Interactions Between Magnetic Layers Lying Between Soft Boundary Layers

Analytic expressions are derived in the 2D frequency-domain for the interaction between magnetized layers that lie between two sheets of soft magnetic material. For example, in writing and reading with perpendicular magnetic recording, a multilayer `hard' magnetic medium lies between the soft magnetic underlayer (SUL) of the medium and the soft structures (including shields) that form the read and write heads. The expression for the interaction between different layers is an extension of earlier work, however the derivation of the self-interaction of a single layer is novel as is the translation of these interactions into tensor form in Cartesian coordinates suitable for micromagnetic modeling.

I. Introduction

Computing the interaction fields between magnetic elements is a key step in solving micromagnetic problems. To avoid a large time-consuming convolution, the computation may be handled in the frequency domain [1]. The magnetization in an entire layer is taken into the frequency domain, multiplied by the 2D transfer-function, and then back-transformed to give the fields in another layer. Although the magnetization may evolve with time or as a solution converges, the transfer function from magnetization to field is fixed throughout the process. The transfer function may be computed in spatial domain and then transformed to frequency domain or it may be computed directly in the frequency domain. The latter approach, discussed here, will be shown to conveniently allow soft layers (with linear B-H characteristics) to be included above and below the interacting layers.