EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 59 / No 1 (January-February 2025) ESAIM: M2AN, 59 1 (2025) 167-199 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
Page(s) 167 - 199
DOI https://doi.org/10.1051/m2an/2024065
Published online 14 January 2025
  1. C. Abert, G. Hrkac, M. Page, D. Praetorius, M. Ruggeri and D. Suess, Spin-polarized transport in ferromagnetic multilayers: an unconditionally convergent FEM integrator. Comput. Math. Appl. 68 (2014) 639–654. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  2. J. Ahrens, B. Geveci and C. Law, ParaView: an end-user tool for large-data visualization, in Visualization Handbook, edited by C.D. Hansen and C.R. Johnson. Elsevier (2005) 717–731. [CrossRef] [Google Scholar]
  3. F. Alouges, A new finite element scheme for Landau–Lifchitz equations. Discrete Contin. Dyn. Syst. Ser. S 1 (2008) 187–196. [MathSciNet] [Google Scholar]
  4. F. Alouges and P. Jaisson, Convergence of a finite element discretization for the Landau–Lifshitz equation in micromagnetism. Math. Models Methods Appl. Sci. 16 (2006) 299–316. [CrossRef] [MathSciNet] [Google Scholar]
  5. F. Alouges and A. Soyeur, On global weak solutions for Landau–Lifshitz equations: existence and nonuniqueness. Nonlinear Anal. 18 (1992) 1071–1084. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bach, M. Cicalese, L. Kreutz and G. Orlando, The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling. Calc. Var. Partial Differ. Equ. 60 (2021) 149. [CrossRef] [Google Scholar]
  7. A. Bach, M. Cicalese, L. Kreutz and G. Orlando. The antiferromagnetic XY model on the triangular lattice: topological singularities. Indiana Univ. Math. J. 71 (2022) 2411–2475. [CrossRef] [MathSciNet] [Google Scholar]
  8. V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono and Y. Tserkovnyak, Antiferromagnetic spintronics. Rev. Mod. Phys. 90 (2018) 015005. [CrossRef] [Google Scholar]
  9. S. Bartels, Numerical Methods for Nonlinear Partial Differential Equations. Vol. 47 of Springer Series in Computational Mathematics. Springer (2015). [CrossRef] [Google Scholar]
  10. S. Bartels, Projection-free approximation of geometrically constrained partial differential equations. Math. Comput. 85 (2016) 1033–1049. [Google Scholar]
  11. A. Braides, Γ-Convergence for Beginners. Vol. 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2002). [Google Scholar]
  12. W.F. Brown, Micromagnetics. Interscience Tracts on Physics and Astronomy. Interscience Publishers (1963). [Google Scholar]
  13. F. Bruckner, M. Feischl, T. Führer, P. Goldenits, M. Page, D. Praetorius, M. Ruggeri and D. Suess, Multiscale modeling in micromagnetics: existence of solutions and numerical integration. Math. Models Methods Appl. Sci. 24 (2014) 2627–2662. [CrossRef] [MathSciNet] [Google Scholar]
  14. F. Cutugno, L. Sanchez-Tejerina, R. Tomasello, M. Carpentieri and G. Finocchio, Micromagnetic understanding of switching and self-oscillations in ferrimagnetic materials. Appl. Phys. Lett. 118 (2021) 052403. [CrossRef] [Google Scholar]
  15. L.C. Evans, Weak Convergence Methods for Nonlinear Partial Differential Equations. Vol. 74 of CBMS Regional Conference Series in Mathematics. Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (1990). [CrossRef] [Google Scholar]
  16. L.C. Evans, Partial Differential Equations. Vol. 19 of Graduate Studies in Mathematics, 2nd edition. American Mathematical Society (2010). [CrossRef] [Google Scholar]
  17. A. Fert, N. Reyren and V. Cros, Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2 (2017) 17031. [CrossRef] [Google Scholar]
  18. G. Hrkac, C.-M. Pfeiler, D. Praetorius, M. Ruggeri, A. Segatti and B. Stiftner, Convergent tangent plane integrators for the simulation of chiral magnetic skyrmion dynamics. Adv. Comput. Math. 45 (2019) 1329–1368. [CrossRef] [MathSciNet] [Google Scholar]
  19. S.K. Kim, G.S.D. Beach, K.-J. Lee, T. Ono, T. Rasing and H. Yang, Ferrimagnetic spintronics. Nat. Mater. 21 (2022) 24–34. [CrossRef] [PubMed] [Google Scholar]
  20. J. Kraus, C.-M. Pfeiler, D. Praetorius, M. Ruggeri and B. Stiftner, Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics. J. Comput. Phys. 398 (2019) 108866. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Li, J. Chen, R. Du and X.-P. Wang, Numerical methods for antiferromagnets. IEEE Trans. Magn. 56 (2020) 1–9. [Google Scholar]
  22. P. Li, C. Xie, R. Du, J. Chen and X.-P. Wang, Two improved Gauss–Seidel projection methods for Landau–Lifshitz–Gilbert equation. J. Comput. Phys. 401 (2020) 109046. [CrossRef] [MathSciNet] [Google Scholar]
  23. C.T. Ma, X. Li and S.J. Poon, Micromagnetic simulation of ferrimagnetic TbFeCo films with exchange coupled nanophases. J. Magn. Magn. Mater. 417 (2016) 197–202. [CrossRef] [Google Scholar]
  24. E. Martínez, V. Raposo and O. Alejos, Current-driven domain wall dynamics in ferrimagnets: micromagnetic approach and collective coordinates model. J. Magn. Magn. Mater. 491 (2019) 165545. [CrossRef] [Google Scholar]
  25. N. Ntallis and K.G. Efthimiadis, Micromagnetic simulation of an antiferromagnetic particle. Comput. Mater. Sci. 97 (2015) 42–47. [CrossRef] [Google Scholar]
  26. V. Puliafito, R. Khymyn, M. Carpentieri, B. Azzerboni, V. Tiberkevich, A. Slavin and G. Finocchio, Micromagnetic modeling of terahertz oscillations in an antiferromagnetic material driven by the spin Hall effect. Phys. Rev. B 99 (2019) 024405. [CrossRef] [Google Scholar]
  27. A. Ramage and E.C. Gartland Jr, A preconditioned nullspace method for liquid crystal director modeling. SIAM J. Sci. Comput. 35 (2013) B226–B247. [CrossRef] [Google Scholar]
  28. A. Salimath, F. Zhuo, R. Tomasello, G. Finocchio and A. Manchon, Controlling the deformation of antiferromagnetic skyrmions in the high-velocity regime. Phys. Rev. B 101 (2020) 024429. [CrossRef] [Google Scholar]
  29. L. Sánchez-Tejerina, V. Puliafito, P. Khalili Amiri, M. Carpentieri and G. Finocchio, Dynamics of domain-wall motion driven by spin-orbit torque in antiferromagnets. Phys. Rev. B 101 (2020) 014433. [CrossRef] [Google Scholar]
  30. J. Schöberl, Netgen/NGSolve (2023). https://ngsolve.org.v6.2.2302. [Google Scholar]
  31. L.R. Scott and S. Zhang, Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54 (1990) 483–493. [Google Scholar]
  32. M. Struwe, Variational methods – applications to nonlinear partial differential equations and hamiltonian systems, in Vol. 34 of Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics, 4th edition. Springer-Verlag, Berlin (2008). [Google Scholar]
  33. R. Tomasello, L. Sanchez-Tejerina, V. Lopez-Dominguez, F. Garescì, A. Giordano, M. Carpentieri, P.K. Amiri and G. Finocchio, Domain periodicity in an easy-plane antiferromagnet with Dzyaloshinskii–Moriya interaction. Phys. Rev. B 102 (2020) 224432. [CrossRef] [Google Scholar]
  34. X.-P. Wang, C.J. García-Cervera and E. Weinan, A Gauss–Seidel projection method for micromagnetics simulations. J. Comput. Phys. 171 (2001) 357–372. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you