Magnetostriction in Amorphous Ferromagnets

Abstract

The change in length of a sample upon magnetization is a common phenomenon in all materials and it is known as linear magnetostriction. The macroscopic magnetostriction reflects the existence of interactions between the the local spin direction and the local strain. The physics underlying such magnetoelastic coupling can be understood from the concept of local magnetic anisotropy. The atomic magnetic moment is coupled to the atomic charge distribution through the spin-orbit interaction. On the other hand the electronic cloud interacts with the charge of the neighbouring atoms. When both neighbourhood atomic distribution and electronic charge distribution are anisotropic the total energy depends on the spin direction. This local anistropy, known as single-ion coupling, should be proportional to the spin-orbit interaction strength. Two-ion coupling originated by anisotropic exchange interaction is the second source of local magnetic anisotropy. For this case the strength of the anisotropy is also governed by the strength of the spin-orbit interaction (1,2). If we consider uniaxial local anisotropies they can be described by an energy term as Dcos2θ where θ is the angle between the magnetic moment and the local easy axes. For 3-d ferromagnets D is typically 105 erg/cm3 whereas it reaches a value of 107erg/cm3 for 4f samples. This difference in D values is a natural consequence of difference in atomic weight and therefore in spin-orbit interaction strength. The local anisotropy, being originated by electrical forces, is expected to change under local strains which change the arrangement and distances of neighbour atomic sites. The strain derivative of the local anisotropy is the magnetoelastic coefficient, B, which explains the linear magnetostriction phenomenon.