Phonon anomalies and charge dynamics in Fe_{1-x}Cu_{x}Cr_{2}(6)

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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Fe(3d)transition.

Using an ionic picture with localized Fe d states,alter-natively,the transition at2000cm−1may correspond to a transition between the lower e doublet and the t2triplet of the Fe d-states split in a tetrahedral crystal-field.The expected crystal-field splitting for Fe2+located in the tetrahedral site of the spinel structure is rather weak40 and a splitting of the order2000−3000cm−1seems rea-sonable.Further support for this interpretation comes from the observation of crystal-field transitions as mea-sured for diluted Fe2+in CdIn2S4.Here a crystal-field splitting of approximately2500cm−1has been reported by Wittekoek et al.41

The appearance of the broad excitation for x=0.5 in the mid-infrared region at about2500cm−1,how-ever,cannot be explained easily.In an ionic picture only trivalent iron and monovalent copper are expected for x=0.5,15,16and recent x-ray photoelectron spec-troscopy18strongly favors the existence of only mono-valent Cu for x=0.5.Therefore,one can exclude the possibility that the broad excitation may be attributed to Fe2+similarly to the well-defined electronic excita-tion for x=0.Nevertheless,it has been concluded from M¨o ssbauer experiments in Fe1−x Cu x Cr2S4,that an ionic picture is not applicable at all.42For x=0.3and T<T C the complicated M¨o ssbauer spectra indicate two different Fe sites corresponding to Fe2+and Fe3+,while for T>T C a single line pointed towards a fast elec-tron exchange between these two sites.For x=0.5the line pattern for T>T C evidenced the existence of Fe3+ and a strong delocalization of the Cu d-derived electrons. Hence,further studies beyond the scope of this paper are needed to clarify the nature of this mid-infrared excita-tion.

In the following we will discuss the optical conduc-tivity results in the low frequency range in

compari-son with the dc conductivity data reported in Ref.23. The room-temperature spectra for the concentrations x=0.2and0.5,shown in Fig.5have been used to estimate the Drude-like conductivity.For all tempera-tures,the spectra could satisfactorily be described us-ing a plasma frequencyωp=12000cm−1and a dielec-tric constantǫ∞=10.6for x=0.2,which is close to the valueǫ∞=11.5for x=0.For x=0.5we used ωp=5000cm−1and an enhanced dielectric constant ǫ∞=15.5.The enhancedǫ∞indicates strong changes in the electronic excitation spectrum at higher frequencies, but due to the complexity of the spectrum in this energy region there is also a larger uncertainty inǫ∞for x=0.5. The decrease of the plasma frequency by a factor of2.4 can be explained by a decrease of the charge carrier den-sity,as Fe1−x Cu x Cr2S4approaches a metal-to-insulator transition close to x=0.5.With these values,the con-ductivity below500cm−1could reasonably befitted for all temperatures as indicated by the dashed lines in Fig.3 for the spectra at5K and300K.

The resulting temperature dependences of the dc con-ductivity(upper panel)and relaxation ratesγ∝τ−1

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FIG.6:(Color online)Upper panel:Temperature dependence of the dc conductivity of Fe1−x Cu x Cr2S4as determined from fits to the reflectivity(see text).The dc conductivities as observed from4-probe measurements23are indicated by solid lines and were scaled to the room temperature optical values. Lower panel:Temperature dependence of the Drude-like re-laxation rates.Ferrimagnetic ordering temperatures are indi-cated by arrows.The dashed and dash-dotted lines are drawn to guide the eye.

(lower panel)are shown in Fig.6.The dc conductivities as derived from4-probe measurements23are indicated by solid lines.The dc conductivities were scaled at room temperature,utilizing a factor of1.6for x=0.2and a factor of1.05for x=0.5.Above100K the4-probe dc results and the dc values as derived from the optical measurements follow a similar temperature dependence. However,at low temperatures the dc measurements are dominated by localization effects,which appear much weaker in the high-frequency(>100cm−1)derived op-tical data.That localization effects are most significant in the low-frequency(”dc”)transport measurements be-comes clear from the fact that in doped semiconductors the conductivity below the FIR regime increases almost linearly with frequency.43In the sample with x=0.5, which exhibits the lower conductivity,localization effects dominate already at higher temperatures.This may be attributed to a significant decrease of the charge-carrier density and concomitant increase of disorder due to the statistical distribution of the Cu ions in the lattice,39fur-ther discarding the possibility of A-site order of Fe and Cu for Fe1−x Cu x Cr2S4.