Theoretical background

I. Basic micromagnetic concept and main energy contributions

Theoretical micromagnetics as founded by W.F.Brown is a phenomenology for the evaluation of the total magnetic free energy Etot of a ferromagnetic body if its geometry, material parameters and the magnetization configuration are known. In its 'minimal' version micromagnetics takes into account four energy contributions:


Energy in the external field Eext:


Magnetocrystalline anisotropy energy Ean (e.g., uniaxial case):


Exchange stiffness energy Eexch (isotropic exchange assumed):


Magnetodipolar interaction energy (stray or demagnetizing) field energy Edem:


where the demagnetizing field Hdem can be calculated as a convolution of the magnetization distribution inside a ferromagnet with the dipolar interaction kernel.

II. Finite-difference approximations of the energy contributions used in MicroMagus

Notation:

Mi - magnetization in the cell # i, mi = Mi/Mi
Hiext - external field averaged over the cell # i
DVi - cell volume

1. External field


2. Anisotropy (Ki anisotropy constants)
3. Exchange (Jij exchange coeff., kij exch. weakening, aij angle between Mi and Mj)


4. Stray field (Wij interaction coeff. between cells i and j)