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Magnetostriction is a change of a material's shape or dimensions associated with its magnetization. A magnetic field can therefore produce strain without a contact force. The resulting magnetoelastic coupling lets a ferromagnet convert changes of magnetic state into mechanical motion; a constraint can instead turn the preferred deformation into stress. James Prescott Joule published his study of iron and steel bars in 1847.^[ref]

The surprising point is that reversing the magnetization need not reverse the deformation. A material can prefer a longer axis along either $+\mathbf{m}$ or $-\mathbf{m}$: an axis has no arrow. Isotropic linear magnetostriction vanishes excludes one particular linear constitutive term, while saturated isotropic magnetostrictive strain supplies a nonzero response with a quadratic dependence on the magnetic direction. The pulsed-field optical magnetostriction experiment shows how an actual length change can be resolved, and quadratic magnetostriction and frequency doubling separates an illustrative response law from a measured material curve.