Calculator for magnetostatic energy and demagnetizing factor

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Calculator for the magnetostatic energy and demagnetizing factor of a uniformly magnetized ferromagnetic prism

This tool (Javascript program) calculates the magnetostatic self energy and demagnetizing factor of a uniformly magnetized ferromagnetic rectangular prism analytically [1].

200_prism.png

Geometry of a regular prism with edge lengths 2a,2b,2c

This provides a quick and simple test if a micromagnetic code calculates the magnetostatic energy correctly. As input the 3 edge lengths of the prism and the magnetization saturation are required.

Dz is the demagnetizing factor when the body is magnetized uniformly along the z-axis.

a [nm]
b [nm]
c [nm]
Js [Tesla]
demagnetizing factor Dz
Energy density [kJ/m3
Energy [kB 300 K] 

Explanation

This calculator evaluates the following formula:

$ \begin{array}{l} \pi D_z = \\ \frac{b^2-c^2}{2bc} \ln\left(\frac{\sqrt{a^2+b^2+c^2}-a}{\sqrt{a^2+b^2+c^2}+a}\right)+ \frac{a^2-c^2}{2ac} \ln\left(\frac{\sqrt{a^2+b^2+c^2}-b}{\sqrt{a^2+b^2+c^2}+b}\right)+ \\ \frac{b}{2c} \ln\left(\frac{\sqrt{a^2+b^2}+a}{\sqrt{a^2+b^2}-a}\right)+ \frac{a}{2c} \ln\left(\frac{\sqrt{a^2+b^2}+b}{\sqrt{a^2+b^2}-b}\right)+ \\ \frac{c}{2a} \ln\left(\frac{\sqrt{b^2+c^2}-b}{\sqrt{b^2+c^2}+b}\right)+ \frac{c}{2b} \ln\left(\frac{\sqrt{a^2+c^2}-a}{\sqrt{a^2+c^2}+a}\right)+ \\ 2 \arctan\left(\frac{ab}{c\sqrt{a^2+b^2+c^2}}\right)+ \\ \frac{a^3+b^3-2c^3}{3abc}+ \frac{a^2+b^2-2c^2}{3abc} \sqrt{a^2+b^2+c^2}+ \\ \frac{c}{ab}\left(\sqrt{a^2+c^2}+\sqrt{b^2+c^2}\right)- \\ \frac{(a^2+b^2)^{3/2}+(b^2+c^2)^{3/2}+(c^2+a^2)^{3/2}}{3abc} \end{array} $

The self energy per volume unit then becomes: $ 2 \pi D_z M_s^2 $

Note that: $ D_x + D_y + D_z = 1 $

JavaScript code developed, published under GPL, and contributed by Rok Dittrich.

[1] Amikam Aharoni, "Demagnetizing factors for rectangular ferromagnetic prisms"
J. Appl. Phys. 83 (1998) 3432 [ J. Appl. Phys. 1 ], [ J. Appl. Phys. 2 ]


magpar - Parallel Finite Element Micromagnetics Package
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