Recent Analytical Developments in Micromagnetics

The Science of Hysteresis

Volumn 2-3, Issue , 2006, Pages 269-381

  Mayergoyz, Isaak D ^a  

^a UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84884761415     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-012480874-4/50015-4     Document Type: Chapter

References (117)

1. Stoner E.C., Wohlfarth E.P. A mechanism of magnetic hysteresis in heterogeneous alloys. Phil. Trans. Roy. Soc. London A 1948, 240:599-642.
2. Gioia G., James R.D. Micromagnetics of very thin films. Proc. Roy. Soc. London Ser. A 1997, 453:213-223.
3. Moser R. Ginzburg-Landau vortices for thin magnetic films. AMRX Appl. Math. Res. Express 2003, 1:1-32.
4. Moser R. Boundary vortices for thin ferromagnetic films. Arch. Ration. Mech. Anal. 2004, 174:267-300.
5. R.V. Kohn and V. Slastikov, 'Another thin film limit of micro-magnetics', Arch. Ration. Mech. Anal, in press.
6. Desimone A., Kohn R.V., Müller S., Otto F., Schäfer R. A reduced theory for thin film micromagnetics. Comm. Pure Appl. Math. 2002, 55:1408-1460.
7. Desimone A., Kohn R.V., Müller S., Otto F., Schäfer R. Two-dimensional modelling of soft ferromagnetic films. Proc. Roy. Soc. A 2001, 457:2983-2991.
8. Desimone A., Kohn R.V., Müller S., Otto F., Schäfer R. Low energy domain patterns in soft ferromagnetic films. J. Magnetism Magn. Mat. 2002, 242-245:1047-1051.
9. Alouges F., Riviére T., Serfaty S. Néel and cross-tie wall energies for planar magnetic configurations. ESAIM Control Optim. Calc. Var. 2002, 8:31-68.
10. Melcher C. The logarithmic tail of Néel walls in thin films. Arch. Ration. Mech. Anal. 2003, 168:83-113.
11. Melcher C. Logarithmic lower bounds for Néel walls. Calc. Var. 2004, 21:209-219.
12. Desimone A., Knüpfer H., Otto F. 2-d stability of the Néel wall. SFB 611 preprint 2005, 224.
13. Otto F. Cross-over in scaling laws: a simple example from micromagnetics. Proceedings of the International Congress of Mathematicians 2002, Vol. III:829-838. Beijing, 2002, Higher Ed. Press, Beijing.
14. Cantero-álvarez R., Otto F. Critical fields in ferromagnetic thin films: Identification of four regimes. SFB 611 Preprint 2004, 128.
15. see http://www-mathphys.iam.uni-bonn.de, J. Nonlinear Science, in press.
16. Cantero-álvarez R., Otto F. Oscillatory buckling mode in thin-film nucleation. SFB 611 Preprint 2004, 148.
17. see http://www-mathphys.iam.uni-bonn.de, J. Nonlinear Science, in press.
18. Cantero-Alvarez R., Otto F. Nucleation in ferromagnetic thin-films: a supercritical bifurcation. SFB 611 Preprint 2005, 227. see. http://www.mathphys.iam.uni.
19. J. Ko, 'The construction of a partially regular solution to the Landau-Lifshitz-Gilbert equations in R2', submitted to Nonlinearity.
20. R.V. Kohn, F. Otto, M.G. Reznikoff, and E. Vanden-Eijnden, 'Action minimization and sharp interface limits for the stochastic Allen-Cahn equation', su.
21. R.V. Kohn, M.G. Reznikoff, and E. Vanden-Eijnden, 'Micromagnetics at finite temperature and large deviation theory', J. Nonlinear Science, in press.
22. H. McGahagan, 'An approximation scheme for Schrödinger maps', preprint.
23. Desimone A. Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica 1995, 30:591-603.
24. Ball J.M., Taheri A., Winter M. Local minimizers in micromagnetics and related problems. Calc. Var. 2002, 14:1-27.
25. Alouges F., Conti S., Desimone A., Pokern Y. Energetics and switching of quasi-uniform states in small ferromagnetic particles. M2AN Math. Model. Numer. Anal. 2004, 38:235-248.
26. Desimone A. Energy minimizers for large ferromagnetic bodies. Arch. Ration. Mech. Anal. 1993, 125:99-143.
27. Pedregal P. Relaxation in ferromagnetism: the rigid case. J. Nonlinear Sci. 1994, 4:105-125.
28. Tartar L. On mathematical tools for studying partial differential equations of continuum physics: H-measures and Young measures. Developments in Partial Differential Equations and Applications to Mathematical Physics 1992, 201-217. (Ferrara, 1991), Plenum Press, New York. G. Buttazzo, G.P. Galdi, L. Zanghirati (Eds.).
29. Tartar L. Beyond Young measures. Meccanica 1995, 30:505-526.
30. Néel L. Les lois de l'aimantation et de la subdivision en domaines élémentaires d'un monocristal de fer I-III. J. Phys. Rad. 1944, 5:241-251.
31. Néel L. Les lois de l'aimantation et de la subdivision en domaines élémentaires d'un monocristal de fer I-III. J. Phys. Rad. 1944, 5:265-276.
32. Hubert A., Schäfer R. Magnetic Domains 1998, Springer.
33. James R.D., Kinderlehrer D. Frustration in ferromagnetic materials. Continuum Mech. Thermodyn. 1991, 2:215-239.
34. Fonseca I., Leoni G. Relaxation results in micromagnetics. Ricerche di Matematica 2000, XLIX:269-304.
35. Van Den Berg H.A.M. Self-consistent domain theory in soft-ferromagnetic media. II. Basic domain structures in thin film objects. J. Appl. Phys. 1986, 60:1104-1113.
36. Bryant P., Suhl H. Thin-film magnetic patterns in an external field. Appl. Phys. Lett. 1989, 54(22):2224-2226.
37. Melcher C. Néel walls and regularity in thin film micromagnetics. PhD Thesis 2002, University of Leipzig.
38. Ambrosio L., De Lellis C., Mantegazza C. Line energies for gradient vector fields in the plane. Cale. Var. PDE 1999, 9:327-355.
39. Desimone A., Kohn R.V., Müller S., Otto F. A compactness result in the gradient theory of phase transitions. Proc. Roy. Soc. Edinburgh 2001, 131A:833-844.
40. Jabin P.E., Perthame B. Compactness in Ginzburg-Landau energy by kinetic averaging. Comm. Pure Appl. Math. 2001, 54:1096-1109.
41. Jabin P.E., Perthame B., Otto F. Line-energy Ginzburg-Landau models: zero-energy states. Ann. Sc. Norm. Super. Pisa Cl. Sci. 2002, 1(5):187-202.
42. Riviére T., Serfaty S. Limiting domain wall energy for a problem related to micromagnetics. Comm. Pure Appl. Math. 2001, 54(3):294-338.
43. Riviére T., Serfaty S. Compactness, kinetic formulation, and entropies for a problem related to micromagnetics. Comm. Partial Differential Equations 2003, 28:249-269.
44. 2-matrix methods vs. FFT in thin-film stray-field computations. SFB 611 Preprint 2004, 161. seemathphys.iam.uni.
45. Hackbusch W. A sparse matrix arithmetic based on %-matrices', I. Introduction to H-matrices. Computing 1999, 62(2):89-108.
46. 2-matrix approximation of integral operators by interpolation. Appl. Numer. Math. 2002, 43(1-2):129-143.
47. Vanderbei R.J. Linear Programming: Foundations and Extensions 1996, Kluwer, Boston.
48. Sethian J.A. Level Set Methods 1996, Cambridge University Press, Cambridge.
49. Desimone A., Kohn R.V., Müller S., Otto F. Répulsive interaction of Néel walls, and the internal length scale of the cross-tie wall. Multiscale Model. Simul. 2003, 1:57-104.
50. Choksi R., Kohn R.V. Bounds on the micromagnetic energy of a uniaxial ferromagnet. Comm. Pure Appl. Math. 1998, 51:259-289.
51. Choksi R., Kohn R.V., Otto F. Domain branching in uniaxial ferromagnets: a scaling law for the minimum energy. Comm. Math. Phys. 1999, 201:61-79.
52. Hubert A. Stray-field-free magnetization configurations. Phys. Status Solidi 1969, 32:519-534.
53. Labonte A.E. Two-dimensional Bloch-type domain walls in ferromagnetic films. J. Appl. Phys. 1969, 40:2450-2458.
54. Döring W. Mikromagnetismus. Handbook of Physics 1966, Vol. 18/2:341-437. Springer, Berlin. S. Flügge (Ed.).
55. Riedel R., Seeger A. Micromagnetic treatment of Néel walls. Phys. Stat. Sol. (B) 1971, 46:377-384.
56. Garcia-Cervera C.J. Magnetic domains and magnetic domain walls. PhD Thesis 1999, New York University.
57. Garcia-Cervera C.J. One-dimensional magnetic domain walls. Europ. J. Appl. Math. 2004, 15:451-486.
58. Jin W., Kohn R.V. Singular perturbation and the energy of folds. J. Nonlinear Sci. 2000, 10:355-390.
59. Middelhoek S. Domain walls in thin Ni-Fe films. J. Applied Phys. 1963, 34(4):1054-1059.
60. A. DeSimone, J. McCord, F. Otto, and R. Schäfer, in preparation.
61. Lifshitz E. On the magnetic structure of iron. J. Phys. USSR 1944, 8:337-346.
62. Hubert A. Zur Theorie der zweiphasigen Domänenstrukturen in Supraleitern und Ferromagneten. Phys. Stat. Solidi 1967, 24:669-682. (on the theory of two-phase domain structures in superconductors and ferromagnets).
63. Kohn R.V., Müller S. Branching of twins near an austenite twinned-martensite interface. Phil. Mag. A 1992, 66:697-715.
64. Kohn R.V., Müller S. Surface energy and microstructure in coherent phase transitions. Comm. Pure Appl. Math. 1994, 47:405-435.
65. Conti S. Branched microstructures: scaling and asymptotic self-similarity. Comm. Pure Appl. Math. 2000, 53(11):1448-1474.
66. Simon L. Theorems on Regularity and Singularity of Energy Minimizing Maps. Lecture Notes in Mathematics ETH Zürich 1996, Birkhäuser, Basel.
67. Schoen R., Uhlenbeck K. A regularity theory for harmonic maps. J. Diff. Geom. 1982, 17:307-355.
68. Lin F.H. A remark on the map x/xs. C.R. Acad. Sci. Paris Ser. 1987, 1305:529-531.
69. Brezis H., Coron J.M., Lieb E.H. Harmonie maps with defects. Comm. Math. Phys. 1986, 107:649-705.
70. Hélein F. Régularité des applications faiblement harmoniques entre une surface et une sphére. C.R. Acad. Sci. Paris Ser.. I 1990, 311:519-524.
71. Hélein F. Harmonie Maps, Conservation Laws and Moving Frames 1997, Diderot.
72. Riviére T. Everywhere discontinuous harmonie maps into spheres. Acta Math. 1995, 175:197-226.
73. Evans L.C. Partial regularity of stationary harmonic maps. Arch. Ration. Mech. Anal. 1991, 116:101-113.
74. Hardt R., Kinderlehrer D. Some regularity results in ferro-magnetism. Comm. Partial Differential Equations 2000, 25:1235-1258.
75. Carbou G. Regularity for critical points of a nonlocal energy. Calc. Var. 1997, 5:409-433.
76. Alberti G., Müller S. Two-scale Young measures for variational problems with multiple scales. Comm. Pure Appl. Math. 2001, 54:761-825.
77. Landau L.D., Lifshitz E. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Z. Sowjetunion 1935, 8:153-169.
78. Anzellotti G., Baldo S., Visintin A. Asymptotic behavior of the Landau-Lifshitz model of ferromagnetism. Appl. Math. Optim. 1991, 23:171-192.
79. Modica L., Mortola S. Un esempio di F-convergenza. Boll. Un. Mat. Ital. 1977, 14:285-299.
80. Modica L. The gradient theory of phase transitions and the minimal interface criterion. Arch. Ration. Mech. Anal. 1987, 98:123-142.
81. Giusti E. Minimal Surfaces and Functions of Bounded Variations 1984, Birkhäuser, Basel.
82. Evans L.C., Gariepy R.F. Measure Theory and Fine Properties of Functions 1992, CRC Press, Boca Raton.
83. Ambrosio L., Fusco N., Pallara D. Functions of Bounded Variation and Free Discontinuity Problems 2000, Oxford University Press, Oxford.
84. Kléman M. Soft ferromagnets revisited. Phase Transitions 1991, 30:217-232.
85. Bethuel F., Brezis H., Hélein F. Ginzburg-Landau Vortices 1994, Birkhäuser, Basel.
86. Struwe M. On the asymptotic behaviour of the Ginzburg-Landau model in two dimensions. Diff. Int. Eqns. 1994, 7:1613-1624.
87. Struwe M. Erratum: on the asymptotic behaviour of the Ginzburg-Landau model in two dimensions. Diff. Int. Eqns. 1995, 8:224.
88. M. Kurzke, 'Boundary vortices in thin magnetic films', Calc. Var. PDE, in press.
89. Newell A.J., Merrill R.T. Single-domain critical sizes for coercivity and remanence. J. Geophys. Res.-Sol. Ea. 1999, 104(Bl):617-628.
90. Aharoni A. Introduction to the Theory of Ferromagnetism 2000, Oxford University Press, Oxford. 2nd edition.
91. Brown W.E Criterion for uniform micromagnetization. Phys. Rev. 1957, 105:1479-1482.
92. Frei E.H., Shtrikman S., Treves D. Critical size and nucleation field of ideal ferromagnetic particles. Phys. Rev. 1957, 107:446-455.
93. Aharoni A., Shtrikman S. Magnetization curve of the infinite cylinder. Phys. Rev. 1958, 109:1522-1528.
94. Aharoni A. Magnetization curling. Phys. Stat. Sol. 1966, 16:1-42.
95. Brown W.F. Thermal fluctuations of a single-domain particle. Phys. Rev. 1963, 130:1677-1686.
96. Brown G., Novotny M.A., Rikvold P.A. Langevin simulation of thermally activated magnetization reversal in nanoscale pillars. Phys. Rev. B 2001, 64:134422.
97. Garcia-Palacios J.L., Lazaro F.J. Langevin-dynamics study of the dynamical properties of small magnetic particles. Phys. Rev. B 1998, 58:14937-14958.
98. Koch R.H., Grinstein G., Keefe G.A., et al. Thermally assisted magnetization reversal in submicron-sized magnetic thin films. Phys. Rev. Lett. 2000, 84:5419-5422.
99. Gardiner C.W. Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences 2004, Springer, Berlin. 3rd edition.
100. Henkelman G., Jonsson H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 2000, 113:9978-9985.
101. Jonsson H., Mills G., Jacobsen K.W. Nudged elastic band method for finding minimum energy paths of transitions. Classical and Quantum Dynamics in Condensed Phase Simulations 1998, 385. World Scientific, Singapore. B.J. Berne, G. Ciccotti, D.F. Coker (Eds.).
102. Weinan E., Ren W., Vanden-Eijnden E. String method for the study of rare events. Phys. Rev. B 2002, 66:052301.
103. Weinan E., Ren W., Vanden-Eijnden E. Energy landscape and thermally activated switching of submicron-size ferromagnetic elements. J. Appl. Phys. 2003, 93:2275-2282.
104. D. Liu, C.J. Garcia-Cervera and E. Weinan, 'Magnetic switching of ferrromagnetic thin films under thermal perturbation', J. Appl. Phys., in press.
105. De Giorgi E. Sulla convergenza di alcune successioni di integrali del tipo dell'area. Rend. Mat. 1975, 8:277-294.
106. De Giorgi E., Franzoni T. Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 1975, 82:842-850.
107. Dal Maso G. An Introduction to F-convergence 1993, Birkhäuser, Basel.
108. Attouch H. Variational Convergence for Functions and Operators 1984, Pitman, London.
109. Braides A. Y-Convergence for Beginners 2002, Oxford University Press, Oxford.
110. Alberti G. Variational models for phase transitions, an approach via F-convergence. Calculus of Variations and Partial Differential Equations 2000, 95-114. (Pisa, 1996), Springer, Berlin. G. Buttazzo (Ed.).
111. Jost J., Li-Jost X. Calculus of Variations 1998, Cambridge University Press, Cambridge.
112. Carbou G. Thin layers in micromagnetism. Math. Models Methods Appl. Sd. 2001, 11:1529-1546.
113. Carbou G., Fabrie P. Regular solutions for Landau-Lifshitz equation in a bounded domain. Diff. Int. Eqns. 2001, 14:213-229.
114. Carbou G., Fabrie P., Gués O. Couche limites dans un modéle de ferromagnétisme. Comm. Partial Differential Equations 2002, 27:1467-1495.
115. Privorotskii L.A. Thermodynamics of Domain Structures 1976, Wiley, New York.
116. Cartensen C., Praetorius D. Effective simulation of a macroscopic model for stationary micromagnetics. Comput. Methods Appl. Mech. Engrg. 2005, 19(no. 2-5):531-548.
117. Forster H., Schrefl T., Dittrich R., Scholz W., Filder H. Fast Boundary Methods for Computing Demagnetizing Fields. IEEE Trans. Magn. 2003, 39(5):2513-2515.