Calculation of Magnetostatic Fields in Nanostructured Ellipsoidal Cells of Exchange-Coupled Trilayers

Abstract

Numerical calculations based on the finite element method are performed in this study in order to calculate the self-demagnetizing field and the stray field in exchanged-coupled trilayers (Fe-Co-B (t nm)/ Ru (1 nm)/ Fe-Co-B (6 - trim)) with lateral dimensions of 212 nm (long axis) x 106 nm (short axis). Each layer of the cell is assumed to be an ellipsoid so that the self-demagnetizing field is uniform in the entire magnetic layer. The calculations are carried out in both 2D and 3D. The stray field is found to be quite nonuniform even within the magnetic layer and the nonuniformity is more pronounced near the edge. Due to its nonuniformity, the stray field is averaged over the entire magnetic volume in order to obtain the effective stray field within the magnetic layer. 3D calculations show that there is a difference as large as 750 A/m between the effective stray field and the self-demagnetizing field. This difference is duly reflected in the magnetic energy barrier. Detailed calculations; based on the method of using an analytical equation for the total energy, show a significant increase of the magnetic energy barrier from 48 kT to 84 kT at conditions relevant to high-density magnetic random access memory applications.