Strain coupling, microstructure dynamics, and acoustic mode softening in germanium telluride

GeTe is a material of intense topical interest due to its potential in the context of phase-change and nanowire memory devices, as a base for thermoelectric materials, and as a ferroelectric. The combination of a soft optic mode and a Peierls distortion contributes large strains at the cubic-rhombohedral phase transition near 625 K and the role of these has been investigated through their influence on elastic and anelastic properties by resonant ultrasound spectroscopy. The underlying physics is revealed by softening of the elastic constants by ∼30%–45%, due to strong coupling of shear and volume strains with the driving order parameter and consistent with an improper ferroelastic transition which is weakly first order. The magnitude of the softening is permissive of the transition mechanism involving a significant order/disorder component. A Debye loss peak in the vicinity of 180 K is attributed to freezing of the motion of ferroelastic twin walls and the activation energy of ∼0.07 eV is attributed to control by switching of the configuration of long and short Ge-Te bonds in the first coordination sphere around Ge. Precursor softening as the transition is approached from above can be described with a Vogel-Fulcher expression with a similar activation energy, which is attributed to coupling of acoustic modes with an unseen central mode that arises from dynamical clusters with local ordering of the Peierls distortion. The strain relaxation and ferroelastic behavior of GeTe depend on both displacive and order/disorder effects but the dynamics of switching will be determined by changes in the configuration of distorted $\mathrm{GeT}{\mathrm{e}}_6$ octahedra, with a rather small activation energy barrier.

Figure 1

Segments of RUS spectra collected from a rectangular parallelepiped of GeTe with dimensions $1.977\times 3.283\times 4.611\mathrm{m}{\mathrm{m}}^3$ and mass 0.1822 g. Each spectrum has been offset up the $y$ axis in proportion to the temperature at which it was collected. (a) Cooling sequence, ∼760 K to room temperature. (b) Heating sequence, ∼7 K to room temperature.

Figure 2

(a) Temperature dependence of $f^2$ for selected resonances, scaled to overlap near room temperature. A small hysteresis of the transition point between heating (∼630 K) and cooling (∼620 K) indicates weak first order character. The straight line is a fit to data collected at the highest temperatures and extrapolated to lower temperatures in order to represent reference values $f_{\mathrm{o}}^2$ of the cubic structure. (b) Temperature dependence of $Q^{-1}$ from selected resonances, showing a marked break in trend at ∼650 K, a peak in the vicinity of the minimum in $f^2$, and frequency-dependent maxima near 180 K.

Figure 3

Arrhenius plot of frequency $f$ versus $1/T_{\mathrm{m}}$, from the data of Table 1. An activation energy $U=0.066\pm 0.005\mathrm{eV}$ is obtained from the slope and ${\tau }_{\mathrm{o}}=2.8\times {10}^{-8}\pm \sim 1\times {10}^{-8}\mathrm{s}$ from one over the intercept.

Figure 4

Variations of $\mathrm{\Delta }{f}^2=\left(f_{\mathrm{o}}^2-f^2\right)$ with temperature. (a) The data above the transition temperature do not have a linear temperature dependence with slope between −1/2 and −2, as would be expected for a power-law description for $T_{\mathrm{c}}=581\mathrm{K}$. (b) Curves through the data above $T_{\mathrm{tr}}$ are fits of a Vogel-Fulcher equation.

Figure 5

Strain analysis of the $Fm\overline{3}m-R3m$ transition in GeTe, showing weakly first order character. (a) Cell parameter variations compiled from the literature. Straight lines fit to data points for $a$ at the highest temperatures represent the variations of $a_{\mathrm{o}}$ extrapolated to lower temperatures. (b) Curves through the data for $\cos \alpha (\sim e_4\propto q_1^2)$ are fits of Eq. (A12), with $T_{\mathrm{tr}}$ fixed at values specified in the original work and values of the fit parameters given in Table 3. (c) Curves through the data for $e_{\mathrm{a}}(\propto q_1^2)$ are fits of Eq. (A12), with parameters given in Table 3. (d) $e_{\mathrm{a}}$ does not scale linearly with $e_4$ as expected from Eqs. (A8) and (A10) over the entire range.