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.

我们完成了Dabade等人发起的分析。（J Nonlinear Sci 21：415–460，2018）关于立方铁磁体的微磁学，其中磁致伸缩的作用很重要。我们证明了二维样本的总微磁能（包括磁致伸缩贡献）的无标定下界。这对应于无限厚的样品的每单位长度的微磁能。我们分析的结果是，从能量的角度解释了最近在单晶Galfenol圆盘中报道的多尺度之字形Landau状态模式。我们的证明在能量驱动的图案形成中使用了许多成熟的技术。