Superexchange and spin-glass formation in semimagnetic semiconductors

The Mn-Mn superexchange interaction in semimagnetic semiconductors ${\mathit{A}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Mn}}_{\mathit{xB}}$ (where A=Zn, Cd and B=S, Se, Te) is studied within the three-level model of the band structure. We focus on the dependence of the interaction on the interion distance ${\mathit{J}}^{\mathit{dd}}$(r)=${\mathit{J}}_0$f(r). In the present work, the function f(r) is obtained analytically. This, only weakly material-dependent function is found to decrease with Mn-Mn distance much slower than its Gaussian approximation derived previously. The exact form of the decay of the superexchange can be approximated by a power law ${\mathit{J}}_0$ ${\mathit{r}}^{\mathrm{-}8.5}$. This is close to an experimental result, ${\mathit{J}}_0$ ${\mathit{r}}^{\mathrm{-}6.8}$, determined on the basis of the spin-glass transition temperature on the composition. © 1996 The American Physical Society.