Anisotropic contribution of magnetostriction to the elastic compliance constants in hexagonal materials: The Δs-effect

In this paper, we consider the single crystal analogue of the ΔE-effect in hexagonal materials with uniaxial magnetic anisotropy. We define Δs_ijld as the fractional change in the elastic compliance tensor s_ijkl in the demagnetized state relative to its value in the saturated state. The Δs-effect depends in general on the direction of the applied stress and the resulting magnetostrictive strain. We can show, however, that Δs_ijkl is always nonnegative when i=k and j=l. We then consider the measurements of the elastic constants in magnetic materials which have large magnetocrystalline anisotropy. The stresses applied in these measurements are not sufficient to rotate the magnetization away from the magnetically preferred direction, and hence cause no magnetostriction, and no Δs-effect. Therefore, it is not necessary to apply a saturating magnetic field along the easy axis in order to measure the true elastic constants in these materials.