Structure of domain walls in multiple films

Abstract

We derive an approximate solution of the micromagnetic equations for a Néel-type wall in multiple films. A small normal component of magnetization M permits most of the pole distribution to concentrate on the film surfaces. Thus, the magnetic-field energy resides mostly in the nonmagnetic gaps between magnetic films. The wall structure is found to consist of two "wings" having little exchange energy which flank a "kernel" in which only exchange and anisotropy energy terms are significantly involved. The kernel makes secondary contributions to the total width and energy of the wall. In first order, the wing shape is given by Mx = M0 exp{-[(K/πDb)1/2 |x|/M0]}, where K = anisotropy, b = thickness of nonmagnetic layer, x = distance normal to the wall plane, and D = one magnetic layer thickness for a double film or one-half of a thickness for an infinite number of layers. The first-order energy per unit area is 2M 0(πKDb)1/2. This energy is lower than previous results and extends the region of stability for Néel walls (as opposed to Bloch walls) to greater D, especially for small b. © 1966 The American Institute of Physics.