.

Non-centrosymmetric

Qualifying a group that does not contain inversion as a symmetry operation.

Point group

A set of symmetry operations that keep at least one point of the crystal fixed. The point group symmetry is relevant when describing only physical properties of crystals or domain walls.

Ginzburg–Landau type modelling

Modelling approaches that exploit the dependence of the thermodynamical potential on the magnitudes and gradients of order parameter components. For example, it allows one to predict profiles of the course of order parameters across a ferroelectric domain wall.

Fowler–Nordheim behaviour

One of the possible tunnelling behaviours of electrons under a high electric field.

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Nataf, G.F., Guennou, M., Gregg, J.M. et al. Domain-wall engineering and topological defects in ferroelectric and ferroelastic materials. Nat Rev Phys 2, 634–648 (2020). https://doi.org/10.1038/s42254-020-0235-z

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