Combined Raman and infrared investigation of the insulator-to-metal transition in NiS${}_{2-x}$Se${}_x$ compounds

Ambient-condition Raman spectra were collected in the strongly correlated NiS${}_{1-x}$Se${}_x$ pyrite ($0\le x\le 1.2$). Two samples ($x=0$ and $x=0.55$) were studied as a function of pressure up to 10 GPa, and for the $x=0.55$ sample the pressure dependence of the infrared reflectivity was also measured (0–10 GPa). This gave a complete picture of the optical response of that system on approaching the metallic state both by application of pres-sure and/or by Se alloying, which corresponds to a volume expansion. A peculiar nonmonotonic (V-shaped) volume dependence was found for the quasiparticle spectral weight of both pure and Se-doped compounds. In the $x=0.55$ sample the vibrational frequencies of the chalcogen dimer show an anomalous volume dependence on entering the metallic phase. The abrupt softening observed, particularly significant for the Se-Se pair, indicates the relevant role of the softness of the Se-Se bond as previously suggested by theoretical calculations.

Figure 1

$T-x$ (Se content) phase diagram of NiS${}_{2-x}$Se${}_x$ after Ref. 11. Solid symbols indicate the Se content of the investigated samples and working temperature. The pyritic crystal structure is also sketched.

Figure 2

Raman spectra at ambient conditions of NiS${}_{2-x}$Se${}_x$ compounds. Best fit profile (black curve) is reported for the $x=0.00$ sample. DHO phonon contributions and electronic contributions (gray lines) are also reported.

Figure 3

Background-subtracted Raman spectra of the $x=0.00$ (a) and $x=0.55$ (b) NiS${}_{2-x}$Se${}_x$ samples as a function of pressure. The star on the spectrum collected at $P=3.8$ GPa marks the appearance of the $p$470-$p$480 doublet (see text).

Figure 4

Pressure dependence of the phonon frequencies of NiS${}_2$.

Figure 5

Pressure dependence of the phonon frequencies of NiS${}_{1.45}$Se${}_{0.55}$.

Figure 6

(a) $R$($\omega$) measured at the sample-diamond interface at high pressures, and evaluated at ambient pressure (dashed line), from Ref. 10. The best-fit curve of the 6.3 GPa spectrum is also reported (bold line). (b) Optical conductivity ${\sigma }_1$($\omega$) and its components from the best fit of the 6.3 GPa spectrum. (c) Quasiparticle spectral weight SW as a function of $P$ for $x=0.55$ and for $x=0.00$ from Ref. 10.

Figure 7

(a) Quasiparticle spectral weight of NiS${}_{2-x}$Se${}_x$ as a function of volume: open circles, $x=0.00$ (Ref. 10); full circles, $x=0.55$ (present data); triangles, ambient conditions, $x=0.00$, 0.55, 0.60, and 1.20 (Ref. 10). Volume dependencies of the $A$${}_g$ stretching frequencies of the S-S (b), Se-S (c), and Se-Se (d) dimers for $x=0.00$ (open circles), $x=0.55$ samples (full circles), and ambient-condition $x=0.00$, 0.55, 0.60, and 1.20 samples (triangles). Open diamonds and squares in (b) refer to the $p$470 and $p$480 peaks, respectively. The hatched stripe crossing (a) and (b) marks the volume region around 178 A${}^3$; the stripe crossing (b), (c), and (d) marks the volume region around 186 A${}^3$ (see text). Black and gray down triangles on the $V$ axis point out the volume values at ambient conditions for $x=0.00$ and $x=0.55$ samples. In all the panels full lines are guides to the eye.