Inverse magnetostrictive effect
The inverse magnetostrictive effect (also known as Villari effect) is the name given to the change of the magnetic susceptibility of a material when subjected to a mechanical stress.
Whereas magnetostriction characterizes the shape change of a ferromagnetic material during magnetization, the inverse magnetostrictive effect characterizes the change of domain magnetization when a stress is applied to a material. This magnetostriction can be positive (magnetization increased by tension) like in pure iron, or negative (magnetization decreased by tension) like in nickel. In the case of a single stress applied on a single magnetic domain, the magnetic strain energy density can be expressed as:
where is the magnetostrictive expansion at saturation, and the angle between the saturation magnetization and the stressed direction. When and are both positive (like in iron under tension), the energy is minimum for = 0, i.e. when tension is aligned with the saturation magnetization. Consequently, the magnetization is increased by tension.
In fact, magnetostriction is more complex and depends on the direction of the crystal axes. In iron, the  axes are the directions of easy magnetization, while there is little magnetization along the  directions (unless the magnetization becomes close to the saturation magnetization, leading to the change of the domain orientation from  to ). This magnetic anisotropy pushed authors to define two independent longitudinal magnetostrictions and .
- In cubic materials, the magnetostriction along any axis can be defined by a known linear combination of these two constants. For instance, the elongation along  is a linear combination of and .
- Under assumptions of isotropic magnetostriction (i.e. domain magnetization is the same in any crystallographic directions), then and the linear dependence between the elastic energy and the stress is conserved, . Here, , and are the direction cosines of the domain magnetization, and , , those of the bond directions, towards the crystallographic directions.
- Bozorth, R. (1951). Ferromagnetism. Van Nostrand.
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