  Because of large spatial separation of the Mn atoms in Heusler alloys the Mn
3d states belonging to different atoms do not overlap considerably. Therefore
an indirect exchange interaction between Mn atoms should play a crucial role in
the ferromagnetism of the systems. To study the nature of the ferromagnetism of
various Mn-based semi- and full-Heusler alloys we perform a systematic
first-principles calculation of the exchange interactions in these materials.
The calculation of the exchange parameters is based on the frozen-magnon
approach. The calculations show that the magnetism of the Mn-based Heusler
alloys depends strongly on the number of conduction electrons, their spin
polarization and the position of the unoccupied Mn 3d states with respect to
the Fermi level. Various magnetic phases are obtained depending on the
combination of these characteristics. The Anderson's s-d model is used to
perform a qualitative analysis of the obtained results. The conditions leading
to diverse magnetic behavior are identified. If the spin polarization of the
conduction electrons at the Fermi energy is large and the unoccupied Mn 3d
states lie well above the Fermi level, an RKKY-type ferromagnetic interaction
is dominating. On the other hand, the contribution of the antiferromagnetic
superexchange becomes important if unoccupied Mn 3d states lie close to the
Fermi energy. The resulting magnetic behavior depends on the competition of
these two exchange mechanisms. The calculational results are in good
correlation with the conclusions made on the basis of the Anderson s-d model
which provides useful framework for the analysis of the results of
first-principles calculations and helps to formulate the conditions for high
Curie temperature.
