Next: 2.1.4 Zeeman energy
Up: 2.1 Thermodynamic relations
Previous: 2.1.2 Magnetocrystalline anisotropy energy
  Contents
The origin of domains still cannot be explained by the two energy terms above. Another contribution comes from the magnetostatic self-energy, which originates from the classical interactions between magnetic dipoles. For a continuous material it is described by Maxwell's equations
In our magnetostatic problem, we do not have any electric fields or free currents . Thus, there are two remaining equations
The magnetic induction is given by
. A general solution of () is given by
|
(2.12) |
where is the magnetic scalar potential. Inserting the expressions for and in () gives
|
(2.13) |
inside magnetic bodies and
|
(2.14) |
outside in air or vacuum.
These equations have to be solved with the boundary conditions
|
(2.15) |
on the surface of the magnet to obtain and derive from it . is the unit normal to the magnetic body, taken to be positive in outward direction.
In micromagnetics, the magnetization distribution
is given. With relation () the magnetic scalar potential can be calculated from the magnetization distribution. The demagnetizing field
is then obtained by using ().
Finally the magnetostatic energy is given by
Next: 2.1.4 Zeeman energy
Up: 2.1 Thermodynamic relations
Previous: 2.1.2 Magnetocrystalline anisotropy energy
  Contents
Werner Scholz
2000-05-16