Cross-tie walls in 25-45 nm-thick Permalloy films

Abstract

Summary form only given. Cross-tie walls in Permalloy films have been calculated as a function of thickness at 25, 35, 40 and 45 nanometers (nm) using direct integration of the Landau-Lifshitz-Gilbert equation in a Cartesian lattice with periodic boundary conditions along the length of the wall (y-direction). Previously, the Bloch-to-Neel wall transition was found around 35 nm in a study where the two-dimensional (2D) Neel and Bloch walls were considered separately. The present work is extended to a 3D transition, a Bloch-like transition along the wall (or Vertical Bloch Lines (VBLs)), between Neel walls of opposite chirality in a film with in-plane magnetization. This 3D transition is a cross-tie wall, a low energy state, which allows for the long tails of Neel walls to close magnetic flux in the vicinity of the walls.