Magnetostriction is the coupling between a material's magnetic state and its mechanical deformation or stress. A constitutive expansion can contain coefficients constrained by rotational symmetry. In particular, an isotropic material cannot support a nonzero symmetric stress that is linear in a single magnetic-field vector through a third-rank isotropic coefficient.
Under proper rotations a third-rank isotropic tensor is proportional to the Levi-Civita symbol. Its contraction with a field vector is antisymmetric in the two stress indices. A physical symmetric stress therefore vanishes in this linear constitutive model. Under the full orthogonal group an ordinary isotropic third-rank tensor is already zero; the orientation-sensitive Levi-Civita tensor requires the usual pseudotensor distinction.
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Magnetostriction is a phenomenon in which a material changes its shape or dimensions in response to an applied magnetic field. This effect occurs in ferromagnetic and ferrimagnetic materials, where the arrangement of magnetic moments (magnetization) affects the lattice structure of the material. Essentially, as the magnetic domains within the material align in the presence of a magnetic field, the resulting changes in magnetization can lead to a mechanical strain.