Indirect exchange interaction for zero‐gap semiconductors in the Kane model

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Abstract
The magnetic susceptibility of a gapless semimagnetic semiconductor have been calculated. The susceptibility is determined by the exchange interaction between the localized magnetic ions, caused by virtual electron transitions from occupied valence bands to the empty one. The band structure of the semiconductor was described in the framework of the four‐band Kane model. Unlike the previous works, the general equations for the exchange integral have been derived, taking into account the transitions from all three occupied bands into the empty ‘‘light‐hole’’ band. The susceptibility for Hg1−xMgxTe with x=0.01 and x=0.016 and within the temperature range from 5 to 250 K have been calculated. numerically In the numerical calculations, the transitions from the spin‐orbit band have been neglected. The experimental values of the exchange interaction energies for the closest ion pairs (those within one Bravais cell) have been used. The sign of the exchange interaction constant does not change for all distances larger than between those pairs. In the calculations of the susceptibility the general formula has been used, which takes into account the possibility of a ‘‘freeze‐out’’ of the close ion pairs. It is shown that the temperature dependence of the magnetic susceptibility can be described approximately by the expression χ−1=AT/n+BT1/4, where n is the magnetic ion concentration.