Magnetostriction theory of ultrathin freestanding nanofilms

In this paper, a continuum theory for describing the magnetostrictive behavior of magnetic nanofilms is proposed. Surface effects (including surface elastic and surface magnetoelastic effects) as well as symmetry lowering of nanofilms are considered in the theoretical scheme. The spherical symmetry is lowered to the cylindrical one in nearly two-dimensional nanofilms. And then, there are some additional new elastic and magnetoelastic parameters induced by symmetry lowering have to be reckoned into model the magnetostriction of nanofilms rigorously. The application of our theoretical scheme to Fe nanofilms shows good agreement with experiment. The magnetostriction minimum vs film thickness of Fe nanofilms was produced straightforwardly. In addition, the surface elastic and surface magnetoelastic constants are physically reasonable and consistent with most solid surfaces (on the order of 1–10 J/m− 2 for surface elasticity and 10− 2–10− 4 J/m− 2 for surface magnetoelasticity). This fact confirms the great importance of additional new elastic and magnetoelastic parameters in magnetostriction theory of magnetic nanofilms. The relationship (λx = − 2λy = − 2λz) between magnetostrictions breaks down for nanofilms. In addition, when the magnetic field is applied along vertical direction, the magnetostriction of nanofilms behaves different from the case that magnetic field is applied along in-plane direction.