1932

Abstract

Taking a historical perspective, we provide a brief overview of the first-principles modeling of ferroelectric perovskite oxides over the past 30 years. We emphasize how the work done by a relatively small community on the fundamental understanding of ferroelectricity and related phenomena has been at the origin of consecutive theoretical breakthroughs, with an impact going often well beyond the limit of the ferroelectric community. In this context, we first review key theoretical advances such as the modern theory of polarization, the computation of functional properties as energy derivatives, the explicit treatment of finite fields, or the advent of second-principles methods to extend the length and timescale of the simulations. We then discuss how these have revolutionized our understanding of ferroelectricity and related phenomena in this technologically important class of compounds.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-040220-045528
2022-03-10
2024-12-08
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/13/1/annurev-conmatphys-040220-045528.html?itemId=/content/journals/10.1146/annurev-conmatphys-040220-045528&mimeType=html&fmt=ahah

Literature Cited

  1. 1. 
    Valasek J. 1921. Phys. Rev. 17:4475–81
    [Google Scholar]
  2. 2. 
    Busch G, Scherrer P. 1935. Naturwiss 23:43737–37
    [Google Scholar]
  3. 3. 
    Busch G. 1938. Helv. Phys. Acta 11:2269–98
    [Google Scholar]
  4. 4. 
    Wul B, Goldman IM. 1945. C. R. Acad. Sci. URSS 46:139
    [Google Scholar]
  5. 5. 
    Pawley GS, Cochran W, Cowley RA, Dolling G. 1966. Phys. Rev. Lett. 17:14753–55
    [Google Scholar]
  6. 6. 
    Fatuzzo E, Harbeke G, Merz WJ, Nitsche R, Roetschi H, Ruppel W. 1962. Phys. Rev. 127:62036–37
    [Google Scholar]
  7. 7. 
    Kawai H. 1969. Jpn. J. Appl. Phys. 8:7975–76
    [Google Scholar]
  8. 8. 
    Cross LE, Newnham RE 1987. Ceramics and Civilization, Vol. III WD Kingery, 289–305 Westerville, OH: Am. Ceram. Soc.
    [Google Scholar]
  9. 9. 
    Mueller H. 1935. Phys. Rev. 47:2175–91
    [Google Scholar]
  10. 10. 
    Mueller H. 1940. Phys. Rev. 57:9829–39
    [Google Scholar]
  11. 11. 
    Mueller H. 1940. Phys. Rev. 58:6565–73
    [Google Scholar]
  12. 12. 
    Mueller H. 1940. Phys. Rev. 58:9805–11
    [Google Scholar]
  13. 13. 
    Devonshire AF. 1949. Philos. Mag. 40:3091040–63
    [Google Scholar]
  14. 14. 
    Devonshire AF. 1951. Philos. Mag. 42:3331065–79
    [Google Scholar]
  15. 15. 
    Devonshire AF. 1954. Adv. Phys. 3:1085–130
    [Google Scholar]
  16. 16. 
    Cochran W. 1959. Phys. Rev. Lett. 3:9412–14
    [Google Scholar]
  17. 17. 
    Cochran W. 1960. Adv. Phys. 9:36387–423
    [Google Scholar]
  18. 18. 
    Anderson PW 1960.In Fizika Dielectrikoved. GI Skanavipp. 29096 Moscow: Acad. Nauk USSR (in Russian)
    [Google Scholar]
  19. 19. 
    Comès R, Lambert M, Guinier A. 1968. Solid State Commun. 6:10715–19
    [Google Scholar]
  20. 20. 
    Comès R, Lambert M, Guinier A. 1970. Acta Cryst. A26:2244–54
    [Google Scholar]
  21. 21. 
    Lines ME. 1969. Phys. Rev. 177:2797–812
    [Google Scholar]
  22. 22. 
    Migoni R, Bilz H, Bäuerle D. 1976. Phys. Rev. Lett. 37:171155–58
    [Google Scholar]
  23. 23. 
    Bilz H, Benedek G, Bussmann-Holder A. 1987. Phys. Rev. B 35:104840–49
    [Google Scholar]
  24. 24. 
    Hohenberg P, Kohn W. 1964. Phys. Rev. 136:3BB864–71
    [Google Scholar]
  25. 25. 
    Kohn W, Sham LJ. 1965. Phys. Rev. 140:4AA1133–38
    [Google Scholar]
  26. 26. 
    Chadi DJ, Cohen ML. 1973. Phys. Rev. B 8:125747–53
    [Google Scholar]
  27. 27. 
    Monkhorst HJ, Pack JD. 1976. Phys. Rev. B 13:125188–92
    [Google Scholar]
  28. 28. 
    Hamann DR, Schlüter M, Chiang C. 1979. Phys. Rev. Lett. 43:201494–97
    [Google Scholar]
  29. 29. 
    Vanderbilt D. 1990. Phys. Rev. B 41:117892–95
    [Google Scholar]
  30. 30. 
    Ceperley DM, Alder BJ. 1980. Phys. Rev. Lett. 45:7566–69
    [Google Scholar]
  31. 31. 
    Perdew JP, Zunger A. 1981. Phys. Rev. B 23:105048–79
    [Google Scholar]
  32. 32. 
    Car R, Parrinello M. 1985. Phys. Rev. Lett. 55:222471–74
    [Google Scholar]
  33. 33. 
    Baroni S, Giannozzi P, Testa A. 1987. Phys. Rev. Lett. 58:181861–64
    [Google Scholar]
  34. 34. 
    Baroni S, de Gironcoli S, Dal Corso A, Giannozzi P 2001. Rev. Mod. Phys. 73:2515–62
    [Google Scholar]
  35. 35. 
    Pertosa P, Michel-Calendini FM. 1978. Phys. Rev. B 17:42011–20
    [Google Scholar]
  36. 36. 
    Pertosa P, Hollinger G, Michel-Calendini FM. 1978. Phys. Rev. B 18:105177–83
    [Google Scholar]
  37. 37. 
    Michel-Calendini FM, Chermette H, Weber J. 1980. J. Phys. C: Solid State Phys. 13:81427–41
    [Google Scholar]
  38. 38. 
    Rabe KM, Joannopoulos JD. 1987. Phys. Rev. B 36:126631–39
    [Google Scholar]
  39. 39. 
    Rong C, Wang B, Zhao D, Liu S. 2020. WIREs Computat. Mol. Sci. 10:e1461
    [Google Scholar]
  40. 40. 
    Boero M, Oshiyama A. 2015. Encyclopedia of Nanotechnology B Bhushan Dordrecht, Neth: Springer https://doi.org/10.1007/978-94-007-6178-0_100946-1
    [Google Scholar]
  41. 41. 
    Ghosez P, Cockayne E, Waghmare UV, Rabe KM. 1999. Phys. Rev. B 60:2836–43
    [Google Scholar]
  42. 42. 
    Cohen RE. 1992. Nature 358:6382136–38. https://doi.org/10.1038/358136a0
    [Google Scholar]
  43. 43. 
    Spaldin NA. 2012. J. Solid State Chem. 195:2–10. https://doi.org/10.1016/j.jssc.2012.05.010
    [Google Scholar]
  44. 44. 
    Kornev I, Fu H, Bellaiche L. 2004. Phys. Rev. Lett. 93:19196104
    [Google Scholar]
  45. 45. 
    Schlom DG, Chen LQ, Fennie CJ, Gopalan V, Muller DA et al. 2014. MRS Bull. 39:118–30. https://doi.org/10.1557/mrs.2014.1
    [Google Scholar]
  46. 46. 
    Stepkova V, Marton P, Hlinka J. 2015. Phys. Rev. B 92:9094106
    [Google Scholar]
  47. 47. 
    Freimuth F, Mokrousov Y, Wortmann D, Heinze S, Blügel S. 2008. Phys. Rev. B 78:3035120
    [Google Scholar]
  48. 48. 
    McKee RA, Walker FJ, Chisholm MF. 1998. Phys. Rev. Lett. 81:143014–17
    [Google Scholar]
  49. 49. 
    Junquera J, Ghosez P. 2003. Nature 422:506–9
    [Google Scholar]
  50. 50. 
    Bousquet E, Dawber M, Stucki N, Lichtensteiger C, Hermet P et al. 2008. Nature 452:7188732–36
    [Google Scholar]
  51. 51. 
    Maranganti R, Sharma ND, Sharma P. 2006. Phys. Rev. B 74:014110
    [Google Scholar]
  52. 52. 
    Picozzi S. 2018. Handbook of Materials Modeling W Andreoni, S Yip 375–400 Cham, Switz: Springer
    [Google Scholar]
  53. 53. 
    Martin RM. 1974. Phys. Rev. B 9:41998–99
    [Google Scholar]
  54. 54. 
    Resta R. 1992. Ferroelectrics 136:151–55
    [Google Scholar]
  55. 55. 
    Ghosez P, Gonze X, Michenaud JP. 1994. Ferroelectrics 153:191–96
    [Google Scholar]
  56. 56. 
    King-Smith RD, Vanderbilt D 1993. Phys. Rev. B 47:31651–54
    [Google Scholar]
  57. 57. 
    Berry MV. 1984. Proc. R. Soc. Lond. 392: 1802.45–57
    [Google Scholar]
  58. 58. 
    Vanderbilt D, King-Smith RD. 1993. Phys. Rev. B 48:4442–55
    [Google Scholar]
  59. 59. 
    Gonze X, Ghosez P, Godby RW. 1995. Phys. Rev. Lett. 74:204035–38
    [Google Scholar]
  60. 60. 
    Gonze X, Lee C. 1997. Phys. Rev. B 55:1610355–68
    [Google Scholar]
  61. 61. 
    Resta R, Sorella S. 1995. Phys. Rev. Lett. 74:234738–41
    [Google Scholar]
  62. 62. 
    Resta R, Posternak M, Baldereschi A. 1993. Phys. Rev. Lett. 70:71010–13
    [Google Scholar]
  63. 63. 
    Neaton JB, Ederer C, Waghmare UV, Spaldin NA, Rabe KM. 2005. Phys. Rev. B 71:1014113
    [Google Scholar]
  64. 64. 
    Thonhauser T. 2011. Int. J. Mod. Phys. B 25:111429–58
    [Google Scholar]
  65. 65. 
    Stengel M, Vanderbilt D 2016. Flexoelectricity in Solids: From Theory to Applications AK Tagantsev, PV Yudin 31–110 Singapore: World Sci.
    [Google Scholar]
  66. 66. 
    Tan LZ, Zheng F, Young SM, Wang F, Liu S, Rappe AM. 2016. NPJ Comput. Mater. 2:116026
    [Google Scholar]
  67. 67. 
    Resta R. 1994. Rev. Mod. Phys. 66:899
    [Google Scholar]
  68. 68. 
    Resta R, Vanderbilt D 2007. Physics of Ferroelectrics: A Modern Perspective, Topics in Applied Physics 105 KM Rabe, CH Ahn, J-M Triscone 31–68 Berlin: Springer
    [Google Scholar]
  69. 69. 
    Vanderbilt D. 2018. Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  70. 70. 
    Marzari N, Vanderbilt D. 1997. Phys. Rev. B 56:2012847–65
    [Google Scholar]
  71. 71. 
    Ordejón P. 1998. Comput. Mater. Sci. 12:157–91
    [Google Scholar]
  72. 72. 
    Goedecker S. 1999. Rev. Mod. Phys. 71:41085–123
    [Google Scholar]
  73. 73. 
    Marzari N, Mostofi AA, Yates JR, Souza I, Vanderbilt D. 2012. Rev. Mod. Phys. 84:41419–75
    [Google Scholar]
  74. 74. 
    Sai N, Rabe KM, Vanderbilt D. 2002. Phys. Rev. B 66:10104108
    [Google Scholar]
  75. 75. 
    Souza I, Íñiguez J, Vanderbilt D. 2004. Phys. Rev. B 69:8085106
    [Google Scholar]
  76. 76. 
    Nunes RW, Vanderbilt D. 1994. Phys. Rev. Lett. 73:5712–15
    [Google Scholar]
  77. 77. 
    Nunes RW, Gonze X. 2001. Phys. Rev. B 63:15155107
    [Google Scholar]
  78. 78. 
    Umari P, Pasquarello A. 2002. Phys. Rev. Lett. 89:15157602
    [Google Scholar]
  79. 79. 
    Souza I, Íñiguez J, Vanderbilt D. 2002. Phys. Rev. Lett. 89:11117602
    [Google Scholar]
  80. 80. 
    Stengel M, Spaldin NA, Vanderbilt D. 2009. Nat. Phys. 5:4304–8
    [Google Scholar]
  81. 81. 
    Stengel M, Vanderbilt D, Spaldin NA. 2009. Phys. Rev. B 80:22224110
    [Google Scholar]
  82. 82. 
    Wu X, Stengel M, Rabe KM, Vanderbilt D. 2008. Phys. Rev. Lett. 101:8087601
    [Google Scholar]
  83. 83. 
    Stengel M, Vanderbilt D. 2009. Phys. Rev. B 80:24241103
    [Google Scholar]
  84. 84. 
    Stengel M. 2011. Phys. Rev. Lett. 106:13136803
    [Google Scholar]
  85. 85. 
    Stengel M, Aguado-Puente P, Spaldin NA, Junquera J. 2011. Phys. Rev. B 83:23235112
    [Google Scholar]
  86. 86. 
    Fu H, Cohen RE. 2000. Nature 403:6767281–83
    [Google Scholar]
  87. 87. 
    Diéguez O, Vanderbilt D. 2006. Phys. Rev. Lett. 96:5056401
    [Google Scholar]
  88. 88. 
    Royo M, Stengel M. 2019. Phys. Rev. X 9:2021050
    [Google Scholar]
  89. 89. 
    Portigal DL, Burstein E. 1968. Phys. Rev. 170:3673–78
    [Google Scholar]
  90. 90. 
    Malashevich A, Souza I. 2010. Phys. Rev. B 82:24245118
    [Google Scholar]
  91. 91. 
    Martin RM. 1972. Phys. Rev. B 5:41607–13
    [Google Scholar]
  92. 92. 
    Zhong W, King-Smith RD, Vanderbilt D 1994. Phys. Rev. Lett. 72:223618–21
    [Google Scholar]
  93. 93. 
    Ghosez P, Gonze X, Lambin P, Michenaud JP. 1995. Phys. Rev. B 51:106765–68
    [Google Scholar]
  94. 94. 
    Ghosez P, Michenaud JP, Gonze X. 1998. Phys. Rev. B 58:106224–40
    [Google Scholar]
  95. 95. 
    Yu R, Krakauer H. 1995. Phys. Rev. Lett. 74:204067–70
    [Google Scholar]
  96. 96. 
    Ghosez P, Gonze X, Michenaud JP. 1998. Ferroelectrics 206:1205–17
    [Google Scholar]
  97. 97. 
    Amoroso D, Cano A, Ghosez P. 2018. Phys. Rev. B 97:17174108
    [Google Scholar]
  98. 98. 
    Wilk GD, Wallace RM, Anthony JM. 2001. J. Appl. Phys. 89:105243–75
    [Google Scholar]
  99. 99. 
    Gonze X, Vigneron JP. 1989. Phys. Rev. B 39:1813120–28
    [Google Scholar]
  100. 100. 
    Gonze X. 1995. Phys. Rev. A 52:21096–114
    [Google Scholar]
  101. 101. 
    Veithen M, Gonze X, Ghosez P. 2004. Phys. Rev. Lett. 93:18187401
    [Google Scholar]
  102. 102. 
    Veithen M, Gonze X, Ghosez P. 2005. Phys. Rev. B 71:12125107
    [Google Scholar]
  103. 103. 
    Gonze X, Amadon B, Antonius G, Arnardi F, Baguet L et al. 2020. Comput. Phys. Commun. 248:107042
    [Google Scholar]
  104. 104. 
    Curie J, Curie P. 1880. C. R. Acad. Sci 91:294–95
    [Google Scholar]
  105. 105. 
    McKitterick JB. 1983. Phys. Rev. B 28:127384–86
    [Google Scholar]
  106. 106. 
    Vanderbilt D. 2000. J. Phys. Chem. Solids 61:2147–51
    [Google Scholar]
  107. 107. 
    Wu X, Vanderbilt D, Hamann DR. 2005. Phys. Rev. B 72:3035105
    [Google Scholar]
  108. 108. 
    Dal Corso A, Posternak M, Resta R, Baldereschi A. 1994. Phys. Rev. B 50:1510715–21
    [Google Scholar]
  109. 109. 
    Sághi-Szabó G, Cohen RE, Krakauer H. 1998. Phys. Rev. Lett. 80:194321–24
    [Google Scholar]
  110. 110. 
    Baroni S, Giannozzi P, Testa A. 1987. Phys. Rev. Lett. 59:232662–65
    [Google Scholar]
  111. 111. 
    Hamann DR, Wu X, Rabe KM, Vanderbilt D. 2005. Phys. Rev. B 71:3035117
    [Google Scholar]
  112. 112. 
    Tagantsev AK. 1986. Phys. Rev. B 34:85883–89
    [Google Scholar]
  113. 113. 
    Tagantsev AK. 1991. Phase Transit. 35:3–4119–203
    [Google Scholar]
  114. 114. 
    Resta R. 2010. Phys. Rev. Lett. 105:12127601
    [Google Scholar]
  115. 115. 
    Tagantsev AK, Yurkov AS. 2012. J. Appl. Phys. 112:4044103
    [Google Scholar]
  116. 116. 
    Stengel M. 2013. Nat. Commun. 4:2693
    [Google Scholar]
  117. 117. 
    Stengel M. 2014. Phys. Rev. B 90:20201112
    [Google Scholar]
  118. 118. 
    Hong J, Catalan G, Scott JF, Artacho E 2010. J. Phys. Condens. Matter 22:11112201
    [Google Scholar]
  119. 119. 
    Hong J, Vanderbilt D. 2013. Phys. Rev. B 88:17174107
    [Google Scholar]
  120. 120. 
    Stengel M. 2013. Phys. Rev. B 88:17174106
    [Google Scholar]
  121. 121. 
    Royo M, Hahn KR, Stengel M. 2020. Phys. Rev. Lett. 125:21217602
    [Google Scholar]
  122. 122. 
    Brunin G, Miranda HPC, Giantomassi M, Royo M, Stengel M et al. 2020. Phys. Rev. Lett. 125:13136601
    [Google Scholar]
  123. 123. 
    Íñiguez J. 2008. Phys. Rev. Lett. 101:11117201
    [Google Scholar]
  124. 124. 
    Wojdeł JC, Íñiguez J. 2009. Phys. Rev. Lett. 103:26267205
    [Google Scholar]
  125. 125. 
    Bousquet E, Spaldin NA, Delaney KT. 2011. Phys. Rev. Lett. 106:10107202
    [Google Scholar]
  126. 126. 
    Malashevich A, Coh S, Souza I, Vanderbilt D. 2012. Phys. Rev. B 86:9094430
    [Google Scholar]
  127. 127. 
    Scaramucci A, Bousquet E, Fechner M, Mostovoy M, Spaldin NA. 2012. Phys. Rev. Lett. 109:19197203
    [Google Scholar]
  128. 128. 
    Gonze X, Zwanziger JW. 2011. Phys. Rev. B 84:6064445
    [Google Scholar]
  129. 129. 
    Ricci F, Prokhorenko S, Torrent M, Verstraete MJ, Bousquet E. 2019. Phys. Rev. B 99:18184404
    [Google Scholar]
  130. 130. 
    Garrity KF. 2018. Phys. Rev. B 97:2024115
    [Google Scholar]
  131. 131. 
    Smidt TE, Mack SA, Reyes-Lillo SE, Jain A, Neaton JB. 2020. Sci. Data 7:72
    [Google Scholar]
  132. 132. 
    Jain A, Ong SP, Hautier G, Chen W, Richards WD et al. 2013. APL Mater. 1:1011002
    [Google Scholar]
  133. 133. 
    Schmidt J, Marques MRG, Botti S, Marques MAL 2019. npj Comput. Mater 5:83
    [Google Scholar]
  134. 134. 
    Lejaeghere K, Bihlmayer G, Björkman T, Blaha P, Blügel S et al. 2016. Science 351:6280): 10.1126/science.aad3000
    [Google Scholar]
  135. 135. 
    Rabe KM, Ghosez P 2007. Physics of Ferroelectrics: A Modern Perspective, Topics in Applied Physics 105 KM Rabe, CH Ahn, J-M Triscone 117–74 Berlin: Springer
    [Google Scholar]
  136. 136. 
    Zhang Y, Sun J, Perdew JP, Wu X. 2017. Phys. Rev. B 96:3035143
    [Google Scholar]
  137. 137. 
    Cohen RE. 2008. Piezoelectricity: Evolution and Future of a Technology W Heywang, K Lubitz, W Wersing , Vol. 114471–92 Berlin/Heidelberg: Springer
    [Google Scholar]
  138. 138. 
    Cohen RE, Krakauer H. 1990. Phys. Rev. B 42:6416–23
    [Google Scholar]
  139. 139. 
    Tinte S, Íñiguez J, Rabe KM, Vanderbilt D. 2003. Phys. Rev. B 67:6064106
    [Google Scholar]
  140. 140. 
    Wojdeł JC, Hermet P, Ljungberg MP, Ghosez P, Íñiguez J. 2013. J. Phys. Condens. Matter 25:30305401
    [Google Scholar]
  141. 141. 
    Wu Z, Cohen RE. 2006. Phys. Rev. B 73:23235116
    [Google Scholar]
  142. 142. 
    Wu Z, Cohen RE, Singh DJ. 2004. Phys. Rev. B 70:10104112
    [Google Scholar]
  143. 143. 
    Perdew JP, Ruzsinszky A, Csonka GI, Vydrov OA, Scuseria GE et al. 2008. Phys. Rev. Lett. 100:13136406
    [Google Scholar]
  144. 144. 
    Sun J, Remsing R, Zhang Y, Sun Z, Ruzsinszky A et al. 2016. Nat. Chem. 8:9831–36
    [Google Scholar]
  145. 145. 
    Paul A, Sun J, Perdew JP, Waghmare UV. 2017. Phys. Rev. B 95:5054111
    [Google Scholar]
  146. 146. 
    Kingsland M, Lynch KA, Lisenkov S, He X, Ponomareva I. 2020. Phys. Rev. Mater. 4:7073802
    [Google Scholar]
  147. 147. 
    Perdew JP, Ernzerhof M, Burke K. 1996. J. Chem. Phys. 105:229982–85
    [Google Scholar]
  148. 148. 
    Heyd J, Scuseria GE, Ernzerhof M. 2003. J. Chem. Phys. 118:188207–15
    [Google Scholar]
  149. 149. 
    Bilc DI, Orlando R, Shaltaf R, Rignanese GM, Íñiguez J, Ghosez P. 2008. Phys. Rev. B 77:16165107
    [Google Scholar]
  150. 150. 
    Srinivasan V, Gebauer R, Resta R, Car R 2003. AIP Conf. Proc. 677:1168–75
    [Google Scholar]
  151. 151. 
    Lichtensteiger C, Zubko P, Stengel M, Aguado-Puente P, Triscone JM et al. 2012. Oxide Ultrathin Films: Science and Technology G Pacchioni, S Valeri 265–308 Weinheim: Wiley-VCH
    [Google Scholar]
  152. 152. 
    Aguado-Puente P, Junquera J. 2012. Phys. Rev. B 85:184105
    [Google Scholar]
  153. 153. 
    Baker JS, Bowler DR. 2020. Adv. Theory Simul. 3:112000154
    [Google Scholar]
  154. 154. 
    Marton P, Klíč A, Paściak M, Hlinka J. 2017. Phys. Rev. B 96:17174110
    [Google Scholar]
  155. 155. 
    Gu Y, Rabe K, Bousquet E, Gopalan V, Chen LQ. 2012. Phys. Rev. B 85:064117
    [Google Scholar]
  156. 156. 
    Pitike KC, Khakpash N, Mangeri J, Rossetti GA, Nakhmanson SM. 2019. J. Mater. Sci. 54:118381–400
    [Google Scholar]
  157. 157. 
    Zhong W, Vanderbilt D, Rabe KM. 1994. Phys. Rev. Lett. 73:131861–64
    [Google Scholar]
  158. 158. 
    Rabe KM, Waghmare UV. 1995. Phys. Rev. B 52:1813236–46
    [Google Scholar]
  159. 159. 
    Zhong W, Vanderbilt D. 1996. Phys. Rev. B 53:95047–50
    [Google Scholar]
  160. 160. 
    Íñiguez J, Vanderbilt D. 2002. Phys. Rev. Lett. 89:11115503
    [Google Scholar]
  161. 161. 
    Zhong W, Vanderbilt D, Rabe KM. 1995. Phys. Rev. B 52:96301–12
    [Google Scholar]
  162. 162. 
    Waghmare UV, Rabe KM. 1997. Phys. Rev. B 55:106161–73
    [Google Scholar]
  163. 163. 
    Waghmare UV, Rabe KM, Krakauer H Yu R, Wang CZ. 1998. AIP Conf. Proc. 436:132–42
    [Google Scholar]
  164. 164. 
    Vanderbilt D, Zhong W. 1998. Ferroelectrics 206:1181–204
    [Google Scholar]
  165. 165. 
    Yang Y, Xu B, Xu C, Ren W, Bellaiche L. 2018. Phys. Rev. B 97:17174106
    [Google Scholar]
  166. 166. 
    Zhong W, Vanderbilt D. 1995. Phys. Rev. Lett. 74:132587–90
    [Google Scholar]
  167. 167. 
    Kornev IA, Lisenkov S, Haumont R, Dkhil B, Bellaiche L. 2007. Phys. Rev. Lett. 99:22227602
    [Google Scholar]
  168. 168. 
    Bellaiche L, García A, Vanderbilt D. 2000. Phys. Rev. Lett. 84:235427–30
    [Google Scholar]
  169. 169. 
    Kornev IA, Bellaiche L, Janolin PE, Dkhil B, Suard E. 2006. Phys. Rev. Lett. 97:15157601
    [Google Scholar]
  170. 170. 
    Al-Barakaty A, Prosandeev S, Wang D, Dkhil B, Bellaiche L. 2015. Phys. Rev. B 91:21214117
    [Google Scholar]
  171. 171. 
    Akbarzadeh AR, Prosandeev S, Walter EJ, Al-Barakaty A, Bellaiche L 2012. Phys. Rev. Lett. 108:25257601
    [Google Scholar]
  172. 172. 
    George AM, Íñiguez J, Bellaiche L. 2001. Nature 413:54–57
    [Google Scholar]
  173. 173. 
    Lee JH, Waghmare UV, Yu J 2008. J. Appl. Phys. 103:12124106
    [Google Scholar]
  174. 174. 
    Fu H, Bellaiche L. 2003. Phys. Rev. Lett. 91:25257601
    [Google Scholar]
  175. 175. 
    Naumov II, Bellaiche L, Fu H. 2004. Nature 432:7018737–40
    [Google Scholar]
  176. 176. 
    Krakauer H, Yu R, Wang CZ, Rabe KM, Waghmare UV. 1999. J. Phys. Condens. Matter 11:183779–87
    [Google Scholar]
  177. 177. 
    Diéguez O, Tinte S, Antons A, Bungaro C, Neaton JB et al. 2004. Phys. Rev. B 69:21212101
    [Google Scholar]
  178. 178. 
    Garcia A, Vanderbilt D 1998. AIP Conf. Proc. 436:53–60
    [Google Scholar]
  179. 179. 
    Rabe KM, Cockayne E 1998. AIP Conf. Proc. 436:61–70
    [Google Scholar]
  180. 180. 
    Ponomareva I, Tagantsev AK, Bellaiche L. 2012. Phys. Rev. B 85:104101
    [Google Scholar]
  181. 181. 
    Veithen M, Ghosez P. 2005. Phys. Rev. B 71:13132101
    [Google Scholar]
  182. 182. 
    Burton BP, Cockayne E, Waghmare UV. 2005. Phys. Rev. B 72:6064113
    [Google Scholar]
  183. 183. 
    Ponomareva I, Lisenkov S. 2012. Phys. Rev. Lett. 108:16167604
    [Google Scholar]
  184. 184. 
    Lisenkov S, Ponomareva I. 2012. Phys. Rev. B 86:10104103
    [Google Scholar]
  185. 185. 
    Íñiguez J, Bellaiche L. 2001. Phys. Rev. Lett. 87:9095503
    [Google Scholar]
  186. 186. 
    Xu B, Wang D, Zhao HJ, Íñiguez J, Chen XM, Bellaiche L. 2015. Adv. Funct. Mater. 25:243626–33
    [Google Scholar]
  187. 187. 
    Bungaro C, Rabe KM. 2005. Phys. Rev. B 71:035420
    [Google Scholar]
  188. 188. 
    Dick BG, Overhauser AW. 1958. Phys. Rev. 112:190–103
    [Google Scholar]
  189. 189. 
    Tinte S, Stachiotti MG, Sepliarsky M, Migoni RL, Rodriguez CO. 1999. J. Phys. Condens. Matter 11:489679–90
    [Google Scholar]
  190. 190. 
    Vielma JM, Schneider G. 2013. J. Appl. Phys. 114:17174108
    [Google Scholar]
  191. 191. 
    Sepliarsky M, Cohen RE 2002. AIP Conf. Proc. 626:36–44
    [Google Scholar]
  192. 192. 
    Shimada T, Wakahara K, Umeno Y, Kitamura T. 2008. J. Phys. Condens. Matter 20:32325225
    [Google Scholar]
  193. 193. 
    Sepliarsky M, Phillpot SR, Wolf D, Stachiotti MG, Migoni RL. 2001. J. Appl. Phys. 90:94509–19
    [Google Scholar]
  194. 194. 
    Gindele O, Kimmel A, Cain MG, Duggy D. 2015. J. Phys. Chem. C 119:3117784–89
    [Google Scholar]
  195. 195. 
    Sepliarsky M, Wu Z, Asthagiri A, Cohen RE. 2004. Ferroelectrics 301:55–59
    [Google Scholar]
  196. 196. 
    Asthagiri A, Wu Z, Choudhury N, Cohen RE. 2006. Ferroelectrics 333:169–78
    [Google Scholar]
  197. 197. 
    Brown ID. 1981. Structure and Bonding in Crystals New York: Academic. , 1st ed..
    [Google Scholar]
  198. 198. 
    Shin YH, Cooper VR, Grinberg I, Rappe AM. 2005. Phys. Rev. B 71:5054104
    [Google Scholar]
  199. 199. 
    Liu S, Grinberg I, Takenaka H, Rappe AM. 2013. Phys. Rev. B 88:10104102
    [Google Scholar]
  200. 200. 
    Qi Y, Liu S, Grinberg I, Rappe AM. 2016. Phys. Rev. B 94:13134308
    [Google Scholar]
  201. 201. 
    Liu S, Grinberg I, Rappe AM. 2013. J. Phys. Condens. Matter 25:10102202
    [Google Scholar]
  202. 202. 
    Escorihuela-Sayalero C, Wojdeł JC, Íñiguez J. 2017. Phys. Rev. B 95:9094115
    [Google Scholar]
  203. 203. 
    Schmitt MM. 2020. First- and second-principles studies of perovskites PhD Thesis, Université de Liége Belgium:
    [Google Scholar]
  204. 204. 
    Zubko P, Wojdeł JC, Hadjimichael M, Fernández-Pena S, Sené A et al. 2016. Nature 534:7608524–28
    [Google Scholar]
  205. 205. 
    Grinberg I, Shin YH, Rappe AM. 2009. Phys. Rev. Lett. 103:19197601
    [Google Scholar]
  206. 206. 
    Pereira Goncalves MA, Escorihuela-Sayalero C, Garca-Fernández P, Junquera J, Íñiguez J. 2019. Sci. Adv. 5:2eaau7023
    [Google Scholar]
  207. 207. 
    Das S, Tang YL, Hong Z, Gonçalves MAP, McCarter MR et al. 2019. Nature 568:7752368–72
    [Google Scholar]
  208. 208. 
    Lisenkov S, Kornev IA, Bellaiche L. 2009. Phys. Rev. B 79:1012101
    [Google Scholar]
  209. 209. 
    Rahmedov D, Wang D, Íñiguez J, Bellaiche L. 2012. Phys. Rev. Lett. 109:3037207
    [Google Scholar]
  210. 210. 
    García-Fernández P, Wojdeł JC, Íñiguez J, Junquera J. 2016. Phys. Rev. B 93:19195137
    [Google Scholar]
  211. 211. 
    Nishimatsu T 2002–2017. feram: MD simulator for bulk and thin-film ferroelectrics. T Nishimatsu. Accessed November 2021. http://loto.sourceforge.net/feram/
  212. 212. 
    Chen P, Zhao H, Artyukhin S 2021. LINVARIANT. P Chen. Accessed November 2021. https://github.com/PaulChern/LINVARIANT/
  213. 213. 
    Behler J, Parrinello M. 2007. Phys. Rev. Lett. 98:14146401
    [Google Scholar]
  214. 214. 
    Bartók AP, Payne MC, Kondor R, Csányi G. 2010. Phys. Rev. Lett. 104:13136403
    [Google Scholar]
  215. 215. 
    Hajinazar S, Shao J, Kolmogorov AN. 2017. Phys. Rev. B 95:1014114
    [Google Scholar]
  216. 216. 
    Eriksson F, Fransson E, Erhart P 2019. Adv. Theory Simul. 2:51800184
    [Google Scholar]
  217. 217. 
    Jinnouchi R, Lahnsteiner J, Karsai F, Kresse G, Bokdam M. 2019. Phys. Rev. Lett. 122:225701
    [Google Scholar]
  218. 218. 
    Ghosez P, Triscone JM. 2011. Nat. Mater. 10:269–70
    [Google Scholar]
  219. 219. 
    Pauling L. 1929. J. Am. Chem. Soc. 51:41010–26
    [Google Scholar]
  220. 220. 
    Goldschmidt VM. 1926. Sci. Nat. 14:477–85
    [Google Scholar]
  221. 221. 
    King-Smith RD, Vanderbilt D 1994. Phys. Rev. B 49:95828–44
    [Google Scholar]
  222. 222. 
    Benedek NA, Fennie CJ. 2013. J. Phys. Chem. C 117:2613339–49
    [Google Scholar]
  223. 223. 
    Aschauer U, Spaldin NA. 2014. J. Phys. Condens. Matter 26:12122203
    [Google Scholar]
  224. 224. 
    Kim TH, Puggioni D, Yuan Y, Xie L, Zhou H et al. 2016. Nature 533:68–72
    [Google Scholar]
  225. 225. 
    Kim JR, Jang J, Go KJ, Park SY, Roh CJ et al. 2020. Nat. Commun. 11:4944
    [Google Scholar]
  226. 226. 
    Ghosez P, Gonze X, Michenaud JP. 1996. Europhys. Lett. 33:713–18
    [Google Scholar]
  227. 227. 
    Bersuker I. 1966. Phys. Lett. 20:6589–90
    [Google Scholar]
  228. 228. 
    Levanyuk AP, Sannikov D. 1974. Uspekhi Fizicheskikh Nauk 112:561–89
    [Google Scholar]
  229. 229. 
    Lines ME, Glass AM. 1977. Principles and Applications of Ferroelectrics and Related Materials Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  230. 230. 
    Fennie CJ, Rabe KM. 2005. Phys. Rev. B 72:10100103
    [Google Scholar]
  231. 231. 
    Varignon J, Ghosez P. 2013. Phys. Rev. B 87:14140403
    [Google Scholar]
  232. 232. 
    Sai N, Fennie CJ, Demkov AA. 2009. Phys. Rev. Lett. 102:10107601
    [Google Scholar]
  233. 233. 
    Malashevich A, Vanderbilt D. 2008. Phys. Rev. Lett. 101:3037210
    [Google Scholar]
  234. 234. 
    Benedek NA, Fennie CJ. 2011. Phys. Rev. Lett. 106:10107204
    [Google Scholar]
  235. 235. 
    Fukushima T, Stroppa A, Picozzi S, Perez-Mato JM. 2011. Phys. Chem. Chem. Phys. 13:2612186–90
    [Google Scholar]
  236. 236. 
    Rondinelli JM, Fennie CJ. 2012. Adv. Mater. 24:151961–68
    [Google Scholar]
  237. 237. 
    Mulder AT, Benedek NA, Rondinelli JM, Fennie CJ. 2013. Adv. Funct. Mater. 23:384810–20
    [Google Scholar]
  238. 238. 
    Benedek NA, Rondinelli JM, Djani H, Ghosez P, Lightfoot P 2015. Dalton Trans. 44:2310543–58
    [Google Scholar]
  239. 239. 
    Yang Y, Íñiguez J, Mao AJ, Bellaiche L. 2014. Phys. Rev. Lett. 112:5057202
    [Google Scholar]
  240. 240. 
    Varignon J, Bristowe NC, Bousquet É, Ghosez P. 2015. C. R. Phys. 16:2153–67
    [Google Scholar]
  241. 241. 
    Oh YS, Luo X, Huang FT, Wang Y, Cheong SW. 2015. Nat. Mater. 14:407
    [Google Scholar]
  242. 242. 
    Stroppa A, Barone P, Jain P, Perez-Mato JM, Picozzi S. 2013. Adv. Mater. 25:162284–90
    [Google Scholar]
  243. 243. 
    Varignon J, Bristowe NC, Bousquet E, Ghosez P. 2015. Sci. Rep 515364
    [Google Scholar]
  244. 244. 
    Holakovský J 1973. Phys. Status Solidi (b) 56:2615–19
    [Google Scholar]
  245. 245. 
    Gu T, Scarbrough T, Yang Y, Íñiguez J, Bellaiche L, Xiang HJ. 2018. Phys. Rev. Lett. 120:19197602
    [Google Scholar]
  246. 246. 
    Garrity KF, Rabe KM, Vanderbilt D. 2014. Phys. Rev. Lett. 112:12127601
    [Google Scholar]
  247. 247. 
    Veithen M, Ghosez P. 2002. Phys. Rev. B 65:214302
    [Google Scholar]
  248. 248. 
    Li P, Ren X, Guo GC, He L. 2016. Sci. Rep. 6:134085
    [Google Scholar]
  249. 249. 
    Khedidji M, Amoroso D, Djani H. 2021. Phys. Rev. B 103:1014116
    [Google Scholar]
  250. 250. 
    Markov M, Alaerts L, Miranda HPC, Petretto G, Chen W et al. 2021. PNAS 118:17e2026020118
    [Google Scholar]
  251. 251. 
    Kornev IA, Bellaiche L, Bouvier P, Janolin PE, Dkhil B, Kreisel J. 2005. Phys. Rev. Lett. 95:19196804
    [Google Scholar]
  252. 252. 
    Bousquet E, Ghosez P. 2006. Phys. Rev. B 74:180101(R)
    [Google Scholar]
  253. 253. 
    Noheda B, Cox DE, Shirane G, Gonzalo JA, Cross LE, Park SE. 1999. Appl. Phys. Lett. 74:142059–61
    [Google Scholar]
  254. 254. 
    Guo R, Cross LE, Park SE, Noheda B, Cox DE, Shirane G. 2000. Phys. Rev. Lett. 84:235423–26
    [Google Scholar]
  255. 255. 
    Wu Z, Cohen RE. 2005. Phys. Rev. Lett. 95:3037601
    [Google Scholar]
  256. 256. 
    Tinte S, Burton BP, Cockayne E, Waghmare UV. 2006. Phys. Rev. Lett. 97:13137601
    [Google Scholar]
  257. 257. 
    Ganesh P, Cockayne E, Ahart M, Cohen RE, Burton B et al. 2010. Phys. Rev. B 81:14144102
    [Google Scholar]
  258. 258. 
    Nahas Y, Akbarzadeh A, Prokhorenko S, Prosandeev S, Walter R et al. 2017. Nat. Commun. 8:15944
    [Google Scholar]
  259. 259. 
    Amoroso D, Cano A, Ghosez P. 2019. Appl. Phys. Lett. 114:9092902
    [Google Scholar]
  260. 260. 
    Bellaiche L. 2002. Curr. Opin. Solid State Mater. Sci. 6:119–25
    [Google Scholar]
  261. 261. 
    Noheda B. 2002. Curr. Opin. Solid State Mater. Sci. 6:127–34
    [Google Scholar]
  262. 262. 
    Uchino K. 2015. Sci. Technol. Adv. Mater. 16:4046001
    [Google Scholar]
  263. 263. 
    Jiang Z, Zhang R, Li F, Jin L, Zhang N et al. 2016. AIP Adv. 6:6065122
    [Google Scholar]
  264. 264. 
    Li S, Eastman JA, Vetrone JM, Foster CM, Newnham RE, Cross LE. 1997. Jpn. J. Appl. Phys. 36:Part 1, No. 85169–74
    [Google Scholar]
  265. 265. 
    Tybell T, Ahn CH, Triscone JM. 1999. Appl. Phys. Lett. 75:6856–58
    [Google Scholar]
  266. 266. 
    Junquera J, Ghosez P. 2008. J. Comput. Theor. Nanosci. 5:2071–88
    [Google Scholar]
  267. 267. 
    Wang H, Tang F, Dhuvad PH, Wu X. 2020. NPJ Comput. Mater. 6:52
    [Google Scholar]
  268. 268. 
    Dawber M, Rabe KM, Scott JF. 2005. Rev. Mod. Phys. 77:1083–130
    [Google Scholar]
  269. 269. 
    Ramesh R, Schlom DG 2019. Nat. Rev. Mater. 4:257–68
    [Google Scholar]
  270. 270. 
    Forsbergh PW. 1954. Phys. Rev. 93:4686–92
    [Google Scholar]
  271. 271. 
    Pertsev NA, Zembilgotov AG, Tagantsev AK. 1998. Phys. Rev. Lett. 80:91988–91
    [Google Scholar]
  272. 272. 
    Koukhar VG, Pertsev NA, Waser R. 2001. Phys. Rev. B 64:214103
    [Google Scholar]
  273. 273. 
    Diéguez O, Rabe KM, Vanderbilt D. 2005. Phys. Rev. B 72:14144101
    [Google Scholar]
  274. 274. 
    Jiang Z, Zhang R, Wang D, Sichuga D, Jia CL, Bellaiche L. 2014. Phys. Rev. B 89:21214113
    [Google Scholar]
  275. 275. 
    Chapman JBJ, Kimmel AV, Duffy DM. 2017. Phys. Chem. Chem. Phys. 19:64243–50
    [Google Scholar]
  276. 276. 
    Choi KJ, Biegaslki M, Li YL, Sharan A, Schubert J et al. 2004. Science 306:1005–9
    [Google Scholar]
  277. 277. 
    Haeni JH, Irvin P, Chang W, Uecker R, Reiche P et al. 2004. Nature 430:758–61
    [Google Scholar]
  278. 278. 
    Rabe KM. 2005. Curr. Opin. Solid State Mater. Sci. 9:3122–27
    [Google Scholar]
  279. 279. 
    Schlom DG, Chen LQ, Eom CB, Rabe KM, Streiffer SK, Triscone JM. 2007. Annu. Rev. Mater. Res. 37:589–626
    [Google Scholar]
  280. 280. 
    Bousquet E, Spaldin NA, Ghosez P. 2010. Phys. Rev. Lett. 104:3037601
    [Google Scholar]
  281. 281. 
    Goian V, Held R, Bousquet E, Yuan Y, Melville A et al. 2020. Commun. Mater. 1:74
    [Google Scholar]
  282. 282. 
    Ritz ET, Benedek NA. 2020. Phys. Rev. Mater. 4:8084410
    [Google Scholar]
  283. 283. 
    Xiang HJ, Guennou M, Íñiguez J, Kreisel J, Bellaiche L. 2017. Phys. Rev. B 96:5054102
    [Google Scholar]
  284. 284. 
    Bhattacharjee S, Bousquet E, Ghosez P. 2009. Phys. Rev. Lett. 102:11117602
    [Google Scholar]
  285. 285. 
    Diéguez O, González-Vázquez OE, Wojdeł JC, Íñiguez J. 2011. Phys. Rev. B 83:9094105
    [Google Scholar]
  286. 286. 
    Yang Y, Ren W, Stengel M, Yan XH, Bellaiche L. 2012. Phys. Rev. Lett. 109:5057602
    [Google Scholar]
  287. 287. 
    Hong SS, Gu M, Verma M, Harbola V, Wang BY et al. 2020. Science 368:648671–76
    [Google Scholar]
  288. 288. 
    Janovec V. 1958. Czech. J. Phys. 8:13–15
    [Google Scholar]
  289. 289. 
    Kay HF, Dunn JW. 1962. Philos. Mag. 7:842027–34
    [Google Scholar]
  290. 290. 
    Ghosez P, Rabe KM. 2000. Appl. Phys. Lett. 76:192767–69
    [Google Scholar]
  291. 291. 
    Mehta RR, Silverman BD, Jacobs JT. 1973. J. Appl. Phys. 44:3379–85
    [Google Scholar]
  292. 292. 
    Lichtensteiger C, Triscone JM, Junquera J, Ghosez P. 2005. Phys. Rev. Lett. 94:4047603
    [Google Scholar]
  293. 293. 
    Dawber M, Chandra P, Littlewood PB, Scott JF. 2003. J. Phys. Condens. Matter 15:24L393–98
    [Google Scholar]
  294. 294. 
    Stengel M, Spaldin NA. 2006. Nature 443:7112679–82
    [Google Scholar]
  295. 295. 
    Sai N, Kolpak AM, Rappe AM. 2005. Phys. Rev. B 72:2020101
    [Google Scholar]
  296. 296. 
    Al-Saidi WA, Rappe AM. 2010. Phys. Rev. B 82:15155304
    [Google Scholar]
  297. 297. 
    Stengel M, Vanderbilt D, Spaldin NA. 2009. Nat. Mater. 8:5392–97
    [Google Scholar]
  298. 298. 
    Gerra G, Tagantsev AK, Setter N, Parlinski K. 2006. Phys. Rev. Lett. 96:10107603
    [Google Scholar]
  299. 299. 
    Chisholm MF, Luo W, Oxley MP, Pantelides ST, Lee HN. 2010. Phys. Rev. Lett. 105:19197602
    [Google Scholar]
  300. 300. 
    Nagarajan V, Junquera J, He JQ, Jia CL, Lee K et al. 2006. J. Appl. Phys. 100:051609
    [Google Scholar]
  301. 301. 
    Aguado-Puente P, Junquera J. 2008. Phys. Rev. Lett. 100:177601
    [Google Scholar]
  302. 302. 
    Lai BK, Ponomareva I, Naumov II, Kornev I, Fu H et al. 2006. Phys. Rev. Lett. 96:137602
    [Google Scholar]
  303. 303. 
    Neaton JB, Rabe KM. 2003. Appl. Phys. Lett. 82:1586–88
    [Google Scholar]
  304. 304. 
    Dawber M, Stucki N, Lichtensteiger C, Gariglio S, Ghosez P, Triscone JM. 2007. Adv. Mater. 19:4153
    [Google Scholar]
  305. 305. 
    Bousquet E, Junquera J, Ghosez P. 2010. Phys. Rev. B 82:045426
    [Google Scholar]
  306. 306. 
    Mundy JA, Heikes CA, Grosso BF, Segedin DF, Wang Z et al. 2018. arXiv:1812.09615
  307. 307. 
    Esaki L, Laibowitz RB, Stiles PJ. 1971. IBM Tech. Discl. Bull. 13:2161–62
    [Google Scholar]
  308. 308. 
    Tsymbal EY, Kohlstedt H. 2006. Science 313:5784181–83
    [Google Scholar]
  309. 309. 
    Zubko P, Triscone JM. 2009. Nature 460:45–46
    [Google Scholar]
  310. 310. 
    Zhuravlev MY, Sabirianov RF, Jaswal SS, Tsymbal EY. 2005. Phys. Rev. Lett. 94:246802
    [Google Scholar]
  311. 311. 
    Velev JP, Duan CG, Belashchenko KD, Jaswal SS, Tsymbal EY. 2007. Phys. Rev. Lett. 98:13137201
    [Google Scholar]
  312. 312. 
    Garcia V, Fusil S, Bouzehouane K, Enouz-Vedrenne S, Mathur ND et al. 2009. Nature 460:81–84
    [Google Scholar]
  313. 313. 
    Maksymovych P, Jesse S, Yu P, Ramesh R, Baddorf AP, Kalinin SV 2009. Science 324:59331421–25
    [Google Scholar]
  314. 314. 
    Bilc DI, Novaes FD, Íñiguez J, Ordejón P, Ghosez P. 2012. ACS Nano 6:21473–78
    [Google Scholar]
  315. 315. 
    Velev JP, Duan CG, Burton JD, Smogunov A, Niranjan MK et al. 2009. Nano Lett. 9:1427–32
    [Google Scholar]
  316. 316. 
    Burton JD, Tsymbal EY. 2011. Phys. Rev. Lett. 106:157203
    [Google Scholar]
  317. 317. 
    Bibes M, Villegas JE, Barthélémy A. 2011. Adv. Phys. 60:15–84
    [Google Scholar]
  318. 318. 
    Tsymbal E, Gruverman A, Garcia V, Bibes M, Barthélémy A. 2012. MRS Bull. 37:2138–43
    [Google Scholar]
  319. 319. 
    Sai N, Meyer B, Vanderbilt D. 2000. Phys. Rev. Lett. 84:5636–39
    [Google Scholar]
  320. 320. 
    Nakhmanson SM, Rabe KM, Vanderbilt D. 2005. Appl. Phys. Lett. 87:102906
    [Google Scholar]
  321. 321. 
    Lee HN, Christen HM, Chisholm MF, Rouleau CM, Lowndes DH. 2005. Nature 433:395–99
    [Google Scholar]
  322. 322. 
    Hong Z, Chen LQ. 2019. Acta Mater. 164:493–98
    [Google Scholar]
  323. 323. 
    Yamada H, Kawasaki M, Ogawa Y, Tokura Y. 2002. Appl. Phys. Lett. 81:254793–95
    [Google Scholar]
  324. 324. 
    Zanolli Z, Wojdel JC, Niguez JI, Ghosez P. 2013. Phys. Rev. B 88:060102(R)
    [Google Scholar]
  325. 325. 
    Bristowe NC, Varignon J, Fontaine D, Bousquet E, Ghosez P. 2015. Nat. Commun. 6:6677
    [Google Scholar]
  326. 326. 
    Etxebarria I, Perez-Mato JM, Boullay P. 2010. Ferroelectrics 401:17–23
    [Google Scholar]
  327. 327. 
    Zubko P, Gariglio S, Gabay M, Ghosez P, Triscone JM. 2011. Annu. Rev. Condens. Matter Phys. 2:141–65
    [Google Scholar]
  328. 328. 
    Spreitzer M, Klement D, Parkelj Potofnik T, Trstenjak U, Jovanovi Z et al. 2021. APL Mater. 9:4040701
    [Google Scholar]
  329. 329. 
    Zhang X, Demkov AA, Li H, Hu X, Wei Y, Kulik J. 2003. Phys. Rev. B 68:12125323
    [Google Scholar]
  330. 330. 
    Reiner JW, Kolpak AM, Segal Y, Garrity KF, Ismail-Beigi S et al. 2010. Adv. Mater. 22:26–272919–38
    [Google Scholar]
  331. 331. 
    Garrity KF, Kolpak AM, Ismail-Beigi S. 2012. J. Mater. Sci. 47:7417
    [Google Scholar]
  332. 332. 
    Demkov AA, Ponath P, Fredrickson K, Posadas AB, McDaniel MD et al. 2015. Microelectron. Eng. 147:285–89
    [Google Scholar]
  333. 333. 
    Kolpak AM, Ismail-Beigi S. 2012. Phys. Rev. B 85:19195318
    [Google Scholar]
  334. 334. 
    Kolpak AM, Walker FJ, Reiner JW, Segal Y, Su D et al. 2010. Phys. Rev. Lett. 105:217601
    [Google Scholar]
  335. 335. 
    Yu HL, Wu YZ, Jiang XF, Cai MQ, Gu LP, Yang GW. 2013. J. Appl. Phys. 114:17173502
    [Google Scholar]
  336. 336. 
    Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK 2009. Rev. Mod. Phys. 81:1109–62
    [Google Scholar]
  337. 337. 
    Ding J, Wen LW, Li HD, Kang XB, Zhang JM. 2013. Europhys. Lett. 104:117009
    [Google Scholar]
  338. 338. 
    Zanolli Z. 2016. Sci. Rep. 6:31346
    [Google Scholar]
  339. 339. 
    Wang J, Zhang Y, Sahoo MPK, Shimada T, Kitamura T et al. 2018. Sci. Rep. 8:12448
    [Google Scholar]
  340. 340. 
    Zhang Y, He X, Sun M, Wang J, Ghosez P. 2020. Nanoscale 12:85067–74
    [Google Scholar]
  341. 341. 
    Volonakis G, Giustino F. 2015. J. Phys. Chem. Lett. 6:132496–502
    [Google Scholar]
  342. 342. 
    Kakekhani A, Ismail-Beigi S, Altman EI. 2016. Surf. Sci. 650:302–16
    [Google Scholar]
  343. 343. 
    Li Y, Li J, Yang W, Wang X 2020. Nanoscale Horiz. 5:81174–87
    [Google Scholar]
  344. 344. 
    Li D, Zhao MH, Garra J, Kolpak AM, Rappe AM et al. 2008. Nat. Mater. 7:473–77
    [Google Scholar]
  345. 345. 
    Kakekhani A, Ismail-Beigi S. 2015. ACS Catal. 5:84537–45
    [Google Scholar]
  346. 346. 
    Efe I, Spaldin NA, Gattinoni C. 2021. J. Chem. Phys. 154:024702
    [Google Scholar]
  347. 347. 
    Padilla J, Zhong W, Vanderbilt D. 1996. Phys. Rev. B 53:10R5969–73
    [Google Scholar]
  348. 348. 
    Meyer B, Vanderbilt D. 2002. Phys. Rev. B 65:104111
    [Google Scholar]
  349. 349. 
    Lai BK, Ponomareva I, Kornev I, Bellaiche L, Salamo G. 2007. Appl. Phys. Lett. 91:15152909
    [Google Scholar]
  350. 350. 
    Prosandeev S, Lisenkov S, Bellaiche L. 2010. Phys. Rev. Lett. 105:14147603
    [Google Scholar]
  351. 351. 
    Seidel J, Martin LW, He Q, Zhan Q, Chu YH et al. 2009. Nat. Mater. 8:229–34
    [Google Scholar]
  352. 352. 
    Guyonnet J, Gaponenko I, Gariglio S, Paruch P. 2011. Adv. Mater. 23:5377–82
    [Google Scholar]
  353. 353. 
    Diéguez O, Aguado-Puente P, Junquera J, Íñiguez J. 2013. Phys. Rev. B 87:2024102
    [Google Scholar]
  354. 354. 
    Wojdeł JC, Íñiguez J. 2014. Phys. Rev. Lett. 112:24247603
    [Google Scholar]
  355. 355. 
    Avrami M. 1940. J. Chem. Phys. 8:2212–24
    [Google Scholar]
  356. 356. 
    Ishibashi Y, Takagi Y. 1971. J. Phys. Soc. Jpn. 31:2506–10
    [Google Scholar]
  357. 357. 
    Bune AV, Fridkin VM, Ducharme S, Blinov LM, Palto SP et al. 1998. Nature 391:874–77
    [Google Scholar]
  358. 358. 
    Highland MJ, Fister TT, Richard MI, Fong DD, Fuoss PH et al. 2010. Phys. Rev. Lett. 105:167601
    [Google Scholar]
  359. 359. 
    Liu S, Grinberg I, Rappe AM. 2016. Nature 534:7607360–63
    [Google Scholar]
  360. 360. 
    Xu B, Garcia V, Fusil S, Bibes M, Bellaiche L. 2017. Phys. Rev. B 95:10104104
    [Google Scholar]
  361. 361. 
    Wang RV, Fong DD, Jiang F, Highland MJ, Fuoss PH et al. 2009. Phys. Rev. Lett. 102:4047601
    [Google Scholar]
  362. 362. 
    Tagantsev AK, Cross LE, Fousek J. 2010. Domains in Ferroic Crystals and Thin Films New York: Springer
    [Google Scholar]
  363. 363. 
    Íñiguez J, Zubko P, Luk'yanchuk I, Cano A 2019. Nat. Rev. Mater. 4:4243–56
    [Google Scholar]
  364. 364. 
    Yadav AK, Nelson CT, Hsu SL, Hong Z, Clarkson JD et al. 2016. Nature 530:7589198–201
    [Google Scholar]
  365. 365. 
    Mermin ND. 1979. Rev. Mod. Phys. 51:3591–648
    [Google Scholar]
  366. 366. 
    Nahas Y, Prokhorenko S, Louis L, Gui Z, Kornev I, Bellaiche L. 2015. Nat. Commun. 6:18542
    [Google Scholar]
  367. 367. 
    Shafer P, García-Fernández P, Aguado-Puente P, Damodaran AR, Yadav AK et al. 2018. PNAS 115:5915–20
    [Google Scholar]
  368. 368. 
    Yadav AK, Nguyen KX, Hong Z, García-Fernández P, Aguado-Puente P et al. 2019. Nature 565:7740468–71
    [Google Scholar]
  369. 369. 
    Das S, Hong Z, Stoica VA, Gonçalves MAP, Shao YT et al. 2021. Nat. Mater. 20:2194–201
    [Google Scholar]
  370. 370. 
    Zhao HJ, Prosandeev S, Artyukhin S, Bellaiche L. 2021. Nat. Mater. 20:341–45
    [Google Scholar]
  371. 371. 
    Catalan G, Seidel J, Ramesh R, Scott JF 2012. Rev. Mod. Phys. 84:119–56
    [Google Scholar]
  372. 372. 
    Hill NA. 2000. J. Phys. Chem. B 104:296694–709
    [Google Scholar]
  373. 373. 
    Matthias BT. 1949. Phys. Rev. 75:111771
    [Google Scholar]
  374. 374. 
    Wang J, Neaton JB, Zheng H, Nagarajan V, Ogale SB et al. 2003. Science 299:56131719–22
    [Google Scholar]
  375. 375. 
    Catalan G, Scott JF. 2009. Adv. Mater. 21:242463–85
    [Google Scholar]
  376. 376. 
    Fennie CJ, Rabe KM. 2006. Phys. Rev. Lett. 97:26267602
    [Google Scholar]
  377. 377. 
    Khomskii D. 2009. Physics 2:20
    [Google Scholar]
  378. 378. 
    Bousquet E, Cano A. 2016. J. Phys. Condens. Matter 28:12123001
    [Google Scholar]
  379. 379. 
    Fiebig M, Lottermoser T, Meier D, Trassin M. 2016. Nat. Rev. Mater. 1:816046
    [Google Scholar]
  380. 380. 
    Spaldin NA, Ramesh R 2019. Nat. Mater. 18:203–12
    [Google Scholar]
  381. 381. 
    Varignon J, Bristowe NC, Bousquet E, Ghosez P. 2021. Multiferroics: Fundamentals and Applications A Cano, D Meier, M Trassin 293–334 Berlin, Ger: de Gruyter
    [Google Scholar]
  382. 382. 
    Wang Y, Liu X, Burton JD, Jaswal SS, Tsymbal EY. 2012. Phys. Rev. Lett. 109:24247601
    [Google Scholar]
  383. 383. 
    Zhao HJ, Filippetti A, Escorihuela-Sayalero C, Delugas P, Canadell E et al. 2018. Phys. Rev. B 97:5054107
    [Google Scholar]
  384. 384. 
    Hickox-Young D, Puggioni D, Rondinelli JM. 2020. Phys. Rev. B 102:1014108
    [Google Scholar]
  385. 385. 
    He X, Jin K 2016. Phys. Rev. B 94:22224107
    [Google Scholar]
  386. 386. 
    Benedek NA, Birol T. 2016. J. Mater. Chem. C 4:184000–15
    [Google Scholar]
  387. 387. 
    He X, Jin K, Guo H, Ge C 2016. Phys. Rev. B 93:17174110
    [Google Scholar]
  388. 388. 
    Janotti A, Jalan B, Stemmer S, Van de Walle CG. 2012. Appl. Phys. Lett. 100:26262104
    [Google Scholar]
  389. 389. 
    Bruneval F, Varvenne C, Crocombette JP, Clouet E. 2015. Phys. Rev. B 91:2024107
    [Google Scholar]
  390. 390. 
    Anderson PW, Blount EI. 1965. Phys. Rev. Lett. 14:7217–19
    [Google Scholar]
  391. 391. 
    Lu J, Chen G, Luo W, Íñiguez J, Bellaiche L, Xiang H. 2019. Phys. Rev. Lett. 122:22227601
    [Google Scholar]
  392. 392. 
    Zabalo A, Stengel M. 2021. Phys. Rev. Lett. 126:12127601
    [Google Scholar]
  393. 393. 
    Dreyer CE, Coh S, Stengel M. 2021. arXiv:2103.04425
  394. 394. 
    Puggioni D, Rondinelli JM. 2014. Nat. Mater. 5:3432
    [Google Scholar]
  395. 395. 
    Puggioni D, Giovannetti G, Rondinelli JM. 2018. J. Appl. Phys. 124:17174102
    [Google Scholar]
  396. 396. 
    Shi Y, Guo Y, Wang X, Princep AJ, Khalyavin D et al. 2013. Nat. Mater. 12:1024
    [Google Scholar]
  397. 397. 
    Ma C, He X, Jin K 2017. Phys. Rev. B 96:3035140
    [Google Scholar]
  398. 398. 
    Cao Y, Wang Z, Park SY, Yuan Y, Liu X et al. 2018. Nat. Commun. 9:1547
    [Google Scholar]
  399. 399. 
    Picozzi S. 2014. Front. Phys. 2:10
    [Google Scholar]
  400. 400. 
    Di Sante D, Barone P, Bertacco R, Picozzi S. 2013. Adv. Mater. 25:4509–13
    [Google Scholar]
  401. 401. 
    da Silveira LGD, Barone P, Picozzi S. 2016. Phys. Rev. B 93:24245159
    [Google Scholar]
  402. 402. 
    Djani H, Garcia-Castro AC, Tong WY, Barone P, Bousquet E et al. 2019. NPJ Quantum Mater. 4:51
    [Google Scholar]
  403. 403. 
    Yamauchi K, Barone P, Picozzi S. 2019. Phys. Rev. B 100:24245115
    [Google Scholar]
  404. 404. 
    Young SM, Rappe AM. 2012. Phys. Rev. Lett. 109:11116601
    [Google Scholar]
  405. 405. 
    Young SM, Zheng F, Rappe AM. 2012. Phys. Rev. Lett. 109:23236601
    [Google Scholar]
  406. 406. 
    Yang SY, Seidel J, Byrnes SJ, Shafer P, Yang CH et al. 2010. Nat. Nanotechnol. 5:2143–47
    [Google Scholar]
  407. 407. 
    Paillard C, Xu B, Dkhil B, Geneste G, Bellaiche L. 2016. Phys. Rev. Lett. 116:24247401
    [Google Scholar]
  408. 408. 
    Paillard C, Torun E, Wirtz L, Íñiguez J, Bellaiche L. 2019. Phys. Rev. Lett. 123:8087601
    [Google Scholar]
  409. 409. 
    Kutnjak Z, Rožič B, Pirc R 2015. Wiley Encyclopedia of Electrical and Electronics Engineering JG Webster Hoboken, NJ: John Wiley & Sons https://doi.org/10.1002/047134608X.W8244
    [Crossref] [Google Scholar]
  410. 410. 
    Marathe M, Grünebohm A, Nishimatsu T, Entel P, Ederer C. 2016. Phys. Rev. B 93:054110
    [Google Scholar]
  411. 411. 
    Herchig R, Chang CM, Mani BK, Ponomareva I. 2015. Sci. Rep. 5:117294
    [Google Scholar]
  412. 412. 
    Glazkova E, Chang CM, Lisenkov S, Mani BK, Ponomareva I. 2015. Phys. Rev. B 92:6064101
    [Google Scholar]
  413. 413. 
    Cazorla C, Íñiguez J. 2018. Phys. Rev. B 98:17174105
    [Google Scholar]
  414. 414. 
    Cazorla C. 2020. arXiv:2005.04846
  415. 415. 
    Kittel C. 1951. Phys. Rev. 82:5729–32
    [Google Scholar]
  416. 416. 
    Sawaguchi E, Maniwa H, Hoshino S. 1951. Phys. Rev. 83:51078
    [Google Scholar]
  417. 417. 
    Shirane G, Sawaguchi E, Takagi Y. 1951. Phys. Rev. 84:3476–81
    [Google Scholar]
  418. 418. 
    Jona F, Shirane G 1962. Ferroelectric Crystals Oxford/London/New York/Paris: Pergamon
    [Google Scholar]
  419. 419. 
    Rabe KM 2013. Functional Metal Oxides: New Science and Novel Applications SB Ogale, TV Venkatesan, MG Blamire 221–44 Weinheim, Ger: Wiley-VCH
    [Google Scholar]
  420. 420. 
    Tolédano P, Guennou M. 2016. Phys. Rev. B 94:1014107
    [Google Scholar]
  421. 421. 
    Djani H, McCabe EE, Zhang W, Halasyamani PS, Feteira A et al. 2020. Phys. Rev. B 101:134113
    [Google Scholar]
  422. 422. 
    Singh DJ. 1995. Phys. Rev. B 52:1712559–63
    [Google Scholar]
  423. 423. 
    Waghmare UV, Rabe KM. 1997. Ferroelectrics 194:135–47
    [Google Scholar]
  424. 424. 
    Tagantsev AK, Vaideeswaran K, Vakhrushev SB, Filimonov AV, Burkovsky RG et al. 2013. Nat. Commun. 4:2229
    [Google Scholar]
  425. 425. 
    Íñiguez J, Stengel M, Prosandeev S, Bellaiche L. 2014. Phys. Rev. B 90:22220103
    [Google Scholar]
  426. 426. 
    Aramberri H, Cazorla C, Stengel M, Íñiguez J. 2021. arXiv:2107.09685
  427. 427. 
    Baker JS, Paściak M, Shenton JK, Vales-Castro P, Xu B et al. 2021. arXiv:2102.08856
  428. 428. 
    Afanasiev D, Hortensius JR, Ivanov BA, Sasani A, Bousquet E et al. 2021. Nat. Mater. 20:607–11
    [Google Scholar]
  429. 429. 
    Khalsa G, Benedek NA. 2018. NPJ Quantum Mater. 3:115
    [Google Scholar]
  430. 430. 
    Li X, Qiu T, Zhang J, Baldini E, Lu J et al. 2019. Science 364:64451079–82
    [Google Scholar]
  431. 431. 
    Khalsa G, Benedek NA, Moses J 2021. Phys. Rev. X 11:021067
    [Google Scholar]
  432. 432. 
    He L, Vanderbilt D. 2003. Phys. Rev. B 68:134103
    [Google Scholar]
  433. 433. 
    Yang Q, Cao JX, Zhou YC, Zhang Y, Ma Y, Lou XJ. 2013. Appl. Phys. Lett. 103:14142911
    [Google Scholar]
  434. 434. 
    Aschauer U, Pfenninger R, Selbach SM, Grande T, Spaldin NA. 2013. Phys. Rev. B 88:5054111
    [Google Scholar]
  435. 435. 
    Zhou Z, Chu D, Cazorla C. 2021. Sci. Rep. 11:11499
    [Google Scholar]
  436. 436. 
    Lee HJ, Lee M, Lee K, Jo J, Yang H et al. 2020. Science 369:65091343–47
    [Google Scholar]
  437. 437. 
    Xu X, Huang FT, Qi Y, Singh S, Rabe KM et al. 2021. Nat. Mater. 20:826
    [Google Scholar]
  438. 438. 
    Guan Z, Hu H, Shen X, Xiang P, Zhong N et al. 2020. Adv. Electron. Mater. 6:11900818
    [Google Scholar]
  439. 439. 
    Qi L, Ruan S, Zeng YJ. 2021. Adv. Mater. 33:132005098
    [Google Scholar]
  440. 440. 
    Royo M, Stengel M. 2021. arXiv:2012.07961
  441. 441. 
    Springolo M, Royo M, Stengel M. 2021. Phys. Rev. Lett. 127:216801
    [Google Scholar]
  442. 442. 
    Griffin SM, Lilienblum M, Delaney KT, Kumagai Y, Fiebig M, Spaldin NA. 2012. Phys. Rev. X 2:4041022
    [Google Scholar]
  443. 443. 
    Prosandeev S, Grollier J, Talbayev D, Dkhil B, Bellaiche L. 2021. Phys. Rev. Lett. 126:2027602
    [Google Scholar]
  444. 444. 
    Skyrme THR. 1961. Proc. R. Soc. Lond. A 260:127–38
    [Google Scholar]
/content/journals/10.1146/annurev-conmatphys-040220-045528
Loading
/content/journals/10.1146/annurev-conmatphys-040220-045528
Loading

Data & Media loading...

  • Article Type: Review Article