## 3 The shape magnetic anisotropy

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:

 (11)

where is the demagnetization tensor, is the demagnetization field and is the magnetization of the system. Thus the density magnetostatic energy can be described as:

 (12)

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 , , and . The tensor is given by:

 (13)

and the magnetostatic energy density can be written as:

 (14)

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.

Rocio Yanes