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Atomistic Spin-Lattice Dynamics

  • Pui-Wai MaEmail author
  • S. L. Dudarev
Reference work entry
  • 22 Downloads

Abstract

Finite temperature magnetic fluctuations determine a variety of properties of magnetic materials, including their phase stability, their thermodynamic properties, and even the structure of defects formed under irradiation. A fundamental feature of microscopic magnetic fluctuations is the directional non-collinearity of fluctuating atomic magnetic moments, which stems from the rotational invariance of an atomic magnetic Hamiltonian. To model the dynamics of magnetic moments of atoms that move themselves, a fast and computationally efficient simulation approach is required. Spin-lattice dynamics simulates atomic movements as well as rotational and longitudinal fluctuations of atomic magnetic moments within a unified framework, generalizing molecular dynamics to magnetic materials. Collective magnetic and atomic excitations can now be investigated on the microscopic scale, similarly to how transformations of atomic structures can be investigated using molecular dynamics simulations. This chapter outlines theoretical foundations and numerical algorithms of spin-lattice dynamics and describes applications of the method.

Notes

Acknowledgments

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 under grant agreement No 633053 and from the RCUK Energy Programme (grant number EP/P012450/1). To obtain further information on the data and models underlying this paper, please contact PublicationsManager@ukaea.uk. The views and opinions expressed herein do not necessarily reflect those of the European Commission. We would like to thank Duc Nguyen-Manh for providing the data for Fig. 8.

References

  1. Beaujouan D, Thibaudeau P, Barreteau C (2012) Anisotropic magnetic molecular dynamics of cobalt nanowires. Phys Rev B 86:174409. https://link.aps.org/doi/10.1103/PhysRevB.86.174409 ADSCrossRefGoogle Scholar
  2. Brown Jr WF (1963) Thermal fluctuations of a single-domain particle. Phys Rev 130:1677–1686. https://link.aps.org/doi/10.1103/PhysRev.130.1677 ADSCrossRefGoogle Scholar
  3. Chandrasekhar S (1943) Stochastic problems in physics and astronomy. Rev Mod Phys 15:1–89. https://link.aps.org/doi/10.1103/RevModPhys.15.1 ADSMathSciNetCrossRefGoogle Scholar
  4. Coury MEA, Dudarev SL, Foulkes WMC, Horsfield AP, Ma PW, Spencer JS (2016) Hubbard-like Hamiltonians for interacting electrons in s, p, and d orbitals. Phys Rev B 93:075101. https://link.aps.org/doi/10.1103/PhysRevB.93.075101
  5. Daw MS, Baskes MI (1984) Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys Rev B 29:6443–6453. https://link.aps.org/doi/10.1103/PhysRevB.29.6443 ADSCrossRefGoogle Scholar
  6. Derlet PM, Nguyen-Manh D, Dudarev SL (2007) Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals. Phys Rev B 76:054107. https://link.aps.org/doi/10.1103/PhysRevB.76.054107 ADSCrossRefGoogle Scholar
  7. Dudarev SL, Derlet PM (2007) Interatomic potentials for materials with interacting electrons. J Computer-Aided Mater Des 14(Suppl 1):129–140. https://doi.org/10.1007/s10820-007-9073-x, https://link.springer.com/article/10.1007/s10820-007-9073-x
  8. Finnis MW (2003) Interatomic forces in condensed matter. Oxford series on materials modelling. Oxford University Press, OxfordCrossRefGoogle Scholar
  9. Fu CC, Willaime F, Ordejon P (2004) Stability and mobility of mono- and di-interstitials in α-Fe. Phys Rev Lett 92:175503. https://link.aps.org/doi/10.1103/PhysRevLett.92.175503 ADSCrossRefGoogle Scholar
  10. Gilbert TL (2004) A phenomenological theory of damping in ferromagnetic materials. IEEE Trans Magn 40(6):3443–3449.  https://doi.org/10.1109/TMAG.2004.836740 ADSCrossRefGoogle Scholar
  11. Hatano N, Suzuki M (2005) Finding exponential product formulas of higher orders. Springer, Berlin/Heidelberg, pp 37–68. https://doi.org/10.1007/11526216_2 Google Scholar
  12. Kubo R (1966) The fluctuation-dissipation theorem. Rep Prog Phys 29(1):255 http://stacks.iop.org/0034-4885/29/i=1/a=306 ADSCrossRefGoogle Scholar
  13. Landau LD, Lifshitz EM (1935) On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys Z Sowjetunion 8:153–164zbMATHGoogle Scholar
  14. Lavrentiev MY, Nguyen-Manh D, Dudarev SL (2010) Magnetic cluster expansion model for bcc-fcc transitions in Fe and Fe-Cr alloys. Phys Rev B 81:184202. https://link.aps.org/doi/10.1103/PhysRevB.81.184202 ADSCrossRefGoogle Scholar
  15. Lavrentiev MY, Soulairol R, Fu CC, Nguyen-Manh D, Dudarev SL (2011) Noncollinear magnetism at interfaces in iron-chromium alloys: the ground states and finite-temperature configurations. Phys Rev B 84:144203. https://link.aps.org/doi/10.1103/PhysRevB.84.144203 ADSCrossRefGoogle Scholar
  16. Ma PW, Woo CH (2009) Parallel algorithm for spin and spin-lattice dynamics simulations. Phys Rev E 79:046703. https://link.aps.org/doi/10.1103/PhysRevE.79.046703 ADSCrossRefGoogle Scholar
  17. Ma PW, Dudarev SL (2011) Langevin spin dynamics. Phys Rev B 83:134418. https://link.aps.org/doi/10.1103/PhysRevB.83.134418 ADSCrossRefGoogle Scholar
  18. Ma PW, Dudarev SL (2012) Longitudinal magnetic fluctuations in Langevin spin dynamics. Phys Rev B 86:054416. https://link.aps.org/doi/10.1103/PhysRevB.86.054416 ADSCrossRefGoogle Scholar
  19. Ma PW, Woo CH, Dudarev SL (2008) Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron. Phys Rev B 78:024434. https://link.aps.org/doi/10.1103/PhysRevB.78.024434 ADSCrossRefGoogle Scholar
  20. Ma PW, Dudarev SL, Semenov AA, Woo CH (2010) Temperature for a dynamic spin ensemble. Phys Rev E 82:031111. https://link.aps.org/doi/10.1103/PhysRevE.82.031111 ADSCrossRefGoogle Scholar
  21. Ma PW, Dudarev SL, Woo CH (2012) Spin-lattice-electron dynamics simulations of magnetic materials. Phys Rev B 85:184301. https://link.aps.org/doi/10.1103/PhysRevB.85.184301 ADSCrossRefGoogle Scholar
  22. Ma PW, Dudarev SL, Woo CH (2016) SPILADY: a parallel CPU and GPU code for spinlattice magnetic molecular dynamics simulations. Comput Phys Commun 207(Supplement C):350–361. https://doi.org/10.1016/j.cpc.2016.05.017, http://www.sciencedirect.com/science/article/pii/S0010465516301412
  23. Ma PW, Dudarev SL, Wróbel JS (2017) Dynamic simulation of structural phase transitions in magnetic iron. Phys Rev B 96:094418. https://link.aps.org/doi/10.1103/PhysRevB.96.094418 ADSCrossRefGoogle Scholar
  24. Nguyen-Manh D, Horsfield AP, Dudarev SL (2006) Self-interstitial atom defects in bcc transition metals: group-specific trends. Phys Rev B 73:020101. https://link.aps.org/doi/10.1103/PhysRevB.73.020101 ADSCrossRefGoogle Scholar
  25. Omelyan IP, Mryglod IM, Folk R (2001a) Algorithm for molecular dynamics simulations of spin liquids. Phys Rev Lett 86:898–901. https://link.aps.org/doi/10.1103/PhysRevLett.86.898 ADSCrossRefGoogle Scholar
  26. Omelyan IP, Mryglod IM, Folk R (2001b) Molecular dynamics simulations of spin and pure liquids with preservation of all the conservation laws. Phys Rev E 64:016105. https://link.aps.org/doi/10.1103/PhysRevE.64.016105 ADSCrossRefGoogle Scholar
  27. Omelyan IP, Mryglod IM, Folk R (2002) Construction of high-order force-gradient algorithms for integration of motion in classical and quantum systems. Phys Rev E 66:026701. https://link.aps.org/doi/10.1103/PhysRevE.66.026701 ADSCrossRefGoogle Scholar
  28. Perera D, Eisenbach M, Nicholson DM, Stocks GM, Landau DP (2016) Reinventing atomistic magnetic simulations with spin-orbit coupling. Phys Rev B 93:060402. https://link.aps.org/doi/10.1103/PhysRevB.93.060402 ADSCrossRefGoogle Scholar
  29. Pettifor DG (1995) Bonding and structure of molecules and solids. Oxford science publications, Clarendon Press. https://books.google.co.uk/books?id=r7XGPHD24fgC Google Scholar
  30. Tsai SH, Krech M, Landau DP (2004) Symplectic integration methods in molecular and spin dynamics simulations. Braz J Phys 34:384–391. http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332004000300009&nrm=iso ADSCrossRefGoogle Scholar
  31. Tsai SH, Lee HK, Landau DP (2005) Molecular and spin dynamics simulations using modern integration methods. Am J Phys 73(7):615–624. http://doi.org/10.1119/1.1900096 ADSCrossRefGoogle Scholar
  32. Van Kampen N (2011) Stochastic processes in physics and chemistry. North-Holland Personal Library, Elsevier Science. https://books.google.co.uk/books?id=N6II-6HlPxEC zbMATHGoogle Scholar
  33. Wen H, Ma PW, Woo C (2013) Spin-lattice dynamics study of vacancy formation and migration in ferromagnetic bcc iron. J Nucl Mater 440(1):428–434. https://doi.org/10.1016/j.jnucmat.2013.05.054, http://www.sciencedirect.com/science/article/pii/S0022311513008003
  34. Wróbel JS, Nguyen-Manh D, Lavrentiev MY, Muzyk M, Dudarev SL (2015) Phase stability of ternary fcc and bcc Fe-CrNi alloys. Phys Rev B 91:024108. https://link.aps.org/doi/10.1103/PhysRevB.91.024108 ADSCrossRefGoogle Scholar
  35. Zwanzig R (2001) Nonequilibrium statistical mechanics. Oxford University Press. https://books.google.co.uk/books?id=4cI5136OdoMC zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Culham Centre for Fusion EnergyUK Atomic Energy Authority, Culham Science CentreAbingdonUK

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