Role of conduction electrons in mediating exchange interactions in Mn-based Heusler alloys

Because of the large spatial separation of the Mn atoms in Heusler alloys (d(Mn-Mn)>4 angstrom), 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 Curie temperature is estimated within the mean-field approximation. The calculations show that the magnetism of the Mn-based Heusler alloys depends strongly on the number of conduction sp 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 magnetic phase diagram is determined at zero temperature. The results of the calculations are in good agreement with available experimental data. Anderson's s-d model is used to perform a qualitative analysis of the obtained results. The conditions leading to a 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, a Ruderman-Kittel-Kasuya-Yoshida-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 calculation 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.