Micromagnetics of Galfenol

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.