Optical conductivity in multiferroic ${\mathrm{GaV}}_4{\mathrm{S}}_8$ and ${\mathrm{GeV}}_4{\mathrm{S}}_8$: Phonons and electronic transitions

We report on optical spectroscopy on the lacunar spinels ${\mathrm{GaV}}_4{\mathrm{S}}_8$ and ${\mathrm{GeV}}_4{\mathrm{S}}_8$ in the spectral range from 100 to 23 000 ${\mathrm{cm}}^{-1}$ and for temperatures from 5 to 300 K. These multiferroic spinel systems reveal Jahn-Teller driven ferroelectricity and complex magnetic order at low temperatures. We study the infrared-active phonon modes and the low-lying electronic excitations in the cubic high-temperature phase, as well as in the orbitally and in the magnetically ordered low-temperature phases. We compare the phonon modes in these two compounds, which undergo different symmetry-lowering Jahn-Teller transitions into ferroelectric and orbitally ordered phases, and exhibit different magnetic ground states. We follow the splitting of the phonon modes at the structural phase transition and detect additional splittings at the onset of antiferromagnetic order in ${\mathrm{GeV}}_4{\mathrm{S}}_8$. We observe electronic transitions within the $d$-derived bands of the ${\mathrm{V}}_4$ clusters and document a significant influence of the structural and magnetic phase transitions on the narrow electronic band gaps.

Figure 1

Semilogarithmic plot of the frequency dependence of the reflectivity spectra of ${\mathrm{GaV}}_4{\mathrm{S}}_8$ (a) and ${\mathrm{GeV}}_4{\mathrm{S}}_8$ (b) at a series of temperatures between 10 and 300 K. The data at 10 K correspond to the measured reflectivity. The indicated reflectivity scales in (a) and (b) are relevant only for the 10 K data. For clarity, the reflectivities for the higher temperatures were shifted by a constant offset of 0.05 each. Red arrows in both panels indicate the lowest-energy electronic excitations, i.e., the region of the gap edge.

Figure 2

Frequency dependence of the phonon spectra of ${\mathrm{GaV}}_4{\mathrm{S}}_8$ and ${\mathrm{GeV}}_4{\mathrm{S}}_8$ in the FIR range for selected temperatures. Spectra in the cubic high-temperature phases (a), (b) are compared to spectra taken in the paramagnetic and orbitally ordered phases (c), (d) as well as in the magnetically ordered phases (e), (f). The solid lines represent fits to the experimental data as described in the text.

Figure 3

Wave number dependencies of the reflectivity in ${\mathrm{GeV}}_4{\mathrm{S}}_8$ in the regions from (a) 290–350 ${\mathrm{cm}}^{-1}$ and (b) 430–500 ${\mathrm{cm}}^{-1}$ to document the splitting of phonon modes at the JT transition as well as at the onset of AFM order.

Figure 4

Temperature dependence of eigenfrequencies (a), (c), (e), and (g) and damping (b), (d), (f), and (h) of the four phonon modes in ${\mathrm{GaV}}_4{\mathrm{S}}_8$ in semilogarithmic representation. The dashed vertical lines indicate the magnetic and the structural phase transition at $T_{\mathrm{C}}=12.7$ K and $T_{\mathrm{JT}}=44$ K, respectively. The solid lines represent fits of the experimental data assuming anharmonic temperature dependences of eigenfrequencies and damping, as described in the text.

Figure 5

Temperature dependence of eigenfrequencies (a), (c), (e), and (g) and damping (b), (d), (f), and (h) of the four phonon modes observed in ${\mathrm{GeV}}_4{\mathrm{S}}_8$ in semilogarithmic representation. The dashed vertical lines indicate the magnetic and the structural phase transition at $T_{\mathrm{N}}=14.6$ K and $T_{\mathrm{JT}}=30.5$ K, respectively. The solid lines represent fits of the experimental data assuming anharmonic temperature dependences of eigenfrequencies and damping, as described in the text.

Figure 6

Temperature dependence of the optical conductivity of ${\mathrm{GaV}}_4{\mathrm{S}}_8$ for wave numbers up to 5200 ${\mathrm{cm}}^{-1}$ for selected temperatures between 8 and 300 K. The inset shows the temperature dependence of the frequency (in meV) at constant conductivity values of 200 and 400 ${\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$. These values provide an estimate of an apparent energy gap ${\tilde{E}}_{\mathrm{g}}$ (see text). Vertical dashed lines in the inset indicate structural and magnetic ordering temperatures.

Figure 7

Temperature dependence of the optical conductivity of ${\mathrm{GeV}}_4{\mathrm{S}}_8$ for wave numbers up to 7000 ${\mathrm{cm}}^{-1}$ for some selected temperatures between 10 and 300 K. The inset shows the temperature dependence of the frequency (in meV) at constant values of 150 and 200 ${\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$. These values provide an estimate of an apparent energy gap ${\tilde{E}}_{\mathrm{g}}$. Vertical dashed lines in the inset indicate structural and magnetic ordering temperatures.

Figure 8

Linear extrapolation of the optical conductivity in ${\mathrm{GaV}}_4{\mathrm{S}}_8$ to determine the size of the energy gap. Dashed lines indicate the linear extrapolation procedure. The temperature dependence of the gap values is documented in the inset. Vertical dashed lines indicate structural and magnetic ordering temperatures.

Figure 9

Linear extrapolation of the optical conductivity in ${\mathrm{GeV}}_4{\mathrm{S}}_8$ to determine the size of the energy gap. Dashed lines indicate the linear extrapolation procedure. The temperature dependence of the gap values is documented in the inset. Vertical dashed lines indicate structural and magnetic ordering temperatures.

Figure 10

Temperature dependence of the spectral weight in ${\mathrm{GaV}}_4{\mathrm{S}}_8$ (full circles; left scale) and ${\mathrm{GeV}}_4{\mathrm{S}}_8$ (open squares; right scale) as determined by integrating the optical conductivities up to 5000 ${\mathrm{cm}}^{-1}$. Arrows indicate the structural and magnetic phase transitions. The solid lines are drawn to guide the eye.