Magnetic susceptibility, specific heat, and the spin-glass transition in ${\mathrm{Hg}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$

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.