Modelling of Magnetic Stray Fields in Multilayer Magnetic Films with In-Plane or Perpendicular Anisotropy

Abstract

The magnetic stray field is an unavoidable consequence of magnetic multilayers, which may have a significant influence on the performance of spintronic devices. Based on Maxwell’s magnetostatics theory, here we numerically calculated the distributions of magnetic stray fields and self-demagnetizing fields in a series of patterned multilayer thin-film structures with either an in-plane or a perpendicularly magnetized ferromagnetic layer. The stray field above the ferromagnetic layer is inhomogeneous, showing the dramatic changes near the sample edge, but the uniformity in the center region could be improved with the increasing sample size. The stray field strength tends to zero for large samples, increases with the increase in the hard-layer thickness, and decreases with the increase in the distance D away from the ferromagnetic layer. In the multilayer samples, the separately simulated stray field and self-demagnetizing field within the soft layer agree well with the classic magnetostatic relationship of B=μ0(Hd+M). For the in-plane magnetized trilayer sample, the magnetic-flux density within the soft ferromagnetic layer slightly decreases in the antiparallel magnetization alignment and increases in the parallel alignment state with the increase in the intermediate non-magnetic-layer thickness. In contrast, for the sample with the perpendicular magnetization, the magnetic-flux density decreases as the non-magnetic layer is thickened for both the antiparallel and parallel state. This study may provide a theoretical basis for the design of thin-film spintronic devices.