Method of Measuring the Magnetoelastic Coupling Constants of Cylindrical Magnetic Films

Abstract

The magnetoelastic energy of a anisotropic film with an axis of symmetry is B_αα₁²ε₁₁²+ B_βα₂²ε₂₂+ 2B_γα₁α₂ε₁₂, where the B's are magnetoelastic coupling constants, the α's are direction cosines of the magnetization direction, and the ε's are strains. For a film with an easy axis in the circumferential direction (labeled 1), the effect of applying a tension in the axial direction (labeled 2) and introducing a strain ε₂₂ is to change the uniaxial anisotropy field H_k. The B's are related to this change by B_β+σB_α = ΔH_kM/(2_ε22), where M is the magnetization and σρ is Poisson's ratio of the wire substrate. The effect of twisting the wire and introducing a strain ε₁₂ is to rotate the easy direction through an angle φ. For small φ, B_γ is related to this skew angle by B_γ=‐MH_kφ/(2ε₁₂). For an isotropic film the B's are equal. Measurements have been made on a variety of Permalloy films, some with positive and some with negative magnetostriction, electroplated upon 5‐mil wire. If it is assumed that B_β=B_α, B_β is generally found to be larger than B_γ, and not unexpectedly the anisotropy of B is larger in films with large H_k.