Tin telluride: A weakly co-elastic metal

Abstract

We report resonant ultrasound spectroscopy (RUS), dilatometry/magnetostriction, magnetotransport, magnetization, specific-heat, and $^{119}\text{S}\text{n}$ M\"ossbauer spectroscopy measurements on SnTe and ${\text{Sn}}_{0.995}{\text{Cr}}_{0.005}\text{Te}$. Hall measurements at $T=77\text{ }\text{K}$ indicate that our Bridgman-grown single crystals have a $p$-type carrier concentration of $3.4\ifmmode\times\else\texttimes\fi{}{10}^{19}\text{ }{\text{cm}}^{\ensuremath{-}3}$ and that our Cr-doped crystals have an $n$-type concentration of $5.8\ifmmode\times\else\texttimes\fi{}{10}^{22}\text{ }{\text{cm}}^{\ensuremath{-}3}$. Although our SnTe crystals are diamagnetic over the temperature range $2\ensuremath{\le}T\ensuremath{\le}1100\text{ }\text{K}$, 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 $0.5\text{ }\ensuremath{\mu}\text{m}$ distortion at ${T}_{c}\ensuremath{\approx}85\text{ }\text{K}$. 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, ${\ensuremath{\theta}}_{D}$, values of SnTe obtained from $^{119}\text{S}\text{n}$ M\"ossbauer studies show a hardening of phonons in the range 60--115 K $({\ensuremath{\theta}}_{D}=162\text{ }\text{K})$ as compared with the 100--300 K range $({\ensuremath{\theta}}_{D}=150\text{ }\text{K})$. 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 $\ensuremath{\Delta}{C}_{44}/{C}_{44}=A{|(T\ensuremath{-}{T}_{0})/{T}_{0}|}^{\ensuremath{-}\ensuremath{\kappa}}$ with $\ensuremath{\kappa}=0.50\ifmmode\pm\else\textpm\fi{}0.02$, a value indicating a three-dimensional softening of phonon branches at a temperature ${T}_{0}\ensuremath{\sim}75\text{ }\text{K}$, 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.