On a method to calculate the demagnetizing field in a micromagnetic structure

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Abstract
The simultaneous minimization of demagnetizing, exchange, anisotropy, and Zeeman energies in a micromagnetic structure is a difficult problem. The way it has been handled by previous investigators has often involved long running times or full matrices. In this paper, we take the demagnetizing energy into account by calculating the scalar potential φ associated with the demagnetizing field. This involves the calculation of another unknown φ in a problem which already has three unknowns: the components of the magnetization. By using φ, the problem is now uncoupled and the sparsity of the matrices is preserved. The magnetic structures studied here are thin slabs. We want to perform the calculations only on a small part of the slab. Since φ is defined in the whole space, the problem reduces to determining boundary conditions. By assuming that each unknown is periodic within the two directions in the plane of the slab, the domain of the problem reduces to a rectangular cell. The equations given in Ref. 1 are discretized by the finite‐element method and boundary elements are taken on the upper and lower surface to evaluate the scalar potential. This paper will outline the steps of the calculation of φ.

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