Bounds on the Energy of a Soft Cubic Ferromagnet with Large Magnetostriction

Raghavendra Venkatraman, Vivekanand Dabade, Richard D. James

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We complete the analysis initiated in Dabade et al. (J Nonlinear Sci 21:415–460, 2018) on the micromagnetics of cubic ferromagnets in which the role of magnetostriction is significant. We prove ansatz-free lower bounds for the scaling of the total micromagnetic energy including magnetostriction contribution, for a two-dimensional sample. This corresponds to the micromagnetic energy per unit length of an infinitely thick sample. A consequence of our analysis is an explanation of the multi-scale zig-zag Landau state patterns recently reported in single crystal Galfenol disks from an energetic viewpoint. Our proofs use a number of well-developed techniques in energy-driven pattern formation.

Original languageEnglish (US)
Pages (from-to)3367-3388
Number of pages22
JournalJournal of Nonlinear Science
Issue number6
StatePublished - Dec 1 2020
Externally publishedYes

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© 2020, Springer Science+Business Media, LLC, part of Springer Nature.


  • Energy-driven pattern formation
  • Entropies
  • Magnetostriction
  • Micromagnetics


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