Magnetostatic are other sources of the total magnetic anisotropy called the macroscopic shape anisotropy. This concept is clear in the case of homogeneous magnetization in a ellipsoid, where the demagnetization tensor can be introduced in such way that the demagnetization field can be defined as:
is the demagnetization tensor,
is the demagnetization field and
is the magnetization of the system. Thus the density magnetostatic energy can be described as:
If the semiaxes a, b, and c of the ellipsoid represent the axes of the coordination system the
is a diagonal tensor.
An arbitrary direction of the magnetization with respect to the semiaxes can
be characterized by the direction cosine
. The tensor is given
and the magnetostatic energy density can be written as:
For thin films, magnetostatic interaction leads to an additional anisotropy favoring the in-plane anisotropy. In the case of elongated nanoparticles, magnetostatic interactions produce an additional easy axis parallel to the long dimensions.