Low-temperature specific heat and low-field magnetic susceptibility were measured in ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ mixed crystals for $0.002<~x<~0.70$. Three regions of composition can be distinguished in both experiments. For $x<\mathrm{}0.17\mathrm{}$ the crystal is paramagnetic at all temperatures. For $0.17<x<\mathrm{}0.7\mathrm{}$, a spin-glass phase is observed, as evidenced by the characteristic cusp in the susceptibility and a linear temperature dependence of the specific heat in the low-temperature regions. Because the material is an insulator at low temperatures, and the Mn interactions are only antiferromagnetic, we believe that the observed spin-glass phase is produced by the frustration of the lattice. For $x=0.7\mathrm{}$ an antiferromagnetic phase is observed. To understand the experimental behavior of the specific heat and susceptibility as a function of temperature and magnetic field for $0.002<x<\mathrm{}0.17\mathrm{}$, we must assume that the distribution of Mn ions deviates strongly from a random distribution. The number of pairs is more than doubled for $x=0.05\mathrm{}$, and 30% higher for $x=0.1\mathrm{}$, than statistically predicted. The number of larger clusters, like triplets, is also significantly higher. Analysis of the data yielded the value of the exchange integral for the nearest-neighbor interaction to be $\frac{J_{\mathrm{NN}}}{k}=-0.55\mathrm{}\pm 0.05$ K. The interaction is stronger within the larger clusters, and is described by a different exchange constant $\frac{J_{\mathrm{NN}}^{\prime }}{k}=-4.3\mathrm{}$ K.

The influence of charge-carrier concentration on the magnetic properties of the semimagnetic semiconductor [(PbTe${)}_{1\mathrm{-}\mathrm{x}}$(SnTe${)}_{\mathrm{x}}$ ${]}_{1\mathrm{-}\mathrm{y}}$[MnTe] ${}_{\mathrm{y}}{}^{}{}_{}{}^{}$ (x=0.72, y=0.03) is reported. Magnetization, magnetic susceptibility, and specific heat have been measured. For carrier concentrations below p=3×${10}^{20}$ ${\mathrm{cm}}^{\mathrm{-}3}$ the alloy is paramagnetic. For p≥3×${10}^{20}$ ${\mathrm{cm}}^{\mathrm{-}3}$ an abrupt transition to a ferromagnetic phase is observed at helium temperatures. The ferromagnetic transition temperature increases with increasing p. This is the first demonstration of the effect of carrier concentration on the magnetic properties of semimagnetic semiconductors.

We present a systematic experimental study of the high-temperature susceptibility of diluted magnetic (semimagnetic) semiconductors ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Se, ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te, and ${\mathrm{Hg}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Se, and we analyze these together with the previously published results for ${\mathrm{Hg}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te and ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$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.

A systematic study of the low-dc-field magnetic susceptibility and the specific heat has been carried out on mixed ${\mathrm{Hg}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ crystals, in the composition range $0<~x<~0.35$. The alloy with $x=0.35\mathrm{}$ showed spin-glass behavior below $T=10.9\mathrm{}$ K. At this Mn concentration the sample is a very poor conductor at low temperatures, so that the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism cannot be responsible for the spin-glass transition. Also, since the Mn ions interact only antiferromagnetically, the observed spin-glass phase does not result from competition between ferro- and antiferromagnetic interaction. It must therefore be ascribed to the frustration of the antiferromagnetic interactions inherent in an fcc sublattice over which the Mn ions are distributed. For $x<~0.25$, the ${\mathrm{Hg}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ samples remain paramagnetic down to 1 K. Experimental results for the specific heat and the susceptibility for $x<\mathrm{}0.1\mathrm{}$ are discussed in terms of a cluster model which leads to an estimated value of the antiferromagnetic exchange constant $\frac{J}{k}\approx -0.7\mathrm{}\pm 0.3$ K. When a random distribution of Mn ions over the fcc sublattice is assumed, calculated values for the specific heat and the susceptibility differ substantially from the experimental results for the low Mn concentration. This therefore indicates that in real crystals the distribution of Mn ions is very different from random. To obtain agreement between calculated and experimental results, the number of single ions has to be reduced to less than 30% of the number corresponding to a purely random distribution, leading to the conclusion that the magnetic ions prefer to cluster rather than to remain isolated in ${\mathrm{Hg}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$. For HgTe, the Debye temperature ${\Theta }_D$ is 141 K at $T=0\mathrm{}$ K, and goes through an anomalously low minimum value of ${\Theta }_D=77\mathrm{}$ K at 7 K. A very small linear term in the low-temperature specific heat of HgTe gives an estimate of the electric charge carrier density in the ${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ range.

A magnetic-field—and temperature—dependent line is observed in the Raman spectra of a $n$-type semimagnetic semiconductor: ${\mathrm{Cd}}_{0.95}$ ${\mathrm{Mn}}_{0.05}$Se. It is attributed to spin-flip Raman scattering, with "giant" Stokes shift: 75 ${\mathrm{cm}}^{-1\mathrm{}}$ in 1 T at 1.6 K. A small zero-field Stokes shift is observed, which is attributed to an exchange-induced magnetic molecule under the electronic orbit of neutral donors.