Tin telluride: A weakly co-elastic metal

We report resonant ultrasound spectroscopy (RUS), dilatometry/magnetostriction, magnetotransport, magnetization, specific-heat, and ${}^{119}\text{S}\text{n}$ Mössbauer spectroscopy measurements on SnTe and ${\text{Sn}}_{0.995}{\text{Cr}}_{0.005}\text{Te}$. Hall measurements at $T=77\text{K}$ indicate that our Bridgman-grown single crystals have a $p$-type carrier concentration of $3.4\times {10}^{19}{\text{cm}}^{-3}$ and that our Cr-doped crystals have an $n$-type concentration of $5.8\times {10}^{22}{\text{cm}}^{-3}$. Although our SnTe crystals are diamagnetic over the temperature range $2\le T\le 1100\text{K}$, the Cr-doped crystals are room-temperature ferromagnets with a Curie temperature of 294 K. For each sample type, three-terminal capacitive dilatometry measurements detect a subtle $0.5\mu \text{m}$ distortion at $T_c\approx 85\text{K}$. Whereas our RUS measurements on SnTe show elastic hardening near the structural transition, pointing to co-elastic behavior, similar measurements on ${\text{Sn}}_{0.995}{\text{Cr}}_{0.005}\text{Te}$ show a pronounced softening, pointing to ferroelastic behavior. Effective Debye temperature, ${\theta }_D$, values of SnTe obtained from ${}^{119}\text{S}\text{n}$ Mössbauer studies show a hardening of phonons in the range 60–115 K $\left({\theta }_D=162\text{K}\right)$ as compared with the 100–300 K range $\left({\theta }_D=150\text{K}\right)$. In addition, a precursor softening extending over approximately 100 K anticipates this collapse at the critical temperature and quantitative analysis over three decades of its reduced modulus finds $\Delta C_{44}/C_{44}=A{\left|\left(T-T_0\right)/T_0\right|}^{-\kappa }$ with $\kappa =0.50\pm 0.02$, a value indicating a three-dimensional softening of phonon branches at a temperature $T_0\sim 75\text{K}$, considerably below $T_c$. We suggest that the differences in these two types of elastic behaviors lie in the absence of elastic domain-wall motion in the one case and their nucleation in the other.

Figure 1

(Color online) Temperature evolution of magnetization of ${\text{Sn}}_{0.995}{\text{Cr}}_{0.005}\text{Te}$. In this plot, the Curie-Weiss region is only in the temperature range for $T>300\text{K}$. The parameters from a fit to the data above this region gives the Weiss constant $T_W=290\text{K}$, indicating ferromagnetic ordering. Above the ordering region, the effective number of Bohr magnetons is $p=3.3$. For paramagnetic ${\text{Cr}}^{2+}$ and ${\text{Cr}}^{3+}$, we have $p=4.9$ and for $p=3.8$, respectively. Thus $p=3.3$ is a reasonable value and indicates the Cr is in the $+3$ valence state.

Figure 2

Temperature dependence of the recoilless fraction, $f$, for the temperature regimes: (a) 60–115 K and (b) 90–300 K, respectively. The derived ${\theta }_D$ values of 162 K and 150 K, respectively, indicates a hardening of the phonon spectrum in the low-temperature phase.

Figure 3

(Color online) Temperature evolution of the spontaneous strain, ${\left[\Delta L/L\right]}_{\text{spontaneous}}$, in the low-temperature $R3m$ phase. The analysis used to determine the excess strain is discussed in the text. The curve through the data is the best fit of Eq. (10). Parameters deduced from this fit are given in the text.

Figure 4

(Color online) Dependence of the transition temperature on pressure and on the carrier concentration as derived from Landau theory including the quantum saturation [data points from Sugai et al. (Ref. 30)]. Shown also is the predicted pressure dependence of $T_c$ from the Landau parameters established in this paper.

Figure 5

(Color online) Upper panel: temperature evolution of the shear modulus $C_{44}$, expressed as the square of the lowest resonant frequency of the sample measured in a RUS experiment. Notice the different scales for the left- and right-ordinate axes. Lower panel: internal friction (loss) of the modes.

Figure 6

(Color online) Log-log plot of the precursor softening versus the reduced temperature $T-T_0$. The theoretical softening is $\Delta C_{44}=A{\left(T-T_0\right)}^{-\kappa }$ with $\kappa =0.5$.