Inverse magnetostrictive effect

The inverse magnetostrictive effect, magnetoelastic effect or Villari effect is the change of the magnetic susceptibility of a material when subjected to a mechanical stress. The inverse magnetostrictive effect, magnetoelastic effect or Villari effect is the change of the magnetic susceptibility of a material when subjected to a mechanical stress. The magnetostriction λ {displaystyle lambda } characterizes the shape change of a ferromagnetic material during magnetization, whereas the inverse magnetostrictive effect characterizes the change of sample magnetization M {displaystyle M} (for given magnetizing field strength H {displaystyle H} ) when mechanical stresses σ {displaystyle sigma } are applied to the sample. Under a given uni-axial mechanical stress σ {displaystyle sigma } , the flux density B {displaystyle B} for a given magnetizing field strength H {displaystyle H} may increase or decrease. The way in which a material responds to stresses depends on its saturation magnetostriction λ s {displaystyle lambda _{s}} . For this analysis, compressive stresses σ {displaystyle sigma } are considered as negative, whereas tensile stresses are positive.According to Le Chatelier's principle: ( d λ d H ) σ = ( d B d σ ) H {displaystyle left({frac {dlambda }{dH}} ight)_{sigma }=left({frac {dB}{dsigma }} ight)_{H}} This means, that when the product σ λ s {displaystyle sigma lambda _{s}} is positive, the flux density B {displaystyle B} increases under stress. On the other hand, when the product σ λ s {displaystyle sigma lambda _{s}} is negative, the flux density B {displaystyle B} decreases under stress. This effect was confirmed experimentally. In the case of a single stress σ {displaystyle sigma } acting upon a single magnetic domain, the magnetic strain energy density E σ {displaystyle E_{sigma }} can be expressed as: E σ = 3 2 λ s σ sin 2 ⁡ ( θ ) {displaystyle E_{sigma }={frac {3}{2}}lambda _{s}sigma sin ^{2}( heta )} where λ s {displaystyle lambda _{s}} is the magnetostrictive expansion at saturation, and θ {displaystyle heta } is the angle between the saturation magnetization and the stress's direction. When λ s {displaystyle lambda _{s}} and σ {displaystyle sigma } are both positive (like in iron under tension), the energy is minimum for θ {displaystyle heta } = 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 λ 100 {displaystyle lambda _{100}} and λ 111 {displaystyle lambda _{111}} .