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Ferromagnetic shape-memory alloys have recently emerged as a new class of active materials showing very large magnetic-field-induced extensional strains. Recently, a single crystal of a tetragonally distorted Heusler alloy in the NiMnGa system has shown a 5% shear strain at room temperature in a field of 4 kOe. The magnetic and crystallographic aspects of the twin-boundary motion responsible for this effect are described. Ferromagnetic shape-memory alloys strain by virtue of the motion of the boundaries separating adjacent twin variants. The twin-boundary motion is driven by the Zeeman energy difference between the adjacent twins due to their nearly orthogonal magnetic easy axes and large magnetocrystalline anisotropy. The twin boundary constitutes a nearly 90° domain wall. Essentially, twin-boundary motion shorts out the more difficult magnetization rotation process. The field and stress dependence of the strain are reasonably well accounted for by minimization of a simple free energy expression including Zeeman energy, magnetic anisotropy energy, internal elastic energy, and external stress. Models indicate the limits to the magnitude of the field-induced strain and point to the material parameters that make the effect possible. The field-induced strain in ferromagnetic shape-memory alloys is contrasted with the more familiar phenomenon of magnetostriction. © 2000 American Institute of Physics.