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.
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K. Runge, B. Pannetier, EuroPhys. Lett. 24, 737 (1993)
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)
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)
E. Serret, P. Butaud, B. Pannetier, EuroPhys. Lett. 59, 225 (2002)
J.R. Kirtley, C.C. Tsuei, A. Ariando, H.J.H. Smilde, H. Hilgenkamp, Phys. Rev. B 72, 6518 (2005)
J. Trastoy, M. Malnou, C. Ulysse, R. Bernard, N. Bergeal, G. Faini, J. Lesueur, J. Briatico, J.E. Villegas, Nat. Nanotechnol. 9, 710 (2014)
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)
E. Olive, P. Molho, Phys. Rev B 58, 9238 (1998)
E.Y. Vedmedenko, H.P. Oepen, J. Kirschner, Phys. Rev. Lett. 90, 137203 (2003)
P. Mellado, A. Concha, L. Mahadevan, Phys. Rev. Lett. 109, 257203 (2012)
E. Ganz, F. Xiong, I.-S. Hwang, J. Golovchenko, Phys. Rev. B 43, 7316 (1991)
J.M. Carpinelli, H.H. Weitering, E.W. Plummer, Surf. Sci. 401, L457 (1998)
B. Ressel, J. Slezák, K.C. Prince, V. Cháb, Phys. Rev. B 66, 035325 (2002)
L. Ottaviano, C. Di Teodoro, S. Santucci, G. Profeta, Phys. Low-Dimens. Struct. 3/4, 149 (2003)
L. Ottaviano, B. Ressel, C. Di Teodoro, G. Profeta, S. Santucci, V. Cháb, K.C. Prince, Phys. Rev. B, 67, 045401 (2003)
M. Tanaka, E. Saitoh, H. Miyajima, T. Yamaoka, Y. Iye, J. Appl. Phys. 97, 10J710 (2005)
M. Tanaka, E. Saitoh, H. Miyajima, T. Yamaoka, Y. Iye, Phys. Rev. B, 73, 052411 (2006)
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)
A. Libal, C. Reichhardt, C.J. Olson Reichhardt, Phys. Rev. Lett. 97, 228302 (2006)
Y. Han, Y. Shokef, A.M. Alsayed, P. Yunker, T.C. Lubensky, A.G. Yodh, Nature 456, 898 (2008)
C.J.O. Reichhardt, A. Libal, C. Reichhardt, New J. Phys. 14, 025006 (2012)
J. Loehr, A. Ortiz-Ambriz, P. Tierno, Phys. Rev. Lett. 117, 168001 (2016)
A. Ortiz-Ambriz, P. Tierno, Nat. Commun. 7, 10575 (2016)
G. Toulouse, Commun. Phys. 2, 115 (1977)
J. Vannimenus, G. Toulouse, J. Phys. C: Solid State Phys. 10, L537 (1977)
G. Toulouse, in The Frustration Model (Springer, Berlin, Heidelberg, 1980), Vol. 115
A.Y. Klimenko, Open Thermodyn. J. 6, 1 (2012)
S.T. Bramwell, M.J.P. Gingras, P.C.W. Holdsworth, Spin Ice (World Scientific, Singapore, 2013)
C. Nisoli, R. Moessner, P. Schiffer, Rev. Mod. Phys. 85, 1473 (2013)
C. Nisoli, Topology by design in magnetic nano-materials: artificial spin ice. https://doi.org/arXiv:1711.00921v1 (2017)
C.H. Marrows, Experimental studies of artificial spin ice. https://doi.org/arXiv:1611.00744v1 (2017)
L.J. Heyderman, R.L. Stamps, J. Phys.: Condens. Matter 25, 363201 (2013)
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)
C. Nisoli, R.F. Wang, J. Li, W.F. McConville, P.E. Lammert, P. Schiffer, V.H. Crespi, Phys. Rev. Lett. 98, 217203 (2007)
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)
E. Mengotti, L.J. Heyderman, A. Fraile Rodriguez, A. Bisig, L. Le Guyader, F. Nolting, H.B. Braun, Phys. Rev. B 78, 144402 (2008)
J. Li, X. Ke, S. Zhang, D. Garand, C. Nisoli, P. Lammert, V.H. Crespi, P. Schiffer, Phys. Rev. B 81, 092406 (2010)
J.P. Morgan, A. Bellew, A. Stein, S. Langridge, C.H. Marrows, Front. Phys. 1, 28 (2013)
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)
R.H. Swendsen, J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987)
U. Wolff, Phys. Rev. Lett. 62, 361 (1989)
R.G. Melko, M.J.P. Gingras, J. Phys.: Condens. Matter 16, R1277 (2004)
S.A. Daunheimer, O. Petrova, O. Tchernyshyov, J. Cumings, Phys. Rev. Lett. 107, 167201 (2011)
Z. Budrikis, P. Politi, R.L. Stamps, J. Appl. Phys. 111, 07E109 (2012)
Z. Budrikis, P. Politi, R.L. Stamps, New J. Phys. 14, 045008 (2012)
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)
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)
J.P. Morgan, A. Stein, S. Langridge, C.H. Marrows, Nat. Phys. 7, 75 (2011)
J. Cumings, Nat. Phys. 7, 7 (2011)
J.P. Morgan, J. Akerman, A. Stein, C. Phatak, R.M.L. Evans, S. Langridge, C.H. Marrows, Phys. Rev. B 87, 024405 (2013)
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)
C. Marrows, Nat. Phys. 9, 324 (2013)
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)
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)
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)
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)
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)
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)
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)
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)
J.M. Porro, A. Bedoya-Pinto, A. Berger, P. Vavassori, New J. Phys. 15, 055012 (2013)
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)
L.J. Heyderman, Nat. Nanotechnol. 8, 705 (2013)
V. Kapaklis, U.B. Arnalds, A. Farhan, R.V. Chopdekar, A. Balan, A. Scholl, L.J. Heyderman, B. Hjörvarsson, Nat. Nanotechnol. 9, 514 (2014)
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)
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)
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)
J. Drisko, S. Daunheimer, J. Cumings, Phys. Rev. B 91, 224406 (2015)
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)
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)
P. Fendley, J. Phys. A: Math. Gen. 39, 15445 (2006)
C. Nisoli, J. Li, X. Ke, D. Garand, P. Schiffer, V.H. Crespi, Phys. Rev. Lett. 105, 047205 (2010)
J.T. Chalker, Spin liquids and frustrated magnetism, 2010
L. Balents, Nature 464, 199 (2010)
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
M.E. Brooks-Bartlett, S.T. Banks, L.D.C. Jaubert, A. Harman-Clarke, P.C.W. Holdsworth, Phys. Rev. X 4, 011007 (2014)
L.D.C. Jaubert, SPIN 5, 1540005 (2015)
G.H. Wannier, Phys. Rev. 79, 357 (1950)
I. Syôzi, Progr. Theor. Phys. 6, 306 (1951)
K. Kanô, S. Naya, Progr. Theor. Phys. 10, 158 (1953)
G. Möller, R. Moessner, Phys. Rev. B 80, 140409 (2009)
G.-W. Chern, P. Mellado, O. Tchernyshyov, Phys. Rev. Lett. 106, 207202 (2011)
J. Villain, Z. Phys. B Condens. Matter 33, 31 (1979)
J.F. Nagle, J. Math. Phys. 7, 1484 (1966)
E.H. Lieb, Phys. Rev. Lett. 18, 692 (1967)
J.D. Bernal, R.H. Fowler, J. Chem. Phys. 1, 515 (1933)
L. Pauling, J. Am. Chem. Soc. 57, 2680 (1935)
A.J. Macdonald, P.C.W. Holdsworth, R.G. Melko, J. Phys.: Condens. Matter 23, 164208 (2011)
A.S. Wills, R. Ballou, C. Lacroix, Phys. Rev. B 66, 144407 (2002)
M.J. Harris, S.T. Bramwell, D.F. McMorrow, T. Zeiske, K.W. Godfrey, Phys. Rev. Lett. 79, 2554 (1997)
R. Moessner, Phys. Rev. B 57, R5587 (1998)
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)
Y. Qi, T. Brintlinger, J. Cumings, Phys. Rev. B 77, 094418 (2008)
C. Castelnovo, R. Moessner, S.L. Sondhi, Nature 451, 42 (2008)
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)
I.A. Chioar, N. Rougemaille, B. Canals, Phys. Rev. B 93, 214410 (2016)
B. Yee, Magnetic ordering of dipolar spin ice in mod- erate [111] field. https://doi.org/hdl.handle.net/10012/10803 (2016)
J. Hamp, R. Moessner, C. Castelnovo, Phys. Rev. B 98, 144439 (2018)
Y. Perrin, B. Canals, N. Rougemaille, Nature 540, 410 (2016)
Z. Budrikis, P. Politi, R.L. Stamps, Phys. Rev. Lett. 107, 217204 (2011)
Z. Budrikis, Solid State Phys. 65, 109 (2014)
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)
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)
J.P. Morgan, A. Stein, S. Langridge, C.H. Marrows, New J. Phys. 13, 105002 (2011)
C. Phatak, M. Pan, A.K. Petford-Long, S. Hong, M. De Graef, New J. Phys. 14, 075028 (2012)
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)
C. Phatak, A.K. Petford-Long, O. Heinonen, M. Tanase, M. De Graef, Phys. Rev. B 83, 174431 (2011)
S.D. Pollard, V. Volkov, Y. Zhu, Phys. Rev. B 85, 180402(R) (2012)
E.H. Lieb, Phys. Rev. 162, 162 (1967)
R.C. Silva, F.S. Nascimento, L.A.S. Mól, W.A. Moura-Melo, A.R. Pereira, New J. Phys. 14, 015008 (2012)
G.-W. Chern, M.J. Morrison, C. Nisoli, Phys. Rev. Lett. 111, 177201 (2013)
I. Gilbert, G.-W. Chern, S. Zhang, L. O’Brien, B. Fore, C. Nisoli, P. Schiffer, Nat. Phys. 10, 671 (2014)
F.S. Nascimento, L.A.S. Mól, W.A. Moura-Melo, A.R. Pereira, New J. Phys. 14, 115019 (2012)
M.J. Morrison, T.R. Nelson, C. Nisoli, New J. Phys. 15, 045009 (2013)
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)
E. Östman, H. Stopfel, I.-A. Chioar, U.B. Arnalds, A. Stein, V. Kapaklis, B. Hjörvarsson, Nat. Phys. 14, 375 (2018)
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)
C.L. Henley, Ann. Rev. Condens. Matter Phys. 1, 179 (2010)
C.L. Henley, Phys. Rev. B 71, 014424 (2005)
D.A. Garanin, B. Canals, Phys. Rev. B 59, 443 (1999)
B. Canals, D.A. Garanin, Eur. Phys. J. B 26, 439 (2002)
B. Canals, D.A. Garanin, Can. J. Phys. 79, 1323 (2001)
J. Villain, Solid State Commun. 10, 967 (1972)
R. Youngblood, J.D. Axe, B.M. McCoy, Phys. Rev. B 21, 5212 (1980)
M.J. Harris, M.P. Zinzin, Mod. Phys. Lett. B 10, 417 (1996)
J. Rehn, R. Moessner, Philos. Trans. R. Soc. A 374, 20160093 (2016)
F. Rys, Helv. Phys. Acta 36, 537 (1963)
E.H. Lieb, Phys. Rev. Lett. 18, 1046 (1967)
G. Möller, R. Moessner, Phys. Rev. Lett. 96, 237202 (2006)
D. Thonig, S. Reißaus, I. Mertig, J. Henk, J. Phys: Condens. Matter 26, 266006 (2014)
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)
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)
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)
Y.-L. Xie, Z.-Z. Du, Z.-B. Yan, J.-M. Liu, Sci. Rep. 5, 15875 (2015)
S. Ladak, D.E. Read, G.K. Perkins, L.F. Cohen, W.R. Branford, Nat. Phys. 6, 359 (2010)
E. Mengotti, L.J. Heyderman, A.F. Rodriguez, F. Nolting, R.V. Huegli, H.-B. Braun, Nat. Phys. 7, 68 (2011)
S. Ladak, D. Read, T. Tyliszczak, W.R. Branford, L.F. Cohen, New J. Phys. 13, 023023 (2011)
S. Ladak, D.E. Read, W.R. Branford, L.F. Cohen, New J. Phys. 13, 063032 (2011)
A. Schumann, P. Szary, E.Y. Vedmedenko, H. Zabel, New J. Phys. 14, 035015 (2012)
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)
A. Leon, Curr. Appl. Phys. 13, 2014 (2013)
K. Zeissler, S.K. Walton, S. Ladak, D.E. Read, T. Tyliszczak, L.F. Cohen, W.R. Branford, Sci. Rep. 3, 1252 (2013)
N. Rougemaille, F. Montaigne, B. Canals, M. Hehn, H. Riahi, D. Lacour, J.-C. Toussaint, New J. Phys. 15, 035026 (2013)
S. Ladak, S.K. Walton, K. Zeissler, T. Tyliszczak, D.E. Read, W.R. Branford, L.F. Cohen, New J. Phys. 14, 045010 (2012)
Y. Shen, O. Petrova, P. Mellado, S. Daunheimer, J. Cumings, O. Tchernyshyov, New J. Phys. 14, 035022 (2012)
A. Pushp, T. Phung, C. Rettner, B.P. Hughes, S.-H. Yang, L. Thomas, S.S.P. Parkin, Nat. Phys. 9, 505 (2013)
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)
D.M. Burn, M. Chadha, W.R. Branford, Phys. Rev. B 92, 214425 (2015)
K. Zeissler, M. Chadha, E. Lovell, L.F. Cohen, W.R. Branford, Sci. Rep. 6, 30218 (2016)
D.M. Burn, M. Chadha, W.R. Branford, Phys. Rev. B 95, 104417 (2017)
P. Azaria, H.T. Diep, H. Giacomini, Phys. Rev. Lett. 59, 1629 (1987)
C. Castelnovo, R. Moessner, S.L. Sondhi, Ann. Rev. Condens. Matter Phys. 3, 35 (2012)
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)
O. Benton, Phys. Rev. B 94, 104430 (2016)
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)
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)
C. Nisoli, V. Kapaklis, P. Schiffer, Nat. Phys. 13, 200 (2017)
V. Schánilec, Y. Perrin, S. Le Denmat, B. Canals, N. Rougemaille, Artificial vertex systems by design. unpublished.
Y. Perrin, B. Canals, N. Rougemaille, Proposal to explore different variants of the six-vertex model using artificial square ice systems. unpublished.
S. Gliga, A. Kakay, L.J. Heyderman, R. Hertel, O.G. Heinonen, Phys. Rev. B 92, 060413(R) (2015)
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)
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)
A. Glavic, B. Summers, A. Dahal, J. Kline, W. Van Herck, A. Sukhov, A. Ernst, D.K. Singh, Adv. Sci. 1700856 (2018)
J. Drisko, T. Marsh, J. Cumings, Nat. Commun. 8, 14009 (2017)
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)
M. Ewerlin, D. Demirbas, F. Brüssing, O. Petracic, A.A. Ünal, S. Valencia, F. Kronast, H. Zabel, Phys. Rev. Lett. 110, 177209 (2013)
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)
R.P. Cowburn, Phys. Rev. B 65, 092409 (2002)
D. Li, C. Yu, J. Pearson, S.D. Bader, Phys. Rev. B 66, 020404(R) (2002)
A. Imre, G. Csaba, G.H. Bernstein, W. Porod, V. Metlushko, Superlattices Microstruct. 34, 513 (2003)
V.D. Nguyen, Y. Perrin, S. Le Denmat, B. Canals, N. Rougemaille, Phys. Rev. B 96, 014402 (2017)
D. Louis, D. Lacour, M. Hehn, V. Lomakin, T. Hauet, F. Montaigne, Nat. Mater. 17 1076 (2018)
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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
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DOI: https://doi.org/10.1140/epjb/e2018-90346-7