We study the micromagnetics of soft cubic ferromagnets with large magnetostriction, with the goal of understanding the microstructure and behavior of recently reported single-crystal Galfenol samples [Chopra and Wuttig in Nature 521(7552):340–343, 2015]. First, taking the no-exchange formulation of the micromagnetics energy [De Simone and James in J Mech Phys Solids 50(2):283–320, 2002], we construct minimizing sequences that yield local average magnetization and strain curves matching the experimental findings of Chopra and Wuttig (2015). Then, reintroducing a sharp-interface version of the exchange energy [Choksi and Kohn in Commun Pure Appl Math 51(3):259–289, 1998], we construct normal and zig-zag Landau states; within the parameter regime of Galfenol, we show that the latter achieves lower-energy scaling via equipartition of energy between the 90 ∘ wall energy, 180 ∘ wall energy and the anisotropy energy. This forms the first step in adapting the program of Kohn and Müller [Philos Mag A 66(5):697–715, 1992] to explain why certain magnetic microstructures are observed over others.
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Acknowledgements This work is a part of the Ph.D. dissertation of VD, and he was supported by a Doctoral Dissertation Fellowship provided by the Graduate School of the University of Minnesota. RV thanks his Ph.D. thesis advisers Professors Peter Sternberg and Dmitry Golovaty for their support and encouragement. He acknowledges the support from NSF DMS-1101290 and NSF DMS-1362879 and the Indiana University College of Arts and Sciences Dissertation Year Fellowship. The work of RDJ was supported by NSF (DMREF-1629026), and it also benefitted from the support of ONR (N00014-14-1-0714), AFOSR (FA9550-15-1-0207) and the MURI Program (FA9550-12-1-0458, FA9550-16-1-0566). Also, we would like to thank the anonymous referees for their detailed comments that considerably increased the clarity of the paper.
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- Cubic ferromagnets
- Pattern formation
- Scaling laws