Inverse magnetostrictive effect

The inverse magnetostrictive effect, magnetoelastic effect or Villari effect, after its discoverer Emilio Villari, is the change of the magnetic susceptibility of a material when subjected to a mechanical stress. The magnetostriction characterizes the shape change of a ferromagnetic material during magnetization, whereas the inverse magnetostrictive effect characterizes the change of sample magnetization (for given magnetizing field strength ) when mechanical stresses are applied to the sample. Under a given uni-axial mechanical stress , the flux density for a given magnetizing field strength may increase or decrease. The way in which a material responds to stresses depends on its saturation magnetostriction . For this analysis, compressive stresses are considered as negative, whereas tensile stresses are positive. According to Le Chatelier's principle: This means, that when the product is positive, the flux density increases under stress. On the other hand, when the product is negative, the flux density decreases under stress. This effect was confirmed experimentally. In the case of a single stress acting upon a single magnetic domain, the magnetic strain energy density can be expressed as: where is the magnetostrictive expansion at saturation, and is the angle between the saturation magnetization and the stress's 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 [100] axes are the directions of easy magnetization, while there is little magnetization along the [111] directions (unless the magnetization becomes close to the saturation magnetization, leading to the change of the domain orientation from [111] to [100]). This magnetic anisotropy pushed authors to define two independent longitudinal magnetostrictions and .