Exact demagnetisation field for periodic one-dimensional array of rectangular prisms

TL;DR

This paper derives an exact analytical expression for the magnetic field of a periodic array of rectangular prisms, improving accuracy in micromagnetic simulations especially for thin prisms.

Contribution

It introduces a new analytical solution for the field of periodic prism arrays, validated numerically and compared favorably with existing methods.

Findings

Exact on-axis field for infinite array of prisms derived.

Excellent convergence demonstrated for the new method.

Comparison shows improved accuracy over macrogeometry and uniform magnetisation approaches.

Abstract

The magnetic field from a uniformly magnetised, rectangular prism is known exactly, which is the basis for a large number of micromagnetic simulations. Here we derive an analytical solution for the field from a periodically repeating infinite array of prisms aligned end-to-end, which becomes exact on the center axis in the limit of infinitesimally thin prisms. Using the same method we derive the on-axis field for a one-dimensional array of point dipoles. We validate the obtained results numerically and furthermore compare with the common macrogeometry approach and more recent uniform magnetisation method, demonstrating an excellent convergence rate for the novel method.