Analysis of film strain and stress in a film-substrate cantilever system

The bending problem of a magnetic film-nonmagnetic substrate cantilever system is studied by using the principle of energy minimization. Emphasis is placed on the analysis of geometrical and physical parameter dependence of the neutral plane, internal film stress and strain of the cantilever system, and then the influence of such a parameter on the bending characteristic is presented. The results indicate, owing to the anisotropic expanding feature of the magnetostriction, that the neutral plane is generally anisotropic, and moves downwards rapidly with the increasing thickness ratio. Meanwhile, the bounding rigidity of substrate on the film will decrease with the increasing thickness ratio, and thus release the film stress, i.e., it decreases, but the film strain increases. The effect of Poisson’s ratio of the materials on the film strain, the stress and the neutral plane in the direction transverse to the magnetization is prominent. For the strain and the stress in the magnetization, however, the role of Poisson’s ratio is inconspicuous. This property is due to the initiative elongating (or contracting) feature of the magnetic film along its magnetization. Supported by the National Natural Science Foundation of China (Grant No. 10762001), the Key Project of the Chinese Ministry of Education (Grant No. 206024), and the Program for New Century Excellent Talents in University of China (Grant No. NCET-2005-0272)