Theory of magnetostriction with applications to TbxDy1-xFe2

We present a new approach to magnetostriction that is formulated to describe materials with large magnetostriction. The main idea of the theory is to derive precisely from lattice considerations the potential wells of the anisotropy energy. The theory exhibits frustration in the sense explored by the authors in the rigid case (James and Kinderlehrer [1990]), with fine domains modeled by minimizing sequences. The theory is applied to the material TbxDyi-xFe2. The theory predicts accurately the domain structures observed by Lord[1990] in growth twinned crystals, and suggests a mechanism of magnetostriction involving a switch from a coarse domain structure to a different finer domain structure.