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

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. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS OPTIONS Access

through your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $29.99 / 30 days cancel any time Learn more Subscribe to

this journal Receive 12 digital issues and online access to articles $99.00 per year only $8.25 per issue Learn more Buy this article * Purchase on SpringerLink * Instant access to full

article PDF Buy now Prices may be subject to local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our FAQs *

Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS ELECTRIC-FIELD-INDUCED DOMAIN WALLS IN WURTZITE FERROELECTRICS Article 16 April 2025 FERROELECTRIC POLARIZATION AND MAGNETIC

STRUCTURE AT DOMAIN WALLS IN A MULTIFERROIC FILM Article Open access 19 July 2024 GIANT CONDUCTIVITY OF MOBILE NON-OXIDE DOMAIN WALLS Article Open access 25 June 2021 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 * Aizu, K. Possible species of ferromagnetic, ferroelectric,

and ferroelastic crystals. _Phys. Rev. B_ 2, 754–772 (1970). ADS  Google Scholar  * Wadhawan, V. _Introduction to Ferroic Materials_ (Gordon and Breach, 2000). * Van Aken, B. B., Rivera,

J.-P., Schmid, H. & Fiebig, M. Observation of ferrotoroidic domains. _Nature_ 449, 702–705 (2007). ADS  Google Scholar  * Schmid, H. Multi-ferroic magnetoelectrics. _Ferroelectrics_ 162,

317–338 (1994). Google Scholar  * Fiebig, M., Lottermoser, T., Meier, D. & Trassin, M. The evolution of multiferroics. _Nat. Rev. Mater._ 1, 16046 (2016). ADS  Google Scholar  *

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

  * 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  * 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  * 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  * Stepkova, V., Marton, P. & Hlinka, J. Ising lines: natural topological defects within ferroelectric Bloch walls. _Phys. Rev. B_ 92, 094106 (2015). ADS  Google Scholar  *

Seidel, J. (ed.) _Topological Structures in Ferroic Materials_ (Springer, 2016). * Stepkova, V. & Hlinka, J. On the possible internal structure of the ferroelectric Ising lines in

BaTiO3. _Phase Transit._ 90, 11–16 (2017). Google Scholar  * Parkin, S. S. P., Hayashi, M. & Thomas, L. Magnetic domain-wall racetrack memory. _Science_ 320, 190–194 (2008). ADS  Google

Scholar  * 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  *

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  * 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  * Yang, S. Y. et al. Above-bandgap voltages from ferroelectric photovoltaic

devices. _Nat. Nanotechnol._ 5, 143–147 (2010). ADS  Google Scholar  * Vul, B. M., Guro, G. M. & Ivanchik, I. I. Encountering domains in ferroelectrics. _Ferroelectrics_ 6, 29–31 (1973).

Google Scholar  * Catalan, G., Seidel, J., Ramesh, R. & Scott, J. F. Domain wall nanoelectronics. _Rev. Mod. Phys._ 84, 119–156 (2012). ADS  Google Scholar  * Sharma, P., Schoenherr, P.

& Seidel, J. Functional ferroic domain walls for nanoelectronics. _Materials_ 12, 2927 (2019). ADS  Google Scholar  * Seidel, J. Domain walls as nanoscale functional elements. _J. Phys.

Chem. Lett._ 3, 2905–2909 (2012). Google Scholar  * Salje, E. K. H. Multiferroic domain boundaries as active memory devices: trajectories towards domain boundary engineering. _ChemPhysChem_

11, 940–950 (2010). Google Scholar  * Whyte, J. R. & Gregg, J. M. A diode for ferroelectric domain-wall motion. _Nat. Commun._ 6, 7361 (2015). ADS  Google Scholar  * Sharma, P. et al.

Nonvolatile ferroelectric domain wall memory. _Sci. Adv._ 3, e1700512 (2017). ADS  Google Scholar  * Sharma, P. et al. Conformational domain wall switch. _Adv. Funct. Mater._ 29, 1807523

(2019). Google Scholar  * 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  * McConville, J. P. V. et al. Ferroelectric domain wall memristor. _Adv. Funct. Mater._ 30, 2000109 (2020). Google Scholar  * Chai, X. et

al. Nonvolatile ferroelectric field-effect transistors. _Nat. Commun._ 11, 2811 (2020). ADS  Google Scholar  * 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  * 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  * Mundy, J. A. et al. Functional electronic inversion layers at ferroelectric domain walls.

_Nat. Mater._ 16, 622–627 (2017). ADS  Google Scholar  * Schaab, J. et al. Electrical half-wave rectification at ferroelectric domain walls. _Nat. Nanotechnol._ 13, 1028–1034 (2018). ADS 

Google Scholar  * 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  * Frenkel, Y. et al.

Imaging and tuning polarity at SrTiO3 domain walls. _Nat. Mater._ 16, 1203–1208 (2017). ADS  Google Scholar  * 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  * Seidel, J., Vasudevan, R. K. & Valanoor, N. Topological structures in

multiferroics — domain walls, skyrmions and vortices. _Adv. Electron. Mater._ 2, 1500292 (2016). Google Scholar  * Seidel, J. Nanoelectronics based on topological structures. _Nat. Mater._

18, 188–190 (2019). Google Scholar  * Meier, D. Functional domain walls in multiferroics. _J. Phys. Condens. Matter_ 27, 463003 (2015). ADS  Google Scholar  * Tagantsev, A. K., Cross, L. E.

& Fousek, J. _Domains in Ferroic Crystals and Thin Films_ (Springer, 2010). * Zhirnov, V. A. A contribution to the theory of domain walls in ferroelectrics. _Sov. Phys. JETP_ 35, 822–825

(1959). MathSciNet  Google Scholar  * 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  * Lajzerowicz, J. & Niez, J. J. Phase transition in a domain wall. _J. Phys. Lett._ 40, 165–169 (1979). Google Scholar  * 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  * 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  * 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  * Hlinka, J. et al. Phase–field modelling of 180°

“Bloch walls” in rhombohedral BaTiO3. _Phase Transit._ 84, 738–746 (2011). Google Scholar  * 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  * 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  * Wojdeł, J. C. & Íñiguez, J. Ferroelectric transitions at ferroelectric domain walls found

from first principles. _Phys. Rev. Lett._ 112, 247603 (2014). ADS  Google Scholar  * 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  * Morozovska, A. N., Kalinin, S. V. & Eliseev, E. A. in _Flexoelectricity in Solids_ 311–336 (World Scientific,

2016). * Lee, D. et al. Mixed Bloch–Néel–Ising character of 180° ferroelectric domain walls. _Phys. Rev. B_ 80, 060102 (2009). ADS  Google Scholar  * 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  * 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  * 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  * 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  * De Luca, G. et al. Domain wall architecture in tetragonal ferroelectric thin films. _Adv. Mater._ 29, 1605145 (2017). Google Scholar  * Janovec, V. A symmetry approach to

domain structures. _Ferroelectrics_ 12, 43–53 (1976). Google Scholar  * Janovec, V. Symmetry and structure of domain walls. _Ferroelectrics_ 35, 105–110 (1981). Google Scholar  * Janovec, V.

& Přívratská, J. in _International Tables for Crystallography_ 449–505 (International Union of Crystallography, 2006). * Janovec, V. & Kopský, V. Layer groups, scanning tables and

the structure of domain walls. _Ferroelectrics_ 191, 23–28 (1997). Google Scholar  * Janovec, V., Schranz, W., Warhanek, H. & Zikmund, Z. Symmetry analysis of domain structure in KSCN

crystals. _Ferroelectrics_ 98, 171–189 (1989). Google Scholar  * Kopský, V. The scanning for layer groups and positional dependence of domain wall energy and structure. _Ferroelectrics_ 376,

168–175 (2008). Google Scholar  * 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  * 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  * Přívratská, J. & Janovec, V. Examination of point group symmetries of non-ferroelastic domain walls. _Ferroelectrics_ 191, 17–21 (1997).

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

Scholar  * 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 

* 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  * 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  * 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  * 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  * 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  * 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  * 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  * 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  * 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

  * 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  * Pöttker, H. & Salje, E. K. H. Flexoelectricity,

incommensurate phases and the Lifshitz point. _J. Phys. Condens. Matter_ 28, 075902 (2016). ADS  Google Scholar  * 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  * 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  * 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  * Zhao, Z. et al. Interaction

of low-energy electrons with surface polarity near ferroelastic domain boundaries. _Phys. Rev. Mater._ 3, 043601 (2019). Google Scholar  * Casals, B. et al. Low-temperature dielectric

anisotropy driven by an antiferroelectric mode in SrTiO3. _Phys. Rev. Lett._ 120, 217601 (2018). ADS  Google Scholar  * 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  * Novak, J. & Salje, E. K. H. Surface structure of domain walls. _J. Phys.

Condens. Matter_ 10, L359–L366 (1998). ADS  Google Scholar  * 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  * Barrett, N. et al. Full field electron spectromicroscopy applied to ferroelectric materials. _J. Appl. Phys._ 113, 187217 (2013). ADS  Google Scholar  *

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  * 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  * 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  * 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  * 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  * Seidel, J. et al. Conduction at domain walls in oxide multiferroics. _Nat. Mater._ 8, 229–234 (2009). ADS  Google Scholar  * 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  * Farokhipoor, S. & Noheda, B.

Conduction through 71° domain walls in BiFeO3 thin films. _Phys. Rev. Lett._ 107, 127601 (2011). ADS  Google Scholar  * Chiu, Y.-P. et al. Atomic-scale evolution of local electronic

structure across multiferroic domain walls. _Adv. Mater._ 23, 1530–1534 (2011). Google Scholar  * 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  * 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  * Seidel, J. et al. Domain wall conductivity in

La-doped BiFeO3. _Phys. Rev. Lett._ 105, 197603 (2010). ADS  Google Scholar  * Campanini, M. et al. Imaging and quantification of charged domain walls in BiFeO3. _Nanoscale_ 12, 9186–9193

(2020). Google Scholar  * Maksymovych, P. et al. Dynamic conductivity of ferroelectric domain walls in BiFeO3. _Nano Lett._ 11, 1906–1912 (2011). ADS  Google Scholar  * 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  * Vasudevan, R. K. et al. Domain wall geometry

controls conduction in ferroelectrics. _Nano Lett._ 12, 5524–5531 (2012). ADS  Google Scholar  * 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  * 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  * Lee, J. H. et al. Spintronic functionality of BiFeO3 domain walls. _Adv. Mater._ 26, 7078–7082 (2014). Google Scholar  *

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  * 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  * He, Q. et al.

Magnetotransport at domain walls in BiFeO3. _Phys. Rev. Lett._ 108, 067203 (2012). ADS  Google Scholar  * Yang, J. C. et al. Conduction control at ferroic domain walls via external stimuli.

_Nanoscale_ 6, 10524–10529 (2014). ADS  Google Scholar  * Choi, T. et al. Insulating interlocked ferroelectric and structural antiphase domain walls in multiferroic YMnO3. _Nat. Mater._ 9,

253–258 (2010). ADS  Google Scholar  * Meier, D. et al. Anisotropic conductance at improper ferroelectric domain walls. _Nat. Mater._ 11, 284–288 (2012). ADS  Google Scholar  * 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  *

Holtz, M. E. et al. Topological defects in hexagonal manganites: inner structure and emergent electrostatics. _Nano Lett._ 17, 5883–5890 (2017). ADS  Google Scholar  * Småbråten, D. R. et

al. Charged domain walls in improper ferroelectric hexagonal manganites and gallates. _Phys. Rev. Mater._ 2, 114405 (2018). Google Scholar  * Schoenherr, P. et al. Observation of

uncompensated bound charges at improper ferroelectric domain walls. _Nano Lett._ 19, 1659–1664 (2019). ADS  Google Scholar  * 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  * 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  * Kumagai, Y. & Spaldin, N. A. Structural domain walls in polar hexagonal manganites. _Nat. Commun._ 4, 1540 (2013). ADS  Google Scholar  * Du, Y. et al. Domain wall

conductivity in oxygen deficient multiferroic YMnO3 single crystals. _Appl. Phys. Lett._ 99, 252107 (2011). ADS  Google Scholar  * 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  * 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  * 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  * 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  * 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  * 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  * Schröder, M. et al.

Conducting domain walls in lithium niobate single crystals. _Adv. Funct. Mater._ 22, 3936–3944 (2012). Google Scholar  * 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  * Sheng, Y. et al. Three-dimensional ferroelectric domain

visualization by Čerenkov-type second harmonic generation. _Opt. Express_ 18, 16539 (2010). ADS  Google Scholar  * Pryakhina, V. I. et al. As-grown domain structure in lithium tantalate with

spatially nonuniform composition. _Ferroelectrics_ 525, 47–53 (2018). Google Scholar  * 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  * 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  * Lu,

H. et al. Electrical tunability of domain wall conductivity in LiNbO3 thin films. _Adv. Mater._ 31, 1902890 (2019). Google Scholar  * 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  * 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  * Werner, C. S. et al. Large and

accessible conductivity of charged domain walls in lithium niobate. _Sci. Rep._ 7, 9862 (2017). ADS  Google Scholar  * 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  * 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 

* 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  * 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  * 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

  * 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  * 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  * 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  * Tselev, A. et al. Microwave

a.c. conductivity of domain walls in ferroelectric thin films. _Nat. Commun._ 7, 11630 (2016). ADS  Google Scholar  * Maksymovych, P. et al. Tunable metallic conductance in ferroelectric

nanodomains. _Nano Lett._ 12, 209–213 (2012). ADS  Google Scholar  * Stolichnov, I. et al. Bent ferroelectric domain walls as reconfigurable metallic-like channels. _Nano Lett._ 15,

8049–8055 (2015). ADS  Google Scholar  * Wei, X.-K. et al. Controlled charging of ferroelastic domain walls in oxide ferroelectrics. _ACS Appl. Mater. Interfaces_ 9, 6539–6546 (2017). Google

Scholar  * Seidel, J. et al. Efficient photovoltaic current generation at ferroelectric domain walls. _Phys. Rev. Lett._ 107, 126805 (2011). ADS  Google Scholar  * 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  * 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  * 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  * Nataf, G. F.

& Guennou, M. Optical studies of ferroelectric and ferroelastic domain walls. _J. Phys. Condens. Matter_ 32, 183001 (2020). ADS  Google Scholar  * 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  * Yadav, A. K. et al. Spatially resolved steady-state

negative capacitance. _Nature_ 565, 468–471 (2019). ADS  Google Scholar  * Zubko, P. et al. Negative capacitance in multidomain ferroelectric superlattices. _Nature_ 534, 524–528 (2016). ADS

  Google Scholar  * Islam Khan, A. et al. Experimental evidence of ferroelectric negative capacitance in nanoscale heterostructures. _Appl. Phys. Lett._ 99, 113501 (2011). ADS  Google

Scholar  * 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  *

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). * 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  * 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  * Bibes, M. & Barthelemy, A. Oxide spintronics. _IEEE Trans. Electron Devices_ 54, 1003–1023 (2007). ADS  Google Scholar  * Kruglyak, V. V., Demokritov, S.

O. & Grundler, D. Magnonics. _J. Phys. D Appl. Phys._ 43, 264001 (2010). ADS  Google Scholar  * 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  * Becher, C. et al. Functional ferroic heterostructures with tunable integral symmetry. _Nat. Commun._

5, 4295 (2014). ADS  Google Scholar  * Vopson, M. M. Fundamentals of multiferroic materials and their possible applications. _Crit. Rev. Solid State Mater. Sci._ 40, 223–250 (2015). ADS 

Google Scholar  * 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  * 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  * 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  * 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  * Guo, H. et al. Interface-induced multiferroism by design in complex oxide superlattices. _Proc. Natl Acad. Sci. USA_ 114,

E5062–E5069 (2017). Google Scholar  * 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  * Benckiser, E. et al. Orbital reflectometry of oxide heterostructures. _Nat. Mater._ 10, 189–193 (2011). ADS  Google Scholar  * 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  * 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  * Dong, G. et al. Super-elastic ferroelectric

single-crystal membrane with continuous electric dipole rotation. _Science_ 366, 475–479 (2019). ADS  Google Scholar  * Nahas, Y. et al. Inverse transition of labyrinthine domain patterns in

ferroelectric thin films. _Nature_ 577, 47–51 (2020). ADS  Google Scholar  * Schupper, N. & Shnerb, N. M. Inverse melting and inverse freezing: a spin model. _Phys. Rev. E_ 72, 046107

(2005). ADS  Google Scholar  * Nadupalli, S., Kreisel, J. & Granzow, T. Increasing bulk photovoltaic current by strain tuning. _Sci. Adv._ 5, eaau9199 (2019). ADS  Google Scholar  * Li,

D. et al. Superconductivity in an infinite-layer nickelate. _Nature_ 572, 624–627 (2019). ADS  Google Scholar  * Catalano, S. et al. Rare-earth nickelates _R_NiO3: thin films and

heterostructures. _Rep. Prog. Phys._ 81, 046501 (2018). ADS  Google Scholar  * Simons, H. et al. Long-range symmetry breaking in embedded ferroelectrics. _Nat. Mater._ 17, 814–819 (2018).

ADS  Google Scholar  * 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  * Mandel, S. Research suggests a new class of ferroelectric materials. _Scilight_ 2020, 041101 (2020). Google Scholar  * Mermin, N. D. The topological theory of defects in

ordered media. _Rev. Mod. Phys._ 51, 591–648 (1979). ADS  MathSciNet  Google Scholar  * Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. _Nature_ 530, 198–201

(2016). ADS  Google Scholar  * Das, S. et al. Observation of room-temperature polar skyrmions. _Nature_ 568, 368–372 (2019). ADS  Google Scholar  * 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  * Mühlbauer, S. et al. Skyrmion lattice

in a chiral magnet. _Science_ 323, 915–919 (2009). ADS  Google Scholar  * Zhao, Z., Ding, X. & Salje, E. K. H. Flicker vortex structures in multiferroic materials. _Appl. Phys. Lett._

105, 112906 (2014). ADS  Google Scholar  * 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  * 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  * 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  * 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  * Juraschek, D. M. et al. Dynamical magnetic field accompanying the motion of ferroelectric domain walls. _Phys. Rev.

Lett._ 123, 127601 (2019). ADS  Google Scholar  * Christensen, D. V. et al. Strain-tunable magnetism at oxide domain walls. _Nat. Phys._ 15, 269–274 (2019). Google Scholar  * 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  * 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  * Xu, R. et al. Ferroelectric polarization reversal via successive ferroelastic transitions. _Nat. Mater._ 14, 79–86 (2015). ADS  Google Scholar  * Liu, S.,

Grinberg, I. & Rappe, A. M. Intrinsic ferroelectric switching from first principles. _Nature_ 534, 360–363 (2016). ADS  Google Scholar  * Ishibashi, Y. & Takagi, Y. Note on

ferroelectric domain switching. _J. Phys. Soc. Jpn._ 31, 506–510 (1971). ADS  Google Scholar  * Ishibashi, Y. & Orihara, H. A theory of D–E hysteresis loop. _Integr. Ferroelectr._ 9,

57–61 (1995). Google Scholar  * Dimmler, K. et al. Switching kinetics in KNO3 ferroelectric thin-film memories. _J. Appl. Phys._ 61, 5467–5470 (1987). ADS  Google Scholar  * 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  * 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  * 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  *

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  * 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  * Gruverman, A., Alexe, M. & Meier, D. Piezoresponse force microscopy and nanoferroic phenomena. _Nat. Commun._ 10, 1661 (2019). ADS  Google Scholar  * Vasudevan, R. K. et al.

Domain wall conduction and polarization-mediated transport in ferroelectrics. _Adv. Funct. Mater._ 23, 2592–2616 (2013). Google Scholar  * Meier, D., Seidel, J., Gregg, M. & Ramesh, R.

_Domain Walls: From Fundamental Properties to Nanotechnology Concepts_ (Oxford Univ. Press, 2020). * 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  * Sethna, J. P., Dahmen, K. A. & Myers, C. R. Crackling noise. _Nature_ 410,

242–250 (2001). ADS  Google Scholar  * Salje, E. K. H. & Dahmen, K. A. Crackling noise in disordered materials. _Annu. Rev. Condens. Matter Phys._ 5, 233–254 (2014). ADS  Google Scholar

  * 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  * Miller, R.

C. On the origin of Barkhausen pulses in BaTiO3. _J. Phys. Chem. Solids_ 17, 93–100 (1960). ADS  Google Scholar  * 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  * 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  * Soprunyuk, V. et al. Strain intermittency due to avalanches in ferroelastic and porous materials. _J.

Phys. Condens. Matter_ 29, 224002 (2017). ADS  Google Scholar  * 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  * 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  * 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  * Kustov, S., Liubimova, I. & Salje, E. K. H. Domain dynamics in

quantum-paraelectric SrTiO3. _Phys. Rev. Lett._ 124, 016801 (2020). ADS  Google Scholar  * 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  * Kirkpatrick, S. & Sherrington, D. Infinite-ranged models of spin-glasses. _Phys. Rev. B_ 17, 4384–4403

(1978). ADS  Google Scholar  * 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  * Eliseev, E. A. et al. Surface effect on domain wall width in ferroelectrics. _J. Appl.

Phys._ 106, 084102 (2009). ADS  Google Scholar  * 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  Download references 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). AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Materials Science, University of Cambridge, Cambridge, UK G. F. Nataf * Department of Physics and Materials

Science, University of Luxembourg, Belvaux, Luxembourg M. Guennou & J. Kreisel * Centre for Nanostructured Media, School of Mathematics and Physics, Queen’s University Belfast, Belfast,

UK J. M. Gregg * Department of Materials Science and Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway D. Meier * Center for Quantum Spintronics,

Department of Physics, Norwegian University of Science and Technology (NTNU), Trondheim, Norway D. Meier * Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic J. Hlinka *

Department of Earth Sciences, University of Cambridge, Cambridge, UK E. K. H. Salje Authors * G. F. Nataf View author publications You can also search for this author inPubMed Google

Scholar * M. Guennou View author publications You can also search for this author inPubMed Google Scholar * J. M. Gregg View author publications You can also search for this author inPubMed 

Google Scholar * D. Meier View author publications You can also search for this author inPubMed Google Scholar * J. Hlinka View author publications You can also search for this author

inPubMed Google Scholar * E. K. H. Salje View author publications You can also search for this author inPubMed Google Scholar * J. Kreisel View author publications You can also search for

this author inPubMed Google Scholar CONTRIBUTIONS All authors have read, discussed and contributed to the writing of the manuscript. CORRESPONDING AUTHOR Correspondence to G. F. Nataf.

ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PEER REVIEW INFORMATION _Nature Reviews Physics_ thanks Ya-Ping Chiu and the other,

anonymous, reviewer(s) for their contribution to the peer review of this work. PUBLISHER’S NOTE Springer Nature remains neutral with regard to jurisdictional claims in published maps and

institutional affiliations. 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. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE 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 Download citation * Accepted: 10 August 2020 * Published: 22

September 2020 * Issue Date: November 2020 * DOI: https://doi.org/10.1038/s42254-020-0235-z SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get

shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative