Magnetostrictive bending of a film-substrate system

Abstract

Relations are derived between the curvatures produced by magnetization of a very thin epitaxial film on a substrate of finite thickness and the magnetoelastic coefficients of the film material. Relations are found both for a free system and for one constrained to be flat in one direction. The derivation includes the important effects of the discontinuity in strain at the interface, which interacts with the changing strain in the film as the system bends. This interaction, which has been omitted in previous derivations, produces curvatures twice as large as previous calculations for given magnetoelastic coefficients. The derivation is based on a specific simple form for the magnetoelastic energy as a function of strains and magnetization direction and proceeds by minimizing the total energy with respect to the two curvatures. Quantitative application is made to a measured system and compared to the results of previous theories. © 1996 The American Physical Society.