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Scale Transitions in Magnetisation Dynamics

Part of: Approximation methods and numerical treatment of dynamical systems Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  05 October 2016

Mikhail Poluektov ,
Olle Eriksson  and
Gunilla Kreiss
Mikhail Poluektov*
Affiliation:
Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden
Olle Eriksson*
Affiliation:
Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 05 Uppsala, Sweden
Gunilla Kreiss*
Affiliation:
Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden
*
*Corresponding author. Email addresses:mikhail.poluektov@it.uu.se (M. Poluektov), olle.eriksson@physics.uu.se (O. Eriksson), gunilla.kreiss@it.uu.se (G. Kreiss)
*Corresponding author. Email addresses:mikhail.poluektov@it.uu.se (M. Poluektov), olle.eriksson@physics.uu.se (O. Eriksson), gunilla.kreiss@it.uu.se (G. Kreiss)
*Corresponding author. Email addresses:mikhail.poluektov@it.uu.se (M. Poluektov), olle.eriksson@physics.uu.se (O. Eriksson), gunilla.kreiss@it.uu.se (G. Kreiss)
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Abstract

Multiscale modelling is a powerful technique, which allows for computational efficiency while retaining small-scale details when they are essential for understanding a finer behaviour of the studied system. In the case of materials modelling, one of the effective multiscaling concepts is domain partitioning, which implies the existence of an explicit interface between various material descriptions, for instance atomistic and continuum regions. When dynamic material behaviour is considered, the major problem for this technique is dealing with reflections of high frequency waves from the interface separating two scales. In this article, a new method is suggested, which overcomes this problem for the case of magnetisation dynamics. The introduction of a damping band at the interface between scales, which absorbs high frequency waves, is suggested. The idea is verified using a number of one-dimensional examples with fine/coarse scale discretisation of a continuum problem of spin wave propagation. This work is the first step towards establishing a reliable atomistic/continuum multiscale transition for the description of the evolution of magnetic properties of ferromagnets.

Keywords

Magnetisation dynamicsspin wavesmultiscale modellingmultigrid methods

MSC classification

Secondary: 65M55: Multigrid methods; domain decomposition 65Z05: Applications to physics 37M05: Simulation
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 4 , October 2016 , pp. 969 - 988
Copyright
Copyright © Global-Science Press 2016 

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References

[1] Beaurepaire, E., Merle, J.-C., Daunois, A., and Bigot, J.-Y.. Ultrafast spin dynamics in ferromagnetic nickel. Physical Review Letters, 76(22):4250–4253, 1996.CrossRefGoogle ScholarPubMed
[2] Stöhr, J., Samant, M. G., Lüning, J., Callegari, A. C., Chaudhari, P., Doyle, J. P., Lacey, J. A., Lien, S. A., Purushothaman, S., and Speidell, J. L.. Liquid crystal alignment on carbonaceous surfaces with orientational order. Science, 292(5525):2299–2302, 2001.CrossRefGoogle ScholarPubMed
[3] Gerrits, T., van den Berg, H. A. M., Hohlfeld, J., Bär, L., and Rasing, T.. Ultrafast precessional magnetization reversal by picosecond magnetic field pulse shaping. Nature, 418(6897):509–512, 2002.CrossRefGoogle ScholarPubMed
[4] Kimel, A. V., Kirilyuk, A., Tsvetkov, A., Pisarev, R. V., and Rasing, T.. Laser-induced ultrafast spin reorientation in the antiferromagnet TmFeO3 . Nature, 429(6994):850–853, 2004.CrossRefGoogle ScholarPubMed
[5] Tudosa, I., Stamm, C., Kashuba, A. B., King, F., Siegmann, H. C., Stöhr, J., Ju, G., Lu, B., and Weller, D.. The ultimate speed of magnetic switching in granular recording media. Nature, 428(6985):831–833, 2004.Google Scholar
[6] Radu, I., Vahaplar, K., Stamm, C., Kachel, T., Pontius, N., Dürr, H. A., Ostler, T. A., Barker, J., Evans, R. F. L., Chantrell, R. W., Tsukamoto, A., Itoh, A., Kirilyuk, A., Rasing, T., and Kimel, A. V.. Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins. Nature, 472(7342):205–208, 2011.CrossRefGoogle ScholarPubMed
[7] Aharoni, A.. Introduction to the theory of ferromagnetism. Oxford University Press, 1996.Google Scholar
[8] Cimrák, I.. A survey on the numerics and computations for the Landau-Lifshitz equation of micromagnetism. Archives of Computational Methods in Engineering, 15(3):277–309, 2008.CrossRefGoogle Scholar
[9] Skubic, B., Hellsvik, J., Nordström, L., and Eriksson, O.. A method for atomistic spin dynamics simulations: implementation and examples. Journal of Physics: Condensed Matter, 20(31):315203, 2008.Google Scholar
[10] Tadmor, E. B. and Miller, R. E.. Modeling materials. Cambridge University Press, 2011.CrossRefGoogle Scholar
[11] Miller, R. E. and Tadmor, E. B.. A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods. Modelling and Simulation in Materials Science and Engineering, 17(5):053001, 2009.CrossRefGoogle Scholar
[12] Qu, S., Shastry, V., Curtin, W. A., and Miller, R. E.. A finite-temperature dynamic coupled atomistic/discrete dislocation method. Modelling and Simulation in Materials Science and Engineering, 13(7):1101–1118, 2005.CrossRefGoogle Scholar
[13] Shiari, B., Miller, R. E., and Klug, D. D.. Multiscale simulation of material removal processes at the nanoscale. Journal of the Mechanics and Physics of Solids, 55(11):2384–2405, 2007.CrossRefGoogle Scholar
[14] Kazantseva, N., Hinzke, D., Nowak, U., Chantrell, R. W., Atxitia, U., and Chubykalo-Fesenko, O.. Towards multiscale modeling of magnetic materials: simulations of FePt. Physical Review B, 77(18):184428, 2008.CrossRefGoogle Scholar
[15] Jourdan, T., Marty, A., and Lançon, F.. Multiscale method for Heisenberg spin simulations. Physical Review B, 77(22):224428, 2008.Google Scholar
[16] Andreas, C., Kákay, A., and Hertel, R.. Multiscale and multimodel simulation of Bloch-point dynamics. Physical Review B, 89(13):134403, 2014.CrossRefGoogle Scholar
[17] Bartels, S. and Prohl, A.. Convergence of an implicit finite element method for the Landau-Lifshitz-Gilbert equation. Siam Journal On Numerical Analysis, 44(4):1405–1419, 2006.CrossRefGoogle Scholar
[18] d’Aquino, M., Serpico, C., and Miano, G.. Geometrical integration of Landau-Lifshitz-Gilbert equation based on the mid-point rule. Journal of Computational Physics, 209(2):730–753, 2005.CrossRefGoogle Scholar