Calculating the demagnetisation factors and their volume distribution within (a) assemblies of discrete magnetic elements and (b) solid magnetic samples of any given shape: A material-independent and multi-scalar polar model approach

Abstract

Measuring the magnetic characteristics of a magnetic sample, it is critical to evaluate the self-demagnetisation field, because it reduces the effective magnetic field experienced by the sample. The demagnetisation factor depends on the shape and nature of the sample, whether it is a solid, ordered assembly of magnetic elements, or randomly packed magnetic powder in a containing vessel. Literature provides limited information on the demagnetisation factor of packed powders, typically for a restricted number of container shapes. This paper introduces algorithms based on a polar model written in MATLAB 2022b, which calculates not only the average demagnetisation factor but also the entire distribution of demagnetisation factors for the constituent particles and, by extension, to any assembly of magnetic elements within a given volume. Furthermore, this study explains how to enhance the efficiency of these algorithms, reduce runtime, and apply them to any container shape.

The validity of the algorithms was assessed by calculating the data for three common container shapes described in literature over a range of aspect ratios: cuboids, ellipsoids, and cylinders. The calculated mean demagnetisation factors matched those found in the literature, typically within 0.05%, 0.1%, and 1%, respectively, for these shapes, demonstrating that the algorithms could be extrapolated to calculate demagnetisation data for any container shape; by extension, the magnetometric demagnetisation factor (zero susceptibility) for any solid shape, a hitherto unattainable parameter.

As the method reduces to calculations based on geometry alone, it is material-independent and can be applied to any macro-, meso-, or microscale of interest.