Magnetic susceptibility of semimagnetic semiconductors: The high-temperature regime and the role of superexchange.

We present a systematic experimental study of the high-temperature susceptibility of diluted magnetic (semimagnetic) semiconductors ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Se, ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te, and ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Se, and we analyze these together with the previously published results for ${\mathrm{Hg}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te and ${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te. Despite their variety, all these materials reveal a common and very systematic pattern of behavior, which displays several interesting features. We formulate a theoretical model for the magnetic susceptibility in these systems in terms of the theory of a randomly dilute Heisenberg magnet, and we determine the dominant exchange integrals for each of the alloys by analyzing the available data according to this theory. The spin of ${\mathrm{Mn}}^{2+}$ ion in the first three compounds is also obtained and is found to be close to the atomic value of S=(5/2). We find quantitative correlations between the exchange integrals for the three tellurides, and similarity for both selenides, and on the basis of these observations we argue that superexchange is the dominant mechanism determining the magnetic behavior of all those systems. Within this mechanism of exchange the p-d (anion-${\mathrm{Mn}}^{2+}$) and the d-d (${\mathrm{Mn}}^{2+}$-${\mathrm{Mn}}^{2+}$) exchange integrals can be related. Since in semimagnetic semiconductors both integrals can be obtained from independent measurements, these materials provide a unique opportunity for detailed experimental testing of superexchange.