Skip to main content
SpringerLink
Log in

Cooperative magnetic phenomena in artificial spin systems: spin liquids, Coulomb phase and fragmentation of magnetism – a colloquium

  • Colloquium
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Two-dimensional arrays of interacting magnetic nanostructures offer a remarkable playground for simulating, experimentally, lattice spin models. Initially designed to capture the low-energy physics of highly frustrated magnets, they quickly became a lab-on-chip platform to investigate cooperative magnetic phenomena often associated with classical frustrated magnetism. This article reviews the many-body physics which can be visualized, directly in real space, through the magnetic imaging of artificial arrays of magnetic nanostructures. Particular attention is paid to classical spin liquid states, magnetic Coulomb phases and magnetic moment fragmentation. Other phenomena, such as complex magnetic ordering, charge crystallization and monopole-like excitations, are also described in light of the recent advances in the field.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Runge, B. Pannetier, EuroPhys. Lett. 24, 737 (1993)

    ADS  Google Scholar 

  2. D. Davidović, S. Kumar, D.H. Reich, J. Siegel, S.B. Field, R.C. Tiberio, R. Hey, K. Ploog, Phys. Rev. Lett. 76, 815 (1996)

    ADS  Google Scholar 

  3. D. Davidović, S. Kumar, D.H. Reich, J. Siegel, S.B. Field, R.C. Tiberio, R. Hey, K. Ploog, Phys. Rev. B 55, 214521 (1997)

    Google Scholar 

  4. E. Serret, P. Butaud, B. Pannetier, EuroPhys. Lett. 59, 225 (2002)

    ADS  Google Scholar 

  5. J.R. Kirtley, C.C. Tsuei, A. Ariando, H.J.H. Smilde, H. Hilgenkamp, Phys. Rev. B 72, 6518 (2005)

    Google Scholar 

  6. J. Trastoy, M. Malnou, C. Ulysse, R. Bernard, N. Bergeal, G. Faini, J. Lesueur, J. Briatico, J.E. Villegas, Nat. Nanotechnol. 9, 710 (2014)

    ADS  Google Scholar 

  7. J.-Y. Ge, V.N. Gladilin, J. Tempere, V.S. Zharinov, J. Van de Vondel, J.T. Devreese, V.V. Moshchalkov, Phys. Rev. B 96, 134515 (2017)

    ADS  Google Scholar 

  8. E. Olive, P. Molho, Phys. Rev B 58, 9238 (1998)

    ADS  Google Scholar 

  9. E.Y. Vedmedenko, H.P. Oepen, J. Kirschner, Phys. Rev. Lett. 90, 137203 (2003)

    ADS  Google Scholar 

  10. P. Mellado, A. Concha, L. Mahadevan, Phys. Rev. Lett. 109, 257203 (2012)

    ADS  Google Scholar 

  11. E. Ganz, F. Xiong, I.-S. Hwang, J. Golovchenko, Phys. Rev. B 43, 7316 (1991)

    ADS  Google Scholar 

  12. J.M. Carpinelli, H.H. Weitering, E.W. Plummer, Surf. Sci. 401, L457 (1998)

    ADS  Google Scholar 

  13. B. Ressel, J. Slezák, K.C. Prince, V. Cháb, Phys. Rev. B 66, 035325 (2002)

    ADS  Google Scholar 

  14. L. Ottaviano, C. Di Teodoro, S. Santucci, G. Profeta, Phys. Low-Dimens. Struct. 3/4, 149 (2003)

    Google Scholar 

  15. L. Ottaviano, B. Ressel, C. Di Teodoro, G. Profeta, S. Santucci, V. Cháb, K.C. Prince, Phys. Rev. B, 67, 045401 (2003)

    ADS  Google Scholar 

  16. M. Tanaka, E. Saitoh, H. Miyajima, T. Yamaoka, Y. Iye, J. Appl. Phys. 97, 10J710 (2005)

    Google Scholar 

  17. M. Tanaka, E. Saitoh, H. Miyajima, T. Yamaoka, Y. Iye, Phys. Rev. B, 73, 052411 (2006)

    ADS  Google Scholar 

  18. R.F. Wang, C. Nisoli, R.S. Freitas, J. Li, W. McConville, B.J. Cooley, M.S. Lund, N. Samarth, C. Leighton, V.H. Crespi, P. Schiffer, Nature 439, 303 (2006)

    ADS  Google Scholar 

  19. A. Libal, C. Reichhardt, C.J. Olson Reichhardt, Phys. Rev. Lett. 97, 228302 (2006)

    ADS  Google Scholar 

  20. Y. Han, Y. Shokef, A.M. Alsayed, P. Yunker, T.C. Lubensky, A.G. Yodh, Nature 456, 898 (2008)

    ADS  Google Scholar 

  21. C.J.O. Reichhardt, A. Libal, C. Reichhardt, New J. Phys. 14, 025006 (2012)

    Google Scholar 

  22. J. Loehr, A. Ortiz-Ambriz, P. Tierno, Phys. Rev. Lett. 117, 168001 (2016)

    ADS  Google Scholar 

  23. A. Ortiz-Ambriz, P. Tierno, Nat. Commun. 7, 10575 (2016)

    ADS  Google Scholar 

  24. G. Toulouse, Commun. Phys. 2, 115 (1977)

    Google Scholar 

  25. J. Vannimenus, G. Toulouse, J. Phys. C: Solid State Phys. 10, L537 (1977)

    ADS  Google Scholar 

  26. G. Toulouse, in The Frustration Model (Springer, Berlin, Heidelberg, 1980), Vol. 115

  27. A.Y. Klimenko, Open Thermodyn. J. 6, 1 (2012)

    Google Scholar 

  28. S.T. Bramwell, M.J.P. Gingras, P.C.W. Holdsworth, Spin Ice (World Scientific, Singapore, 2013)

  29. C. Nisoli, R. Moessner, P. Schiffer, Rev. Mod. Phys. 85, 1473 (2013)

    ADS  Google Scholar 

  30. C. Nisoli, Topology by design in magnetic nano-materials: artificial spin ice. https://doi.org/arXiv:1711.00921v1 (2017)

  31. C.H. Marrows, Experimental studies of artificial spin ice. https://doi.org/arXiv:1611.00744v1 (2017)

  32. L.J. Heyderman, R.L. Stamps, J. Phys.: Condens. Matter 25, 363201 (2013)

    Google Scholar 

  33. R.F. Wang, J. Li, W. McConville, C. Nisoli, X. Ke, J.W. Freeland, V. Rose, M. Grimsditch, P. Lammert, V.H. Crespi, P. Schiffer, J. Appl. Phys. 101, 09J104 (2007)

    Google Scholar 

  34. C. Nisoli, R.F. Wang, J. Li, W.F. McConville, P.E. Lammert, P. Schiffer, V.H. Crespi, Phys. Rev. Lett. 98, 217203 (2007)

    ADS  Google Scholar 

  35. X. Ke, J. Li, C. Nisoli, P.E. Lammert, W. McConville, R.F. Wang, V.H. Crespi, P. Schiffer, Phys. Rev. Lett. 101, 037205 (2008)

    ADS  Google Scholar 

  36. E. Mengotti, L.J. Heyderman, A. Fraile Rodriguez, A. Bisig, L. Le Guyader, F. Nolting, H.B. Braun, Phys. Rev. B 78, 144402 (2008)

    ADS  Google Scholar 

  37. J. Li, X. Ke, S. Zhang, D. Garand, C. Nisoli, P. Lammert, V.H. Crespi, P. Schiffer, Phys. Rev. B 81, 092406 (2010)

    ADS  Google Scholar 

  38. J.P. Morgan, A. Bellew, A. Stein, S. Langridge, C.H. Marrows, Front. Phys. 1, 28 (2013)

    Google Scholar 

  39. N. Rougemaille, F. Montaigne, B. Canals, A. Duluard, D. Lacour, M. Hehn, R. Belkhou, O. Fruchart, S. El Moussaoui, A. Bendounan, F. Maccherozzi, Phys. Rev. Lett. 106, 057209 (2011)

    ADS  Google Scholar 

  40. R.H. Swendsen, J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987)

    ADS  Google Scholar 

  41. U. Wolff, Phys. Rev. Lett. 62, 361 (1989)

    ADS  Google Scholar 

  42. R.G. Melko, M.J.P. Gingras, J. Phys.: Condens. Matter 16, R1277 (2004)

    ADS  Google Scholar 

  43. S.A. Daunheimer, O. Petrova, O. Tchernyshyov, J. Cumings, Phys. Rev. Lett. 107, 167201 (2011)

    ADS  Google Scholar 

  44. Z. Budrikis, P. Politi, R.L. Stamps, J. Appl. Phys. 111, 07E109 (2012)

    Google Scholar 

  45. Z. Budrikis, P. Politi, R.L. Stamps, New J. Phys. 14, 045008 (2012)

    ADS  Google Scholar 

  46. Z. Budrikis, J.P. Morgan, J. Akerman, A. Stein, P. Politi, S. Langridge, C.H. Marrows, R.L. Stamps, Phys. Rev. Lett. 109, 037203 (2012)

    ADS  Google Scholar 

  47. Z. Budrikis, J.P. Morgan, J. Akerman, A. Stein, P. Politi, S. Langridge, C.H. Marrows, R.L. Stamps, Erratum: Disorder strength and field-driven ground state domain formation in artificial spin ice: Experiment, simulation, and theory (vol 109, 037203, pg 2012). Phys. Rev. Lett. 110 (2013)

  48. J.P. Morgan, A. Stein, S. Langridge, C.H. Marrows, Nat. Phys. 7, 75 (2011)

    Google Scholar 

  49. J. Cumings, Nat. Phys. 7, 7 (2011)

    Google Scholar 

  50. J.P. Morgan, J. Akerman, A. Stein, C. Phatak, R.M.L. Evans, S. Langridge, C.H. Marrows, Phys. Rev. B 87, 024405 (2013)

    ADS  Google Scholar 

  51. A. Farhan, P.M. Derlet, A. Kleibert, A. Balan, R.V. Chopdekar, M. Wyss, L. Anghinolfi, F. Nolting, L.J. Heyderman, Nat. Phys. 9, 375 (2013)

    Google Scholar 

  52. C. Marrows, Nat. Phys. 9, 324 (2013)

    Google Scholar 

  53. A. Farhan, P.M. Derlet, A. Kleibert, A. Balan, R.V. Chopdekar, M. Wyss, J. Perron, A. Scholl, F. Nolting, L.J. Heyderman, Phys. Rev. Lett. 111, 057204 (2013)

    ADS  Google Scholar 

  54. A. Farhan, A. Kleibert, P.M. Derlet, L. Anghinolfi, A. Balan, R.V. Chopdekar, M. Wyss, S. Gliga, F. Nolting, L.J. Heyderman, Phys. Rev. B 89, 214405 (2014)

    ADS  Google Scholar 

  55. L. Anghinolfi, H. Luetkens, J. Perron, M.G. Flokstra, O. Sendetskyi, A. Suter, T. Prokscha, P.M. Derlet, S.L. Lee, L.J. Heyderman, Nat. Commun. 6, 8278 (2015)

    ADS  Google Scholar 

  56. U.B. Arnalds, J. Chico, H. Stopfel, V. Kapaklis, O. Barenbold, M.A. Verschuuren, U. Wolff, V. Neu, A. Bergman, B. Hjörvarsson, New J. Phys. 18, 023008 (2016)

    ADS  Google Scholar 

  57. O. Sendetskyi, L. Anghinolfi, V. Scagnoli, G. Moller, N. Leo, A. Alberca, J. Kohlbrecher, J. Luning, U. Staub, L.J. Heyderman, Phys. Rev. B 93, 224413 (2016)

    ADS  Google Scholar 

  58. S.A. Morley, D. Alba Venero, J.M. Porro, S.T. Riley, A. Stein, P. Steadman, R.L. Stamps, S. Langridge, C.H. Marrows, Phys. Rev. B 95, 104422 (2017)

    ADS  Google Scholar 

  59. V. Kapaklis, U.B. Arnalds, A. Harman-Clarke, E.Th. Papaioannou, M. Karimipour, P. Korelis, A. Taroni, P.C.W. Holdsworth, S.T. Bramwell, B. Hjörvarsson, New J. Phys. 14, 035009 (2012)

    ADS  Google Scholar 

  60. U.B. Arnalds, A. Farhan, R.V. Chopdekar, V. Kapaklis, A. Balan, E. Th. Papaioannou, M. Ahlberg, F. Nolting, L.J. Heyderman, B. Hjörvarsson, Appl. Phys. Lett. 101, 112404 (2012)

    ADS  Google Scholar 

  61. J.M. Porro, A. Bedoya-Pinto, A. Berger, P. Vavassori, New J. Phys. 15, 055012 (2013)

    ADS  Google Scholar 

  62. S. Zhang, I. Gilbert, C. Nisoli, G.-W. Chern, M.J. Erickson, L. O’Brien, C. Leighton, P.E. Lammert, V.H. Crespi, P. Schiffer, Nature 500, 553 (2013)

    ADS  Google Scholar 

  63. L.J. Heyderman, Nat. Nanotechnol. 8, 705 (2013)

    ADS  Google Scholar 

  64. V. Kapaklis, U.B. Arnalds, A. Farhan, R.V. Chopdekar, A. Balan, A. Scholl, L.J. Heyderman, B. Hjörvarsson, Nat. Nanotechnol. 9, 514 (2014)

    ADS  Google Scholar 

  65. F. Montaigne, D. Lacour, I.A. Chioar, N. Rougemaille, D. Louis, S. Mc Murtry, H. Riahi, B. Santos Burgos, T.O. Mentes, A. Locatelli, B. Canals, M. Hehn, Sci. Rep. 4, 5702 (2014)

    Google Scholar 

  66. U.B. Arnalds, M. Ahlberg, M.S. Brewer, V. Kapaklis, E.Th. Papaioannou, M. Karimipour, P. Korelis, A. Stein, S. Olafsson, T.P.A. Hase, B. Hjörvarsson, Appl. Phys. Lett. 105, 042409 (2014)

    ADS  Google Scholar 

  67. I.A. Chioar, B. Canals, D. Lacour, M. Hehn, B. Santos Burgos, T.O. Mentes, A. Locatelli, F. Montaigne, N. Rougemaille, Phys. Rev. B 90, 220407(R) (2014)

    ADS  Google Scholar 

  68. J. Drisko, S. Daunheimer, J. Cumings, Phys. Rev. B 91, 224406 (2015)

    ADS  Google Scholar 

  69. B. Canals, I.-A. Chioar, V.-D. Nguyen, M. Hehn, D. Lacour, F. Montaigne, A. Locatelli, T.O. Mentes, B. Santos Burgos, N. Rougemaille, Nat. Commun. 7, 11446 (2016)

    ADS  Google Scholar 

  70. M.S. Andersson, S.D. Pappas, H. Stopfel, E. Ostman, A. Stein, P. Nordblad, R. Mathieu, B. Hjörvarsson, V. Kapaklis, Sci. Rep. 6, 37097 (2016)

    ADS  Google Scholar 

  71. P. Fendley, J. Phys. A: Math. Gen. 39, 15445 (2006)

    Google Scholar 

  72. C. Nisoli, J. Li, X. Ke, D. Garand, P. Schiffer, V.H. Crespi, Phys. Rev. Lett. 105, 047205 (2010)

    ADS  Google Scholar 

  73. J.T. Chalker, Spin liquids and frustrated magnetism, 2010

  74. L. Balents, Nature 464, 199 (2010)

    ADS  Google Scholar 

  75. G. Misguich, in Quantum Spin Liquids and Fractionalization in Introduction to Frustrated Magnetism, edited by C. Lacroix, P. Mendels, F. Mila (Springer, New York, 2011), Vol. 164

  76. M.E. Brooks-Bartlett, S.T. Banks, L.D.C. Jaubert, A. Harman-Clarke, P.C.W. Holdsworth, Phys. Rev. X 4, 011007 (2014)

    Google Scholar 

  77. L.D.C. Jaubert, SPIN 5, 1540005 (2015)

    ADS  Google Scholar 

  78. G.H. Wannier, Phys. Rev. 79, 357 (1950)

    ADS  MathSciNet  Google Scholar 

  79. I. Syôzi, Progr. Theor. Phys. 6, 306 (1951)

    ADS  MathSciNet  Google Scholar 

  80. K. Kanô, S. Naya, Progr. Theor. Phys. 10, 158 (1953)

    ADS  Google Scholar 

  81. G. Möller, R. Moessner, Phys. Rev. B 80, 140409 (2009)

    Google Scholar 

  82. G.-W. Chern, P. Mellado, O. Tchernyshyov, Phys. Rev. Lett. 106, 207202 (2011)

    ADS  Google Scholar 

  83. J. Villain, Z. Phys. B Condens. Matter 33, 31 (1979)

    ADS  Google Scholar 

  84. J.F. Nagle, J. Math. Phys. 7, 1484 (1966)

    ADS  Google Scholar 

  85. E.H. Lieb, Phys. Rev. Lett. 18, 692 (1967)

    ADS  Google Scholar 

  86. J.D. Bernal, R.H. Fowler, J. Chem. Phys. 1, 515 (1933)

    ADS  Google Scholar 

  87. L. Pauling, J. Am. Chem. Soc. 57, 2680 (1935)

    Google Scholar 

  88. A.J. Macdonald, P.C.W. Holdsworth, R.G. Melko, J. Phys.: Condens. Matter 23, 164208 (2011)

    ADS  Google Scholar 

  89. A.S. Wills, R. Ballou, C. Lacroix, Phys. Rev. B 66, 144407 (2002)

    ADS  Google Scholar 

  90. M.J. Harris, S.T. Bramwell, D.F. McMorrow, T. Zeiske, K.W. Godfrey, Phys. Rev. Lett. 79, 2554 (1997)

    ADS  Google Scholar 

  91. R. Moessner, Phys. Rev. B 57, R5587 (1998)

    ADS  Google Scholar 

  92. I.A. Chioar, N. Rougemaille, A. Grimm, O. Fruchart, E. Wagner, M. Hehn, D. Lacour, F. Montaigne, B. Canals, Phys. Rev. B 90, 064411 (2014)

    ADS  Google Scholar 

  93. Y. Qi, T. Brintlinger, J. Cumings, Phys. Rev. B 77, 094418 (2008)

    ADS  Google Scholar 

  94. C. Castelnovo, R. Moessner, S.L. Sondhi, Nature 451, 42 (2008)

    ADS  Google Scholar 

  95. S. Zhang, J. Li, I. Gilbert, J. Bartell, M.J. Erickson, Y. Pan, P.E. Lammert, C. Nisoli, K.K. Kohli, R. Misra, V.H. Crespi, N. Samarth, C. Leighton, P. Schiffer, Phys. Rev. Lett. 109, 087201 (2012)

    ADS  Google Scholar 

  96. I.A. Chioar, N. Rougemaille, B. Canals, Phys. Rev. B 93, 214410 (2016)

    ADS  Google Scholar 

  97. B. Yee, Magnetic ordering of dipolar spin ice in mod- erate [111] field. https://doi.org/hdl.handle.net/10012/10803 (2016)

  98. J. Hamp, R. Moessner, C. Castelnovo, Phys. Rev. B 98, 144439 (2018)

    ADS  Google Scholar 

  99. Y. Perrin, B. Canals, N. Rougemaille, Nature 540, 410 (2016)

    ADS  Google Scholar 

  100. Z. Budrikis, P. Politi, R.L. Stamps, Phys. Rev. Lett. 107, 217204 (2011)

    ADS  Google Scholar 

  101. Z. Budrikis, Solid State Phys. 65, 109 (2014)

    Google Scholar 

  102. Z. Budrikis, K.L. Livesey, J.P. Morgan, J. Akerman, A. Stein, S. Langridge, C.H. Marrows, R.L. Stamps, New J. Phys. 14, 035014 (2012)

    ADS  Google Scholar 

  103. K.K. Kohli, A.L. Balk, J. Li, S. Zhang, I. Gilbert, P.E. Lammert, V.H. Crespi, P. Schiffer, N. Samarth, Phys. Rev. B 84, 180412(R) (2011)

    ADS  Google Scholar 

  104. J.P. Morgan, A. Stein, S. Langridge, C.H. Marrows, New J. Phys. 13, 105002 (2011)

    ADS  Google Scholar 

  105. C. Phatak, M. Pan, A.K. Petford-Long, S. Hong, M. De Graef, New J. Phys. 14, 075028 (2012)

    ADS  Google Scholar 

  106. J. Perron, L. Anghinolfi, B. Tudu, N. Jaouen, J.-M. Tonnerre, M. Sacchi, F. Nolting, J. Luening, L.J. Heyderman, Phys. Rev. B 88, 214424 (2013)

    ADS  Google Scholar 

  107. C. Phatak, A.K. Petford-Long, O. Heinonen, M. Tanase, M. De Graef, Phys. Rev. B 83, 174431 (2011)

    ADS  Google Scholar 

  108. S.D. Pollard, V. Volkov, Y. Zhu, Phys. Rev. B 85, 180402(R) (2012)

    ADS  Google Scholar 

  109. E.H. Lieb, Phys. Rev. 162, 162 (1967)

    ADS  Google Scholar 

  110. R.C. Silva, F.S. Nascimento, L.A.S. Mól, W.A. Moura-Melo, A.R. Pereira, New J. Phys. 14, 015008 (2012)

    ADS  Google Scholar 

  111. G.-W. Chern, M.J. Morrison, C. Nisoli, Phys. Rev. Lett. 111, 177201 (2013)

    ADS  Google Scholar 

  112. I. Gilbert, G.-W. Chern, S. Zhang, L. O’Brien, B. Fore, C. Nisoli, P. Schiffer, Nat. Phys. 10, 671 (2014)

    Google Scholar 

  113. F.S. Nascimento, L.A.S. Mól, W.A. Moura-Melo, A.R. Pereira, New J. Phys. 14, 115019 (2012)

    ADS  Google Scholar 

  114. M.J. Morrison, T.R. Nelson, C. Nisoli, New J. Phys. 15, 045009 (2013)

    ADS  Google Scholar 

  115. I.R.B. Ribeiro, F.S. Nascimento, S.O. Ferreira, W.A. Moura-Melo, C.A.R. Costa, J. Borme, P.P. Freitas, G.M. Wysin, C.I.L. de Araujo, A.R. Pereira, Sci. Rep. 7, 13982 (2017)

    ADS  Google Scholar 

  116. E. Östman, H. Stopfel, I.-A. Chioar, U.B. Arnalds, A. Stein, V. Kapaklis, B. Hjörvarsson, Nat. Phys. 14, 375 (2018)

    Google Scholar 

  117. I. Gilbert, Y. Lao, I. Carrasquillo, L. O’Brien, J.D. Watts, M. Manno, C. Leighton, A. Scholl, C. Nisoli, P. Schiffer, Nat. Phys. 12, 162 (2015)

    Google Scholar 

  118. C.L. Henley, Ann. Rev. Condens. Matter Phys. 1, 179 (2010)

    ADS  Google Scholar 

  119. C.L. Henley, Phys. Rev. B 71, 014424 (2005)

    ADS  Google Scholar 

  120. D.A. Garanin, B. Canals, Phys. Rev. B 59, 443 (1999)

    ADS  Google Scholar 

  121. B. Canals, D.A. Garanin, Eur. Phys. J. B 26, 439 (2002)

    ADS  Google Scholar 

  122. B. Canals, D.A. Garanin, Can. J. Phys. 79, 1323 (2001)

    ADS  Google Scholar 

  123. J. Villain, Solid State Commun. 10, 967 (1972)

    ADS  Google Scholar 

  124. R. Youngblood, J.D. Axe, B.M. McCoy, Phys. Rev. B 21, 5212 (1980)

    ADS  Google Scholar 

  125. M.J. Harris, M.P. Zinzin, Mod. Phys. Lett. B 10, 417 (1996)

    ADS  Google Scholar 

  126. J. Rehn, R. Moessner, Philos. Trans. R. Soc. A 374, 20160093 (2016)

    ADS  Google Scholar 

  127. F. Rys, Helv. Phys. Acta 36, 537 (1963)

    Google Scholar 

  128. E.H. Lieb, Phys. Rev. Lett. 18, 1046 (1967)

    ADS  Google Scholar 

  129. G. Möller, R. Moessner, Phys. Rev. Lett. 96, 237202 (2006)

    ADS  Google Scholar 

  130. D. Thonig, S. Reißaus, I. Mertig, J. Henk, J. Phys: Condens. Matter 26, 266006 (2014)

    Google Scholar 

  131. T. Fennell, P.P. Deen, A.R. Wildes, K. Schmalzl, D. Prabhakaran, A.T. Boothroyd, R.J. Aldus, D.F. McMorrow, S.T. Bramwell, Science 326, 415 (2009)

    ADS  Google Scholar 

  132. L.A. Mól, R.L. Silva, R.C. Silva, A.R. Pereira, W.A. Moura-Melo, B.V. Costa, J. Appl. Phys. 106, 063913 (2009)

    ADS  Google Scholar 

  133. R.C. Silva, R.J.C. Lopes, L.A.S. Mól, W.A. Moura-Melo, G.M. Wysin, A.R. Pereira, Phys. Rev. B 87, 014414 (2013)

    ADS  Google Scholar 

  134. Y.-L. Xie, Z.-Z. Du, Z.-B. Yan, J.-M. Liu, Sci. Rep. 5, 15875 (2015)

    ADS  Google Scholar 

  135. S. Ladak, D.E. Read, G.K. Perkins, L.F. Cohen, W.R. Branford, Nat. Phys. 6, 359 (2010)

    Google Scholar 

  136. E. Mengotti, L.J. Heyderman, A.F. Rodriguez, F. Nolting, R.V. Huegli, H.-B. Braun, Nat. Phys. 7, 68 (2011)

    Google Scholar 

  137. S. Ladak, D. Read, T. Tyliszczak, W.R. Branford, L.F. Cohen, New J. Phys. 13, 023023 (2011)

    ADS  Google Scholar 

  138. S. Ladak, D.E. Read, W.R. Branford, L.F. Cohen, New J. Phys. 13, 063032 (2011)

    ADS  Google Scholar 

  139. A. Schumann, P. Szary, E.Y. Vedmedenko, H. Zabel, New J. Phys. 14, 035015 (2012)

    ADS  Google Scholar 

  140. R.V. Huegli, G. Duff, B. O’Conchuir, E. Mengotti, L.J. Heyderman, A.F. Rodriguez, F. Nolting, H.-B. Braun, J. Appl. Phys. 111, 07E103 (2012)

    Google Scholar 

  141. A. Leon, Curr. Appl. Phys. 13, 2014 (2013)

    ADS  Google Scholar 

  142. K. Zeissler, S.K. Walton, S. Ladak, D.E. Read, T. Tyliszczak, L.F. Cohen, W.R. Branford, Sci. Rep. 3, 1252 (2013)

    ADS  Google Scholar 

  143. N. Rougemaille, F. Montaigne, B. Canals, M. Hehn, H. Riahi, D. Lacour, J.-C. Toussaint, New J. Phys. 15, 035026 (2013)

    ADS  Google Scholar 

  144. S. Ladak, S.K. Walton, K. Zeissler, T. Tyliszczak, D.E. Read, W.R. Branford, L.F. Cohen, New J. Phys. 14, 045010 (2012)

    ADS  Google Scholar 

  145. Y. Shen, O. Petrova, P. Mellado, S. Daunheimer, J. Cumings, O. Tchernyshyov, New J. Phys. 14, 035022 (2012)

    ADS  Google Scholar 

  146. A. Pushp, T. Phung, C. Rettner, B.P. Hughes, S.-H. Yang, L. Thomas, S.S.P. Parkin, Nat. Phys. 9, 505 (2013)

    Google Scholar 

  147. S.K. Walton, K. Zeissler, D.M. Burn, S. Ladak, D.E. Read, T. Tyliszczak, L.F. Cohen, W.R. Branford, New J. Phys. 17, 013054 (2015)

    ADS  Google Scholar 

  148. D.M. Burn, M. Chadha, W.R. Branford, Phys. Rev. B 92, 214425 (2015)

    ADS  Google Scholar 

  149. K. Zeissler, M. Chadha, E. Lovell, L.F. Cohen, W.R. Branford, Sci. Rep. 6, 30218 (2016)

    ADS  Google Scholar 

  150. D.M. Burn, M. Chadha, W.R. Branford, Phys. Rev. B 95, 104417 (2017)

    ADS  Google Scholar 

  151. P. Azaria, H.T. Diep, H. Giacomini, Phys. Rev. Lett. 59, 1629 (1987)

    ADS  MathSciNet  Google Scholar 

  152. C. Castelnovo, R. Moessner, S.L. Sondhi, Ann. Rev. Condens. Matter Phys. 3, 35 (2012)

    Google Scholar 

  153. S. Petit, E. Lhotel, B. Canals, M. Ciomaga Hatnean, J. Ollivier, H. Muttka, E. Ressouche, A.R. Wildes, M.R. Lees, G. Balakrishnan, Nat. Phys. 12, 746 (2016)

    Google Scholar 

  154. O. Benton, Phys. Rev. B 94, 104430 (2016)

    ADS  Google Scholar 

  155. J.A.M. Paddison, H.S. Ong, J.O. Hamp, P. Mukherjee, X. Bai, M.G. Tucker, N.P. Butch, C. Castelnovo, M. Mourigal, S.E. Dutton, Nat. Commun. 7, 13842 (2016)

    ADS  Google Scholar 

  156. E. Lefrançois, V. Cathelin, E. Lhotel, J. Robert, P. Lejay, C.V. Colin, B. Canals, F. Damay, J. Ollivier, B. Fak, L.C. Chapon, R. Ballou, V. Simonet, Nat. Commun. 8, 209 (2017)

    ADS  Google Scholar 

  157. C. Nisoli, V. Kapaklis, P. Schiffer, Nat. Phys. 13, 200 (2017)

    Google Scholar 

  158. V. Schánilec, Y. Perrin, S. Le Denmat, B. Canals, N. Rougemaille, Artificial vertex systems by design. unpublished.

  159. Y. Perrin, B. Canals, N. Rougemaille, Proposal to explore different variants of the six-vertex model using artificial square ice systems. unpublished.

  160. S. Gliga, A. Kakay, L.J. Heyderman, R. Hertel, O.G. Heinonen, Phys. Rev. B 92, 060413(R) (2015)

    ADS  Google Scholar 

  161. A. Farhan, C.F. Petersen, S. Dhuey, L. Anghinolfi, Q.H. Qin, M. Saccone, S. Velten, C. Wuth, S. Gliga, P. Mellado, M.J. Alava, A. Scholl, S. van Dijken, Nat. Commun. 8, 995 (2017)

    ADS  Google Scholar 

  162. A. Farhan, A. Scholl, C.F. Petersen, L. Anghinolfi, C. Wuth, S. Dhuey, R.V. Chopdekar, P. Mellado, M.J. Alava, S. van Dijken, Nat. Commun. 7, 12635 (2016)

    ADS  Google Scholar 

  163. A. Glavic, B. Summers, A. Dahal, J. Kline, W. Van Herck, A. Sukhov, A. Ernst, D.K. Singh, Adv. Sci. 1700856 (2018)

  164. J. Drisko, T. Marsh, J. Cumings, Nat. Commun. 8, 14009 (2017)

    ADS  Google Scholar 

  165. M. van Kampen, I.L. Soroka, R. Brucas, B. Hjörvarsson, R. Wieser, K.D. Usadel, M. Hanson, O. Kazakova, J. Grabis, H. Zabel, C. Jozsa, B. Koopmans, J. Phys.: Condens. Matter 17, L27 (2004)

    Google Scholar 

  166. M. Ewerlin, D. Demirbas, F. Brüssing, O. Petracic, A.A. Ünal, S. Valencia, F. Kronast, H. Zabel, Phys. Rev. Lett. 110, 177209 (2013)

    ADS  Google Scholar 

  167. N. Leo, S. Holenstein, D. Schildknecht, O. Sendetskyi, H. Luetkens, P.M. Derlet, V. Scagnoli, D. Lançon, J.R.L. Mardegan, T. Prokscha, A. Suter, Z. Salman, S. Lee, L.J. Heyderman, Nat. Commun. 9, 2850 (2018)

    ADS  Google Scholar 

  168. R.P. Cowburn, Phys. Rev. B 65, 092409 (2002)

    ADS  Google Scholar 

  169. D. Li, C. Yu, J. Pearson, S.D. Bader, Phys. Rev. B 66, 020404(R) (2002)

    ADS  Google Scholar 

  170. A. Imre, G. Csaba, G.H. Bernstein, W. Porod, V. Metlushko, Superlattices Microstruct. 34, 513 (2003)

    ADS  Google Scholar 

  171. V.D. Nguyen, Y. Perrin, S. Le Denmat, B. Canals, N. Rougemaille, Phys. Rev. B 96, 014402 (2017)

    ADS  Google Scholar 

  172. D. Louis, D. Lacour, M. Hehn, V. Lomakin, T. Hauet, F. Montaigne, Nat. Mater. 17 1076 (2018)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Univ. Grenoble Alpes, CNRS, Institut NEEL, Grenoble INP, 38000, Grenoble, France

    Nicolas Rougemaille & Benjamin Canals

Authors
  1. Nicolas Rougemaille
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benjamin Canals
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicolas Rougemaille.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rougemaille, N., Canals, B. Cooperative magnetic phenomena in artificial spin systems: spin liquids, Coulomb phase and fragmentation of magnetism – a colloquium. Eur. Phys. J. B 92, 62 (2019). https://doi.org/10.1140/epjb/e2018-90346-7

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2018-90346-7

Keywords

Search

Navigation