Optical phonons and magnetoelastic coupling in the ionic conductor ${\mathrm{AgCrSe}}_2$

${\mathrm{AgCrSe}}_2$ is an example of a superionic conductor that has recently attracted attention for its low thermal conductivity. Here we investigate the optical properties of ${\mathrm{AgCrSe}}_2$ in the ordered phase between 14 K and 374 K using reflectivity experiments and compare them to the optical conductivity obtained from electronic structure calculations. The far infrared optical response is dominated by three phonon modes, while six interband transitions are observed in the visible range. We find good agreement between the experimental interband transitions and the calculated optical transitions. From our analysis we find that the phonon parameters display an interesting temperature dependence around the Néel temperature, pointing to a small magnetoelastic coupling. In addition, the lifetimes of the modes indicate that three-phonon processes dominate and the optical phonons decay into low-energy acoustic modes involved in the superionic transition. Finally, we detect a small free charge carrier response through the analysis of Fabry-Perot interference fringes in our reflectivity data.

Figure 1

The measured reflectivity against the photon energy used for selected temperatures. Interband transitions can be observed around 1 eV and 1.5 eV. The inset shows the reflectivity at a photon energy range of 4–50 meV. Three phonons are observed with smaller oscillations between 5 meV and 15 meV.

Figure 2

The real part of the optical conductivity ${\sigma }_1(\omega ,T)$, plotted against photon energy on a log-log scale. We observe three phonon modes in the infrared (see Table 1), and at low temperature a number of Farby-Perot interference fringes (see main text for details). The inset shows the optical conductivity over the full energy range.

Figure 3

(a–c) from left to right, (a) crystal structure viewed along the $b$ axis (Ag in blue, Cr in gray, and Se in orange), (b) crystal structure viewed along the $c$ axis, and (c) the Brillouin zone with several high symmetry points indicated. (d) The electronic band structure of ${\mathrm{AgCrSe}}_2$ calculated along high symmetry lines. An indirect band gap of 0.17 eV is observed, with the valence band maximum at $\mathrm{\Gamma }$ and the conduction band minimum along the $L\text{−}T$ line.

Figure 4

(a) Experimental optical conductivity at 14 K and decomposition in interband transitions. Also shown is the sum of the individual oscillators (dashed yellow line) compared to the experimental data (blue line). (b) Comparison of the optical response calculated in the random phase approximation with experimental oscillator positions. Dashed lines indicate approximate interband transitions determined from the oscillators in (a). The inset shows that the transition associated with the indirect band gap in the calculation around 0.2 eV corresponds well with the onset of interband transitions in the experimental data.

Figure 5

Eigenfrequency ${\mathrm{\Omega }}_0$ for phonon mode 1 (a), phonon 2 (b), and phonon 3 (c). Panels (d) and (e) display the corresponding oscillator strengths $f$. The vertical dashed lines in panels (a)–(e) indicate the Néel temperature. The red lines in panels (d) and (e) are a guide to the eye for the change of slope in the temperature dependence of the oscillator strength. Panel (f) shows the lifetimes associated with the phonon modes as a function of temperature together with fits to Eq. (1) (dashed black lines).

Figure 6

(a) Model calculation of Fabry-Perot interference pattern compared to experimental data based on the Drude-Lorentz model obtained from initial fits. (b) The same calculation, but now with an additional Drude response added to the model. (c) Optical conductivity with and without Drude response. The inset shows the difference between the two models imprinted on the reflectivity.