Phonon anomalies and charge dynamics in Fe_{1-x}Cu_{x}Cr_{2}(5)

A detailed investigation of phonon excitations and charge carrier dynamics in single crystals of Fe_{1-x}Cu_{x}Cr_{2}S_{4} (x = 0, 0.2, 0.4, 0.5) has been performed by using infrared spectroscopy. In FeCr_{2}S_{4} the phonon eigenmodes are strongly affecte

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can be seen in the vicinity of T C for the observable modes a,b,and e.Obviously,the temperature dependence of all phonon frequencies for x=0.5is very weak and no clear anomalies around T C are visible.Within the experimen-tal uncertainties one can detect a slight decrease ofωL towards lower temperatures except for mode c,which

be-haves similarly to the case of FeCr2S4(compare Fig.2). Keeping in mind the influence of spinfluctuations and spin-phonon coupling on the phonon properties in FeCr2S4,Cu-doping seems to reduce these features sig-nificantly.This observation is in agreement with reduced spin-orbit coupling due to the substitution of Jahn-Teller active Fe2+by non Jahn-Teller active Fe3+.Therefore, for x=0.5only Fe3+with a half-filled d-shell is present in the system17,39and the system becomes almost mag-netically isotropic as it was confirmed by ferromagnetic resonance experiments.23

B.Dynamic conductivity and electronic excitations When the reflectivities of the doped compounds with Cu concentrations x=0.2and0.5(Fig.3)are com-pared with that of pure FeCr2S4it becomes clear that contributions from free charge carriers have to be taken into consideration.The metallic-like behavior is most significant for x=0.2,but it becomes reduced again on further doping.For a consistent description of the Drude-type behavior of the doped compounds,it is important to measure the reflectivity spectra to higher energies. The room-temperature reflectivities of Fe1−x Cu x Cr2S4 for x=0.2and0.5are plotted in the upper panel of Fig.5 up to3×104cm−1,corresponding to almost4eV,and are compared to the reflectivity of insulating FeCr2S4. For the Kramers-Kronig analysis of the smoothed reflec-tivity data we used a low-frequency Hagen-Rubens ex-trapolation and a high-frequency extrapolation with a ν−0.5power law up to106cm−1and a subsequentν−4 high-frequency tail.The resulting dynamic conductiv-itiesσ(ν)are shown in the lower panel of Fig.5.We carefully checked the high-frequency extrapolation,also trying smoother extrapolations,but found that the re-sults are not influenced in the relevant energy range be-low20000cm−1.The use of a Hagen-Rubens extrapola-tion is justified by the fact that we have the complete in-formation on the absolute values of the dc conductivities and the corresponding temperature dependences for all compounds,although we are aware of the additional un-certainties originating from the Hagens-Rubens extrapo-lation,specifically for the sample with x=0.5.However, the bestfits of the reflectivity at room temperature,even in the limited spectral range,yielded dc conductivities of 150(Ωcm)−1for x=0.2and35(Ωcm)−1for x=0.5, close to the dc values derived from the4-probe measure-ments on single crystals by Fritsch et al.23

For x=0a weak but well defined electronic transi-tion is observed close to2000cm−1and a further tran-sition appears close to20000cm−1(≈2.5eV).On sub-

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σ

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ν (cm-1)

FIG.5:(Color online)Upper panel:Semi-logarithmic plot of the room-temperature reflectivity vs.wave number in Fe1−x Cu x Cr2S4for Cu concentrations x=0,0.2and0.5. Lower panel:Double-logarithmic plot of the real part of the dynamic conductivityσ1as derived from the reflectivity spec-tra.

stituting iron by copper,metallic behavior shows up and for Fe0.8Cu0.2Cr2S4the dc conductivity is of the order 150(Ωcm)−1.The transition at2000cm−1,becomes almost fully suppressed for x=0.2.Obviously,the d-electrons become strongly delocalized.It is generally ac-cepted that in an ionic picture monovalent Cu is substi-tuted inducing trivalent Fe.Our results suggest that the system behaves as if holes are doped into an insulator driving the compound into a metallic regime.Unexpect-edly,a broad peak appears again close to2500cm−1for x=0.5.

The observed doping dependence of the conduc-tivity spectra as documented in Fig.5can be compared with band-structure calculations of these compounds.17,21,39Local spin-density approximation (LSDA)band-structure calculations predict a half-metallic ground state of FeCr2S4,with a partlyfilled e band at the Fermi level.Correlation effects via LSDA+U yield a splitting of the Fe e band into a lower and up-per Hubbard band characterizing FeCr2S4as a Mott-Hubbard insulator.21The splitting of the e band is of the order of about0.5eV,and,hence,the peak close to 2000cm−1may be interpreted as a transition between the lower and upper Hubbard band.Accordingly,the high-energy excitation can be attributed to a Cr(3d)to