Scalar Spin—Spin Interaction in Solids with Paramagnetic Impurities

Abstract

A band electron interacting with N electrons in a d-shell of a paramag-netic impurity in zinc-blende type semiconductors was considered. The hy-bridization of band and d-states in the crystal field and the nonorthogonality mechanisms of interaction were examined in addition to the standard direct exchange. The Heisenberg-type form was derived for the interaction between a Γ8-electron and an impurity with a half-filled d-shell. The domination of the hybridization mechanism explains the observed sign of the effective exchange constant for Fs electrons in diluted magnetic semiconductors (DMS) and the difference in magnitude of this constant for Mn 2 + and Fe 3+ ions in HgSe. PACS numbers:75.50.Pp, 75.30.-m,71.70.-d It is generally believed that the spin-dependent interaction of band electrons with paramagnetic ions in DMS can be described by an effective Heisenberg type Hamiltonian proportional to the product S. J, where S is the total spin operator of d-electrons and J is the appropriate quasi-angular momentum for the band electron. Such a Hamiltonian has been rigorously derived from the direct exchange interaction for an electron in s-like bands (whatever the number of electrons in the d-shell of the paramagnetic ion) [1] and for an electron in Γ8 bands in zinc-b l e n d e type crystals [2], but only in the case of a half filled d-shell. Incompatible with the direct exchange mechanism, experimental results for DMS gave a negative effective exchange constant β f or Γ8 bands.