The eigenvalues of the isotropic magnetic interaction system extraction from
Internal Field Approximation (IFA) q e computed. on the basis of RKKY for the
complicated magnetic behaviour of Gd, X system X= (Au , Pt , Al , In ) as well
as Gd. From the strength and slope of eigenvalue curves in different ranges of
interaction the strength and sharpness of the magnetic transition can be suggested. It
is shown that the values of the first transition temperature "T " as ferromagnetic
ordering "F.M", as well as its sharpness in the short-range interaction "R ", includes
at least two atomic layers, this being in agreement with reported experimental results.
In the long-range interaction, the second transition is predicted to be of the
antiferromagnetic order "AF.M" for Gd ,Al and Gd , In. It becomes impossible to see
the second transition for Gd Pt and Gd Au as interaction range is increased. For pure
metallic "Gd", however, the transition is shown to be of the helicoidal type in the range
of " 12- 17" A?, where all of these results correspond to experimental observations