Abstract
A single-ion anisotropy mechanism is considered to discuss the volume average of magnetostriction in macroscopically isotropic amorphous ferromagnetic alloys. Within the framework of our phenomenological theory, the macroscopic magnetostrictive strain vanishes only if the volume average of the local anisotropy coefficients vanishes. In contrast, in crystalline materials magnetostriction vanishes if the strain derivative of the anisotropy coefficient vanishes. In transition metal base amorphous ferromagnets the theory satisfactorily explains the observed value of magnetostriction.