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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.

Explanation

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 σ applied on a single magnetic domain, the magnetic strain energy density Eσ can be expressed as:[1]

Eσ=32λsσsin2(θ)

where λs is the magnetostrictive expansion at saturation, and θ the angle between the saturation magnetization and the stressed direction. When λs and σ are both positive (like in iron under tension), the energy is minimum for θ = 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 λ100 and λ111.

  • 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 [110] is a linear combination of λ100 and λ111.
  • Under assumptions of isotropic magnetostriction (i.e. domain magnetization is the same in any crystallographic directions), then λ100=λ111=λ and the linear dependence between the elastic energy and the stress is conserved, Eσ=32λσ(α1γ1+α2γ2+α3γ3)2. Here, α1, α2 and α3 are the direction cosines of the domain magnetization, and γ1, γ2,γ3 those of the bond directions, towards the crystallographic directions.

References

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