Anomalous dependence of $c$-axis polarized Fe ${\mathrm{B}}_{1g}$ phonon mode with Fe and Se concentrations in Fe${}_{1+y}$Te${}_{1-x}$Se${}_x$

We report on an investigation of the lattice dynamical properties in a range of Fe${}_{1+y}$Te${}_{1-x}$Se${}_x$ compounds, with special emphasis on the $c$-axis polarized vibration of Fe with ${\mathrm{B}}_{1g}$ symmetry, a Raman active mode common to all families of Fe-based superconductors. We have carried out a systematic study of the temperature dependence of this phonon mode as a function of Se $x$ and excess Fe $y$ concentrations. In parent compound Fe${}_{1+y}$Te, we observe an unconventional broadening of the phonon between room temperature and magnetic ordering temperature $T_N$. The situation smoothly evolves toward a regular anharmonic behavior as Te is substituted for Se and long-range magnetic order is replaced by superconductivity. Irrespective to Se contents, excess Fe is shown to provide an additional damping channel for the ${\mathrm{B}}_{1g}$ phonon at low temperatures. We performed density functional theory ab initio calculations within the local density approximation to calculate the phonon frequencies, including magnetic polarization and Fe nonstoichiometry in the virtual crystal approximation. We obtained a good agreement with the measured phonon frequencies in the Fe-deficient samples, while the effects of Fe excess are poorly reproduced. This may be due to excess Fe-induced local magnetism and low-energy magnetic fluctuations that cannot be treated accurately within these approaches. As recently revealed by neutron scattering and muon spin rotation studies, these phenomena occur in the temperature range where anomalous decay of the ${\mathrm{B}}_{1g}$ phonon is observed and suggests a peculiar coupling of this mode with local moments and spin fluctuations in Fe${}_{1+y}$Te${}_{1-x}$Se${}_x$.

Figure 1

Room-temperature Raman spectra of the Fe${}_{1.02}$Te, Fe${}_{1.00}$Te${}_{0.78}$Se${}_{0.22}$, Fe${}_{0.99}$Te${}_{0.69}$Se${}_{0.31}$, Fe${}_{0.98}$Te${}_{0.66}$Se${}_{0.34}$, and Fe${}_{0.95}$Te${}_{0.56}$Se${}_{0.44}$ samples (see Table ). Spectra have been shifted vertically for clarity. Eigendisplacements corresponding to the ${\mathrm{A}}_{1g}$(Te/Se) and ${\mathrm{B}}_{1g}$(Fe) are represented schematically.

Figure 2

(a) ${\mathrm{B}}_{1g}$ phonon of the Fe${}_{1.02}$Te sample for selected temperatures (room temperature, $T\sim T_N$, and base temperature). Black squares are the data, and the red line is the fit following the procedure described in the text. Phonon intensity have been normalized and the spectra have been shifted vertically for clarity. (b) Same plot for the Fe${}_{0.95}$Te${}_{0.56}$Se${}_{0.44}$ sample. (c) Same plot for the Fe${}_{1.05}$Te${}_{0.58}$Se${}_{0.42}$ sample.

Figure 3

(Upper panel) Temperature dependence of the ${\mathrm{A}}_{1g}$(Te/Se) mode frequency of the (a) Fe${}_{1.02}$Te, (b) Fe${}_{1.00}$Te${}_{0.78}$Se${}_{0.22}$, (c) Fe${}_{0.99}$Te${}_{0.69}$Se${}_{0.31}$, (d) Fe${}_{0.98}$Te${}_{0.66}$Se${}_{0.34}$, and (e) Fe${}_{0.95}$Te${}_{0.56}$Se${}_{0.44}$ samples. (Lower panel) Temperature dependence of the ${\mathrm{A}}_{1g}$(Te/Se) mode FWHM of the (f) Fe${}_{1.02}$Te, (g) Fe${}_{1.00}$Te${}_{0.78}$Se${}_{0.22}$, (h) Fe${}_{0.99}$Te${}_{0.69}$Se${}_{0.31}$, (i) Fe${}_{0.98}$Te${}_{0.66}$Se${}_{0.34}$, and (j) Fe${}_{0.95}$Te${}_{0.56}$Se${}_{0.44}$ samples.

Figure 4

(Upper panel) Temperature dependence of the ${\mathrm{B}}_{1g}$(Fe) mode frequency of the (a) Fe${}_{1.02}$Te, (b) Fe${}_{1.00}$Te${}_{0.78}$Se${}_{0.22}$, (c) Fe${}_{0.99}$Te${}_{0.69}$Se${}_{0.31}$, (d) Fe${}_{0.98}$Te${}_{0.66}$Se${}_{0.34}$, and (e) Fe${}_{0.95}$Te${}_{0.56}$Se${}_{0.44}$ samples. (Lower panel) Temperature dependence of the ${\mathrm{B}}_{1g}$(Fe) mode FWHM of the (f) Fe${}_{1.02}$Te, (g) Fe${}_{1.00}$Te${}_{0.78}$Se${}_{0.22}$, (h) Fe${}_{0.99}$Te${}_{0.69}$Se${}_{0.31}$, (i) Fe${}_{0.98}$Te${}_{0.66}$Se${}_{0.34}$, and (j) Fe${}_{0.95}$Te${}_{0.56}$Se${}_{0.44}$ samples. Solid lines are fits of the temperature dependence of the ${\mathrm{B}}_{1g}$ phonon frequency and linewidth in the various samples using the anharmonic model described in the text.

Figure 5

(a) Room temperature Raman spectra of the parent Fe${}_{1.02}$Te and Fe${}_{1.09}$Te samples (vertically shifted for clarity). (b) Example of the aging effect on the parent single crystals. The spectrum of powdered TeO${}_2$ from Ref. 47 has been added for comparison.

Figure 6

[(a) and (b)] Temperature dependence of the frequency the ${\mathrm{A}}_{1g}$ and ${\mathrm{B}}_{1g}$ modes in these samples. [(c) and (d)] Temperature dependence of the linewidth the ${\mathrm{A}}_{1g}$ and ${\mathrm{B}}_{1g}$ modes in these samples.

Figure 7

[(a) and (c)] Effect of the Fe excess on the temperature dependence of the ${\mathrm{B}}_{1g}$ mode frequency in Se-substituted samples. [(b) and (d)] Effect of the Fe excess on the temperature dependence of the ${\mathrm{B}}_{1g}$ mode linewidth in Se-substituted samples.