Comptes Rendus
Magnetism in reduced dimensions
Comptes Rendus. Physique, Volume 6 (2005) no. 9, pp. 921-933.

We propose a short overview of a few selected issues of magnetism in reduced dimensions, which are the most relevant to set the background for more specialized contributions to the present Special Issue. Magnetic anisotropy in reduced dimensions is discussed first, on a theoretical basis, then with experimental reports and views from surface to single-atom anisotropy. Then, conventional magnetization states are reviewed, including macrospins, single domains, multidomains, and domain walls in stripes. Dipolar coupling is examined for lateral interactions in arrays, and for interlayer interactions in films and dots. Finally thermally-assisted magnetization reversal and superparamagnetism are presented. For each topic we have sought a balance between well established knowledge and recent developments.

Nous proposons un panorama de quelques aspects du magnétisme en dimensions réduites, appropriés comme toile de fond pour les articles plus spécialisés de ce numéro spécial. L'anisotropie magnétique en dimensions réduites est discutée, sur le plan théorique, puis appuyée par des exemples, allant des surfaces aux atomes individuels. Les configurations d'aimantation les plus courantes sont ensuite décrites : macrospins, monodomaines, multidomaines, parois dans des bandes. Les couplages magnétiques, essentiellement dipolaires, sont décrit pour des réseaux et pour des bi-couches. Enfin nous présentons les effets de l'activation thermique, de la baisse de coercitivité jusqu'au superparamagnétisme. Pour chaque aspect nous avons recherché un équilibre entre résultats établis et développements récents.

Published online:
DOI: 10.1016/j.crhy.2005.10.011
Keywords: Nanomagnetism, Micromagnetism, Magnetic anisotropy, Superparamagnetism, Reduced dimensions
Mot clés : Nanomagnétisme, Micromagnétisme, Anisotropie magnétique, Superparamagnétisme, Dimension réduite

Olivier Fruchart 1; André Thiaville 2

1 Laboratoire Louis-Néel (CNRS), 25, avenue des Martyrs, BP166, 38042 Grenoble cedex 9, France
2 Laboratoire de physique des solides, université Paris-Sud, bâtiment 510, 91405 Orsay cedex, France
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Olivier Fruchart; André Thiaville. Magnetism in reduced dimensions. Comptes Rendus. Physique, Volume 6 (2005) no. 9, pp. 921-933. doi : 10.1016/j.crhy.2005.10.011. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2005.10.011/

[1] U. Gradmann Magnetism in ultrathin transition metal films (K.H.J. Buschow, ed.), Handbook of Magnetic Materials, vol. 7, Elsevier Science Publishers B.V., North-Holland, 1993, pp. 1-96 (Chapter 1)

[2] H.C. Siegmann Surface and 2D magnetism, J. Phys.: Condens. Matter, Volume 4 (1992), p. 8395

[3] P. Poulopoulos; K. Baberschke Magnetism in thin films, J. Phys.: Condens. Matter, Volume 11 (1999), pp. 9495-9515

[4] A. Schuhl, Spin-dependent transport (2005)

[5] D. Sander The magnetic anisotropy and spin reorientation of nanostructures and nanoscale films, J. Phys.: Condens. Matter, Volume 16 (2004), p. R603-R636

[6] L. Néel Anisotropie magnétique superficielle et surstructures d'orientation, J. Phys. Rad., Volume 15 (1954), pp. 225-239

[7] P. Bruno Tight-binding approach to the orbital magnetic moment and magnetocrystalline anisotropy of transition-metal monolayers, Phys. Rev. B, Volume 39 (1989), pp. 865-868

[8] G. van der Laan J. Phys.: Condens. Matter, 10 (1998), pp. 3239-3253

[9] P. Ravindran; A. Kjekshus; H. Fjellvøag; P. James; L. Nordström; B. Johansson; O. Eriksson Phys. Rev. B, 63 (2001), p. 144409

[10] U. Gradmann; J. Müller Flat ferromagnetic exitaxial 48Ni/52Fe(111) films of few atomic layers, Phys. Status Solidi, Volume 27 (1968), p. 313

[11] C. Chappert; P. Bruno Magnetic anisotropy in metallic ultrathin films and related experiments ion cobalt films, J. Appl. Phys., Volume 64 (1988) no. 10, pp. 5336-5341

[12] W.A. Jesser; D. Kuhlmann-Wilsdorf Phys. Status Solidi, 19 (1967), p. 65

[13] U. Gradmann Ferromagnetism near surfaces and in thin films, Appl. Phys., Volume 3 (1974), p. 161

[14] R. Jungblut; M.T. Johnson; J. Ann de Stegge; F.J.A. den Broeder Orientational and structural dependence of magnetic anisotropy of Cu/Ni/Cu sandwiches: Misfit interface anisotropy, J. Appl. Phys., Volume 75 (1994), p. 6424

[15] D. Sander The correlation between mechanical stress and magnetic anisotropy in ultrathin films, Rev. Prog. Phys., Volume 62 (1999), pp. 809-858

[16] D. Sander Stress, strain and magnetostriction in epitaxial films, J. Phys.: Condens. Matter, Volume 14 (2002), pp. 4165-4176

[17] K. Ha; R.C. O'Handley Nonlinear magnetoelastic anisotropy in Cu/Ni/Cu/Si(001) films, J. Appl. Phys., Volume 85 (1999) no. 8, pp. 5282-5284

[18] M. Komelj; M. Fähnle Magnetoelastic effects in ultrathin epitaxial Ni films: an ab initio study, J. Magn. Magn. Mater., Volume 222 (2000), p. L245-L250

[19] T. Gutjahr-Löser; D. Sander; J. Kirschner Magnetoelastic coupling in Ni and Fe monolayers on Cu(001), J. Appl. Phys., Volume 87 (2000) no. 9, pp. 5920-5922

[20] G. Bochi; C.A. Ballentine; H.E. Inglefield; C.V. Thompson; R.C. O'Handley Evidence for strong surface magnetoelastic anisotropy in epitaxial Cu/Ni/Cu(001) sandwiches, Phys. Rev. B, Volume 53 (1996), p. R1729

[21] D. Weller; J. Stöhr; R. Nakajima; A. Carl; M.G. Samant; C. Chappert; R. Mégy; P. Beauvillain; P. Veillet; G.A. Held Microscopic origin of magnetic anisotropy in Au/Co/Au probed with X-ray magnetic circular dichroism, Phys. Rev. Lett., Volume 75 (1995) no. 20, pp. 3753-3755

[22] J. Bansmann; S. Baker; C. Binns; J. Blackman; J.-P. Bucher; J. Dorantes-Dávila; V. Dupuis; L. Favre; D. Kechrakos; A. Kleibert; K.-H. Meiwes-Broer; G.M. Pastor; A. Perez; O. Toulemonde; K.N. Trohidou; J. Tuaillon; Y. Xie Magnetic and structural properties of isolated and assembled clusters, Surf. Sci. Rep., Volume 56 (2005), pp. 189-275

[23] O. Fruchart Epitaxial self-organization: from surfaces to magnetic materials, C. R. Physique, Volume 6 (2005) no. 1, pp. 61-73

[24] O. Fruchart Self-organization on surfaces: foreword, C. R. Physique, Volume 6 (2005) no. 1, pp. 3-9

[25] M. Albrecht; U. Gradmann; T. Furubayashi; W.A. Harrison Magnetic moments in rough Fe surfaces, Europhys. Lett., Volume 20 (1992) no. 1, pp. 65-70

[26] W. Weber; C.H. Back; A. Bischof; C. Würsch; R. Allenspach Morphology-induced oscillations of the magnetic anisotropy in ultrathin Co films, Phys. Rev. Lett., Volume 76 (1996), pp. 1940-1943

[27] A. Dallmeyer; C. Carbone; W. Eberhardt; C. Pampuch; O. Rader; W. Gudat; P. Gambardella; K. Kern Electronic states and magnetism of monoatomic Co and Cu wires, Phys. Rev. B, Volume 61 (2000) no. 8, p. R5133-R5136

[28] P. Gambardella; A. Dallmeyer; K. Maiti; M.C. Malagoli; S. Rusponi; P. Ohresser; W. Eberhardt; C. Carbone; K. Kern Oscillatory magnetic anisotropy in one-dimensional atomic wires, Phys. Rev. Lett., Volume 93 (2004) no. 7, p. 077203

[29] P. Gambardella, Magnetism in monatomic metal wires, J. Phys.: Condens. Matter 15 (S2533–S2546)

[30] P. Gambardella; A. Dallmeyer; K. Maiti; M.C. Malagoli; W. Eberhardt; K. Kern; C. Carbone Ferromagnetism in one-dimensional monoatomic metal chains, Nature, Volume 416 (2002), pp. 301-304

[31] P. Gambardella; S. Rusponi; M. Veronese; S.S. Dhesi; C. Grazioli; A. Dallmeyer; I. Cabria; R. Zeller; P.H. Dederichs; K. Kern; C. Carbone; H. Brune Giant magnetic anisotropy of single cobalt atoms and nanoparticles, Science, Volume 300 (2003) no. 5622, pp. 1130-1133

[32] P. Gambardella; S. Rusponi; T. Cren; H. Brune Magnetic anisotropy from single atoms to large monodomain islands on a metal surface, C. R. Physique, Volume 6 (2005) no. 1, pp. 75-87

[33] R. Guirado-López; J. Dorantes-Dávila; G. Pastor Phys. Rev. Lett., 90 (2003), p. 226402

[34] M. Jamet; W. Wernsdorfer; C. Thirion; D. Mailly; V. Dupuis; P. Mélinon; A. Pérez Phys. Rev. Lett., 86 (2001), pp. 4676-4679

[35] A. Hubert; R. Schäfer Magnetic Domains. The Analysis of Magnetic Microstructures, Springer, Berlin, 1999

[36] M. Beleggia; M. De Graef On the computation of the demagnetization tensor field for an arbitrary particle shape using a Fourier space approach, J. Magn. Magn. Mater., Volume 263 (2003), p. L1-L9

[37] E.C. Stoner Philos. Mag., 36 (1945), p. 803

[38] P. Rhodes; G. Rowlands Demagnetizing energies of uniformly magnetized rectangular blocks, Proc. Leeds Philos. Liter. Soc., Volume 6 (1954), p. 191

[39] A. Aharoni Demagnetizing factors for rectangular ferromagnetic prisms, J. Appl. Phys., Volume 83 (1998) no. 6, pp. 3432-3434

[40] G. Rowlands, Ph.D. thesis, University of Leeds, Leeds, 1956

[41] P. Rhodes; G. Rowlands; D.R. Birchall J. Phys. Soc. Jpn., 17 (1956), p. 543

[42] D.A. Goode; G. Rowlands The demagnetizing energies of a uniformly magnetized cylinder with an elliptic cross-section, J. Magn. Magn. Mater., Volume 267 (2003), pp. 373-385

[43] G. Rowlands On the calculation of acoustic radiation impedance of polygonal-shaped apertures, J. Acoust. Soc. Am., Volume 92 (1992) no. 5, pp. 2961-2963

[44] E.C. Stoner; E.P. Wohlfarth A mechanism of magnetic hysteresis in heterogeneous alloys, Philos. Trans. Roy. Soc. London Ser. A, Volume 240 (1948), pp. 599-642

[45] A. Thiaville Coherent rotation of magnetization in three dimensions: a geometrical approach, Phys. Rev. B, Volume 61 (2000) no. 18, pp. 12221-12232

[46] W. Wernsdorfer Classical and quantum magnetization reversal studies in nanometer-sized particles and clusters (I. Prigogine; S.A. Rice, eds.), Adv. Chem. Phys., vol. 118, Wiley, 2001, pp. 99-190

[47] J.C. Slonczewski, Theory of magnetic hysteresis in films and its applications to computers, Research Memo RM 003.111.224, IBM Research Center, Poughkeepsie, NY, 1956

[48] M. Lederman; S. Schultz; M. Ozaki Phys. Rev. Lett., 73 (1994), pp. 1986-1989

[49] W.F. Brown Thermal fluctuations of a single-domain particle, Phys. Rev., Volume 130 (1963), pp. 1677-1686

[50] C. Thirion; W. Wernsdorfer; D. Mailly Nature Mater., 2 (2003), pp. 524-527

[51] C. Kittel Phys. Rev., 70 (1946), pp. 965-971

[52] A. Aharoni Introduction to the Theory of Ferromagnetism, Clarendon Press, Oxford, 1996

[53] M.A. Schabes; H.N. Bertram Magnetization processes in ferromagnetic cubes, J. Appl. Phys., Volume 64 (1988) no. 3, pp. 1347-1357

[54] W. Rave; K. Fabian; A. Hubert Magnetic states of small cubic particles with uniaxial anisotropy, J. Magn. Magn. Mater., Volume 190 (1998), pp. 332-348

[55] R. Cowburn; D. Koltsov; A. Adeyeye; M. Welland; D. Tricker Phys. Rev. Lett., 83 (1999), pp. 1042-1045

[56] R.P. Cowburn; M.E. Welland Phase transitions in planar magnetic nanostructures, Appl. Phys. Lett., Volume 72 (1998) no. 16, pp. 2041-2043

[57] W. Rave; A. Hubert Magnetic ground state of a thin-film element, IEEE Trans. Magn., Volume 36 (2001) no. 6, p. 3886

[58] A. Aharoni IEEE Trans. Magn., 27 (1991), pp. 4775-4777

[59] A. Thiaville; D. Tomáš; J. Miltat Phys. Status Solidi A, 170 (1998), pp. 125-135

[60] R.P. Cowburn; A.O. Adeyeye; M.E. Welland Configurational anisotropy in nanomagnets, Phys. Rev. Lett., Volume 81 (1998) no. 24, pp. 5414-5417

[61] R. Dittrich; A. Thiaville; J. Miltat; T. Schrefl J. Appl. Phys., 93 (2003), pp. 7891-7893

[62] R.P. Cowburn Property variation with shape in magnetic nanoelements, J. Phys. D: Appl. Phys., Volume 33 (2000), p. R1-R16

[63] Y. Nakatani; Y. Uesaka; N. Hayashi Jpn. J. Appl. Phys., 28 (1989), pp. 2485-2507

[64] B. Yang; D. Fredkin J. Appl. Phys., 79 (1996), pp. 5755-5757

[65] K. Kirk; M. Scheinfein; J. Chapman; S. McVitie; M. Gillies; B. Ward; J. Tennant J. Phys. D: Appl. Phys., 34 (2001), pp. 160-166

[66] M. Grimsditch; A. Berger; J. Johnson; V. Metlushko; B. Ilic; P. Neuzil; R. Kumar Magnetic stability of nano-particles: The role of dipolar instability pockets, Europhys. Lett., Volume 54 (2001) no. 6, pp. 813-819

[67] O. Fruchart; J.-C. Toussaint; B. Kevorkian Micromagnetic model of non-collective magnetization reversal in ultrathin magnetic dots with in-plane uniaxial anisotropy, Phys. Rev. B, Volume 63 (2001) no. 17, p. 174418

[68] M. Eleoui, O. Fruchart, J.C. Toussaint, Micromagnetic model of magnetization reversal of magnetically hard ultrathin dots and stripes, J. Magn. Magn. Mater., in press

[69] M. Dimian; H. Kachkachi J. Appl. Phys., 91 (2002), pp. 7625-7627

[70] In preparation

[71] R. Cowburn; D. Koltsov; A. Adeyeye; M. Welland J. Appl. Phys., 87 (2000), pp. 7067-7069

[72] H.A.M. Van den Berg A micromagnetic approach to the constitutive equation of soft-ferromagnetic media, J. Magn. Magn. Mater., Volume 44 (1984) no. 1–2, pp. 207-215

[73] H.A.M. Van den Berg Self-consistent domain theory in soft-ferromagnetic media. II. Basic domain structures in thin-film objects, J. Appl. Phys., Volume 60 (1986), p. 1104

[74] P. Bryant; H. Suhl Thin-film magnetic patterns in an external field, Appl. Phys. Lett., Volume 54 (1989), p. 78

[75] P. Bryant; H. Suhl Micromagnetic below saturation, J. Appl. Phys., Volume 66 (1989), p. 4329

[76] A. DeSimone; R.V. Kohn; S. Müller; F. Otto; R. Schäfer Two-dimensional modelling of soft ferromagnetic films, Proc. Roy. Soc. London Ser. A, Volume 457 (2001), pp. 2983-2991

[77] R. Hertel; H. Kronmüller Computation of the magnetic domain structure in bulk permalloy, Phys. Rev. B, Volume 60 (1999) no. 10, pp. 7366-7378

[78] P.O. Jubert; J.C. Toussaint; O. Fruchart; C. Meyer; Y. Samson Flux-closure-domain states and demagnetizing energy determination in sub-micron size magnetic dots, Europhys. Lett., Volume 63 (2003) no. 1, pp. 135-141

[79] O. Fruchart; J.C. Toussaint; P.-O. Jubert; W. Wernsdorfer; R. Hertel; J. Kirschner; D. Mailly Angular-dependence of magnetization switching for a multi-domain dot: experiment and simulation, Phys. Rev. B, Volume 70 (2004), p. 172409 (brief report)

[80] K.Y. Guslienko; V. Novosad; Y. Otani; H. Shima; K. Fukamichi Field evolution of magnetic vortex state in ferromagnetic disks, Appl. Phys. Lett., Volume 78 (2001) no. 24, p. 3848

[81] K.Y. Guslienko; K.L. Metlov Evolution and stability of a magnetic vortex in a small cylindrical ferromagnetic particle under applied field, Phys. Rev. B, Volume 63 (2001), p. 100403(R)

[82] P.-O. Jubert; R. Allenspach Analytical approach to the single-domain-to-vortex transition in small magnetic disks, Phys. Rev. B, Volume 70 (2004), p. 144402

[83] S. Cherifi; R. Hertel; J. Kirschner; H. Wang; R. Belkhou; A. Locatelli; S. Heun; A. Pavlovska; E. Bauer Virgin domain structures in mesoscopic Co patterns: Comparison between simulation and experiment, J. Appl. Phys., Volume 98 (2005), p. 043901

[84] M. Hehn; K. Ounadjela; J.P. Bucher; F. Rousseaux; D. Decanini; B. Bartenlian; C. Chappert Nanoscale magnetic domains in mesoscopic magnets, Science, Volume 272 (1996), pp. 1782-1785

[85] J.K. Ha; R. Hertel; J. Kirschner Concentric domains in patterned thin films with perpendicular magnetic anisotropy, Europhys. Lett., Volume 64 (2003) no. 6, pp. 810-815

[86] R. Hertel, O. Fruchart, S. Cherifi, P.-O. Jubert, S. Heun, A. Locatelli, J. Kirschner, Three-dimensional magnetic flux-closure patterns in mesoscopic Fe islands, Phys. Rev. B, in press

[87] M. Schneider; H. Hoffmann; J. Zweck Lorentz microscopy of circular ferromagnetic permalloy nanodisks, Appl. Phys. Lett., Volume 77 (2000) no. 18, pp. 2909-2911

[88] Z.H. Wei; C.R. Chang; N.A. Usov; M.F. Lai; J.C. Wu Evolution of vortex states under external magnetic field, J. Magn. Magn. Mater., Volume 239 (2002), pp. 1-4

[89] M. Rahm; M. Schneider; J. Biberger; R. Pulwey; J. Zweck; D. Weiss; V. Umansky Vortex nucleation in submicrometer ferromagnetic disks, Appl. Phys. Lett., Volume 82 (2003) no. 23, pp. 4110-4112

[90] C.J. García-Cervera; Z. Gimbutas; W. E Accurate numerical methods for micromagnetics simulations with general geometries, J. Comput. Phys., Volume 184 (2003), pp. 37-52

[91] U. Hartmann; H.H. Mende Hysteresis of Néel line motion and effective width of 180° Bloch walls in bulk iron, Phys. Rev. B, Volume 33 (1986) no. 7, pp. 4777-4781

[92] A. Thiaville; J. Miltat Controlled injection of a singular point along a linear magnetic structure, Europhys. J. D, Volume 26 (1994), p. 57

[93] A. Wachowiak; J. Wiebe; M. Bode; O. Pietzsch; M. Morgenstern; R. Wiesendanger Direct observation of internal spin structure of magnetic vortex cores, Science, Volume 298 (2002), pp. 577-580

[94] T. Okuno; K. Shigeto; T. Ono; K. Mibu; T. Shinjo MFM study of magnetic vortex cores in circular permalloy dots: behavior in external field, J. Magn. Magn. Mater., Volume 240 (2002), pp. 1-6

[95] A. Thiaville; J.M. García; R. Dittrich; J. Miltat; T. Schrefl Micromagnetic study of Bloch-point-mediated vortex core reversal, Phys. Rev. B, Volume 67 (2003), p. 094410

[96] L. Piraux; J. George; J. Despres; C. Leroy; E. Ferain; R. Legras; K. Ounadjela; A. Fert Appl. Phys. Lett., 65 (1994), pp. 2484-2486

[97] K. Nielsch; R. Wehrspohn; J. Barthel; J. Kirschner; U. Gösele; S. Fischer; H. Kronmüller Hexagonally ordered 100 nm period nickel nanowire arrays, Appl. Phys. Lett., Volume 79 (2001), pp. 1360-1362

[98] E. Snoeck; R. Dunin-Borkowski; F. Dumestre; P. Renaud; C. Amiens; B. Chaudret; P. Zurcher Appl. Phys. Lett., 82 (2003), pp. 88-90

[99] E. Saitoh; H. Miyajima; T. Yamaoka; G. Tatara Nature, 432 (2004), pp. 203-206

[100] A. Thiaville, Y. Nakatani, Spin Dynamics in Confined Magnetic Structures III, Springer, Berlin, in press

[101] R. McMichael; M. Donahue IEEE Trans. Magn., 33 (1997), pp. 4167-4169

[102] Y. Nakatani; A. Thiaville; J. Miltat J. Magn. Magn. Mater., 290–291 (2005), pp. 750-753

[103] M. Kläui; C. Vaz; J. Bland; L. Heyderman; F. Nolting; A. Pavlovska; E. Bauer; S. Cherifi; S. Heun; A. Locatelli Appl. Phys. Lett., 85 (2004), pp. 5637-5639

[104] N. Schryer; L. Walker J. Appl. Phys., 45 (1974), pp. 5406-5421

[105] H. Forster; T. Schrefl; W. Scholz; D. Suess; V. Tsiantos; J. Fidler J. Magn. Magn. Mater., 249 (2002), pp. 181-186

[106] N. Vernier; D. Allwood; D. Atkinson; M. Cooke; R. Cowburn Europhys. Lett., 65 (2004), pp. 526-532

[107] A. Yamaguchi; T. Ono; S. Nasu; K. Miyake; K. Mibu; T. Shinjo Phys. Rev. Lett., 92 (2004), p. 077205

[108] M. Kläui; P. Jubert; R. Allenspach; A. Bischof; J. Bland; G. Faini; U. Rüdiger; C. Vaz; L. Vila; C. Vouille Phys. Rev. Lett., 94 (2005), p. 106601

[109] S. Zhang; Z. Li Phys. Rev. Lett., 93 (2005), p. 127204

[110] A. Thiaville; Y. Nakatani; J. Miltat; Y. Suzuki Europhys. Lett., 69 (2005), pp. 990-996

[111] P. Bruno Geometrically constrained magnetic wall, Phys. Rev. Lett., Volume 83 (1999) no. 12, p. 2425

[112] O. Pietzsch; A. Kubetzka; M. Bode; R. Wiesendanger Real-space observation of dipolar antiferromagnetism in magnetic nanowires by spin-polarized scanning tunneling spectroscopy, Phys. Rev. Lett., Volume 84 (2000) no. 22, pp. 5212-5215

[113] L. Néel Sur un nouveau mode de couplage entre les aimantations de deux couches minces ferromagnétiques, C. R. Acad. Sci., Volume 255 (1962), pp. 1676-1681

[114] J.C.S. Kools; W. Cula; D. Mauri; T. Lin Effect of finite magnetic film thickness on Néel coupling in spin valves, J. Appl. Phys., Volume 85 (1999) no. 8, pp. 4466-4468

[115] J. Moritz; F. Garcia; J.C. Toussaint; B. Dieny; J.P. Nozières Orange peel coupling in multilayers with perpendicular magnetic anisotropy: Application to (Co/Pt)-based exchange-biased spin-valves, Europhys. Lett., Volume 65 (2004) no. 1, pp. 123-129

[116] H.A.M. Van den Berg Physics and methods for studying metallic multilayers with interlayer exchange coupling and GMR response, Magnetic Multilayers and Giant Magneto-Resistance – Fundamentals and Industrial Applications, Springer Ser. Surface Sci., vol. 37, Springer, Heidelberg, 2000, pp. 179-262

[117] P. Bruno Theory of interlayer exchange interactions in magnetic multilayers, J. Phys.: Condens. Matter, Volume 11 (1999), pp. 9403-9419

[118] L. Thomas; M.G. Samant; S.S.P. Parkin Domain-wall induced coupling between ferromagnetic layers, Phys. Rev. Lett., Volume 84 (2000) no. 8, pp. 1816-1819

[119] L. Thomas; J. Lüning; A. Scholl; F. Nolting; S. Anders; J. Stöhr; S.S.P. Parkin Oscillatory decay of magnetization induced by domain-wall stray fields, Phys. Rev. Lett., Volume 84 (2000) no. 15, pp. 3462-3465

[120] J. Vogel; W. Kuch; R. Hertel; J. Camarero; K. Fukumoto; F. Romanens; S. Pizzini; M. Bonfim; F. Petroff; A. Fontaine; J. Kirschner Influence of domain wall interactions on nanosecond switching in magnetic tunnel junctions | arXiv

[121] J.I. Martin; J. Nogués; K. Liu; J.L. Vicent; I.K. Schuller Ordered magnetic nanostructures: fabrication and properties, J. Magn. Magn. Mater., Volume 256 (2003), pp. 449-501

[122] N. Mikuszeit; E.Y. Vedmedenko; H.P. Oepen Multipole interaction of polarized single-domain particles, J. Phys.: Condens. Matter, Volume 16 (2005), pp. 9037-9045

[123] O. Fruchart; J.-P. Nozières; W. Wernsdorfer; D. Givord; F. Rousseaux; D. Decanini Enhanced coercivity in sub-micrometer-sized ultrathin epitaxial dots with in-plane magnetization, Phys. Rev. Lett., Volume 82 (1999) no. 6, pp. 1305-1308

[124] T. Aign; P. Meyer; S. Lemerle; J.P. Jamet; J. Ferré; V. Mathet; C. Chappert; J. Gierak; C. Vieu; F. Rousseaux; H. Launois; H. Bernas Magnetization reversal in arrays of perpendicularly magnetized ultrathin dots coupled by dipolar interaction, Phys. Rev. Lett., Volume 81 (1998) no. 25, pp. 5656-5659

[125] J.I. Martin; J. Nogués; I.K. Schuller; M.J.V. Bael; K. Temst; C.V. Haesendonck; V.V. Moshchalkov; Y. Bruynseraede Magnetization reversal in long chains of submicrometric Co dots, Appl. Phys. Lett., Volume 72 (1998) no. 2, pp. 225-257

[126] I.D. Mayergoyz Mathematical Models of Hysteresis, Springer-Verlag, New York, 1991

[127] O. Henkel Phys. Status Solidi, 7919 (1964)

[128] S. Thamm; J. Hesse The remanence of a Stoner–Wohlfarth particle ensemble as a function of the demagnetisation process, J. Magn. Magn. Mater., Volume 184 (1998), pp. 245-255

[129] C. Vouille; A. Thiaville; J. Miltat Thermally activated switching of nanoparticles: a numerical study, J. Magn. Magn. Mater., Volume 272–276 (2004), p. e1237-e1238

[130] E. Bonet-Orozco; W. Wernsdorfer; B. Barbara; A. Benoit; D. Mailly; A. Thiaville Three-dimensional magnetization reversal measurements in nanoparticles, Phys. Rev. Lett., Volume 83 (1999) no. 20, pp. 4188-4191

[131] Y. Lu; P.L. Trouilloud; D.W. Abraham; R. Koch; J. Slonczewski; S. Brown; J. Bucchignano; E. O'Sullivan; R.A. Wanner; W.J. Gallagher Observation of magnetic switching in submicron magnetic-tunnel junctions at low frequency, J. Appl. Phys., Volume 85 (1999) no. 8, p. 5267

[132] W. Wernsdorfer; E. Bonet-Orozco; K. Hasselbach; A. Benoit; B. Barbara; N. Demoncy; A. Loiseau; H. Pascard; D. Mailly Experimental evidence of the Néel–Brown model of magnetization reversal, Phys. Rev. Lett., Volume 78 (1997) no. 9, pp. 1791-1794

[133] R. Victora Phys. Rev. Lett., 63 (1989), pp. 457-460

[134] A. Thiaville J. Magn. Magn. Mater., 182 (1998), pp. 5-18

[135] J. Kurkijärvi Intrinsic fluctuations in a superconducting ring closed with a Josephson junction, Phys. Rev. B, Volume 6 (1972), p. 832

[136] J. Ferré Dynamics of the magnetization reversal: from continuous to patterned ferromagnetic films, Spin Dynamics in Confined Magnetic Structures, Springer, Heidelberg, 2001, pp. 127-160

[137] J. Camarero; Y. Pennec; J. Vogel; M. Bonfim; S. Pizzini; M. Cartier; F. Ernult; F. Fettar; B. Dieny Dynamical properties of magnetization reversal in exchange-coupled NiO/Co bilayers, Phys. Rev. B, Volume 64 (2001), p. 172402

[138] J. Moritz; B. Dieny; J.P. Nozières; Y. Pennec; J. Camarero; S. Pizzini Experimental evidence of a 1/H activation law in nanostructures with perpendicular magnetic anisotropy, Phys. Rev. B, Volume 71 (2005), p. 100402

[139] S. Lemerle; J. Ferré; C. Chappert; V. Mathet; T. Giamarchi; P.L. Doussal Domain wall creep in an ising ultrathin magnetic film, Phys. Rev. Lett., Volume 80 (1998), pp. 842-849

[140] H.-B. Braun Thermally activated magnetization reversal in elongated ferromagnetic particles, Phys. Rev. Lett., Volume 71 (1993) no. 21, pp. 3557-3560

[141] H.B. Braun Nucleation in ferromagnetic nanowires – magnetostatics and topology, J. Appl. Phys., Volume 85 (1999) no. 8, pp. 6172-6174

[142] W.T. Coffey; P.J. Cregg; Y.P. Kalmykov On the theory of Debye and Néel relaxation of single domain ferromagnetic particles, Adv. Chem. Phys., Volume 83 (1993), p. 263

[143] O. Fruchart; M. Klaua; J. Barthel; J. Kirschner Self-organized growth of nanosized vertical magnetic pillars on Au(111), Phys. Rev. Lett., Volume 83 (1999) no. 14, pp. 2769-2772

[144] P. Ohresser; N.B. Brookes; S. Padovani; F. Scheurer; H. Bulou Magnetism of small Fe clusters on Au(111) studied by X-ray magnetic circular dichroism, Phys. Rev. B, Volume 64 (2001), p. 104429

[145] S. Rusponi; T. Cren; N. Weiss; M. Epple; L. Claude; P. Buluschek; H. Brune The remarkable difference between surface and step atoms in the magnetic anisotropy of 2D nanostructures, Nat. Mater., Volume 2 (2003), p. 546

[146] R.W. Chantrell; N.Y. Ayoub; J. Popplewell The low field susceptibility of a textured superparamagnetic system, J. Magn. Magn. Mater., Volume 53 (1985), pp. 199-207

[147] O. Fruchart; P.-O. Jubert; C. Meyer; M. Klaua; J. Barthel; J. Kirschner Vertical self-organization of epitaxial magnetic nanostructures, J. Magn. Magn. Mater., Volume 239 (2002), pp. 224-227

[148] O. Fruchart, Auto-organisation épitaxiale: des surfaces aux matériaux magnétiques, Habilitation, Institut National Polytechnique de Grenoble, 2003

[149] Q. Pankhurst; J. Connolly; S.K. Jones; J. Dobson Applications of magnetic nanoparticles in biomedicine, J. Phys. D: Appl. Phys., Volume 36 (2003), p. R167-R181

[150] R.P. Cowburn; M.E. Welland Room temperature magnetic quantum cellular automata, Science, Volume 287 (2000), pp. 1466-1468

[151] H.J.G. Draaisma; W.J.M. de Jonge Surface and volume anisotropy from dipole-dipolar interactions in ultrathin ferromagnetic films, J. Appl. Phys., Volume 64 (1988) no. 7, pp. 3610-3613

[152] H. Dürr; S. Dhesi; E. Dudzik; D. Knabben; G. van der Laan; J. Goedkoop; F. Hillebrecht Spin and orbital magnetization in self-assembled Co clusters on Au(111), Phys. Rev. B, Volume 59 (1999) no. 2, p. R701-R704

[153] T. Koide; H. Miyauchi; J. Okamoto; T. Shidara; A. Fujimori; H. Fukutani; K. Amemiya; H. Takeshita; S. Yuasa; T. Katayama; Y. Suzuki Direct determination of interfacial magnetic moments with a magnetic phase transition in Co nanoclusters on Au(111), Phys. Rev. Lett., Volume 87 (2001), p. 257201

[154] P. Gambardella; S.S. Dhesi; S. Gardonio; C. Grazioli; P. Ohresser; C. Carbone Localized magnetic states of Fe, Co, and Ni impurities on alkali metal films, Phys. Rev. Lett., Volume 88 (2002) no. 4, p. 047202

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