Model of localized state mediated exchange interaction and ferromagnetism in diluted magnetic semiconductors

The real mechanism of ferromagnetism in diluted magnetic semiconductors (DMSs), in particular in GaMnAs, is not yet fully understood. The well-known Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, mediated by itinerant charge carriers, is accepted to be responsible for the ferromagnetism in GaMnAs in its metallic state. At the same time, GaMnAs can be realized in an insulating state when there are no mobile carriers, and holes are localized at acceptors. At not too low Mn concentration, the overlap of acceptor-wave-function tails can be sufficient, and Mn d shells can be aligned by means of indirect mechanism mediated by localized holes. An increase in the content of Mn ions leads to their incorporation into interstitial positions, which in turn leads to self-compensation, i.e., the number of localized holes per paramagnetic center decreases. This means that the pairwise interaction of d shells can be mediated by two holes as well as single hole. In order to study the microscopic mechanism of indirect exchange, the energy and spin structure of molecule-like complexes with one and two charge carriers, localized by field of two paramagnetic ions, is investigated. It is shown that at short interionic distances (high concentration of magnetic component) the established mechanisms of indirect exchange resemble the well-known mechanisms of double- and superexchange with ferro- and antiferromagnetic alignment of magnetic moments, respectively. However, these results that can be found perturbatively, are significantly modified when the interionic distance R increases. Our calculations show that the magnetic ordering in insulating DMS crystal significantly depends not only on the concentration of magnetic component but on the compensation degree as well: cases of low or total compensation correspond to the absence of any magnetic ordering, whereas, the pronounced ferromagnetism is realized at a compensation degree close to a half. The simple estimate for the Curie temperature is derived in the limit of half-compensation.