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

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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scribed elsewhere.17No indication for the existence of secondary phases was found by x-ray diffraction analysis of powdered single crystals.X-ray single-crystal anal-ysis confirmed the high structural homogeneity of the samples.The composition and homogeneity of the sam-ples were examined by electron-probe microanalysis.The samples were optically polished platelets with dimensions of about 3×5×1mm 3.Structural,

magnetic and elec-trical transport data are given in Ref.23.

Two Fourier-transform-infrared spectrometers with a full bandwidth of 10to 8000cm −1(Bruker IFS 113v)and 500to 42000cm −1(Bruker IFS 66v/S)together with a 4He cryostat (Oxford Optistat)were used for measurements of the optical reflectivity in the energy range from 70to 30000cm −1due to small sample di-mensions and for temperatures of 5K <T <300K.In order to investigate small fractions of the sample surface in the range of 0.1mm 2we utilized an IR microscope (Bruker IRscope II),which works in the far-(FIR)and mid-infrared (MIR)range.

III.

EXPERIMENTAL RESULTS AND

DISCUSSION

A.

Phonon excitations

Figure 1shows the temperature dependence of the FIR reflectivity R vs.wave number of pure FeCr 2S 4.In the upper panel R is plotted for 5and 300K.The four visi-ble phonon peaks are attributed to the four IR-active F 1u modes (symmetry group F d 3m ,#227).28To analyze the spectra,we used a 4-parameter fit assuming frequency-dependent damping constants to account for the asym-metry of the phonon peaks.This fitting procedure infers a splitting of the longitudinal and transverse eigenfre-quencies,ωL and ωT ,and the corresponding damping constants,ΓL and ΓT .30The resulting curves describe the measured reflectivity down to 100cm −1very well,with-out assuming an additional contribution of free charge carriers.A representative result of these fits is shown by the solid line in the upper panel of Fig.1for T =5K.The detailed temperature dependence of the reflectivity is visualized in the two-dimensional (2D)contour plot in the lower panel of Fig.1.To enable a comparison of the phonon shift,the peak positions (maxima in R )for T =5K are indicated as vertical lines.Around T C =167K a shift of the phonon frequencies can be observed,especially for the mode d close to 100cm −1.The intensity of this mode strongly depends on temper-ature,too (see upper frame of Fig.1).

The resonance frequencies ωL and ωT (left frames)and the corresponding damping rates ΓL and ΓT (right frames)are shown in Fig.2as a function of temperature.Above the Curie temperature T C =167K,the resonance frequencies ωL and ωT of all modes reveal a similar quasi-linear increase with decreasing temperature,which can be fully ascribed to anharmonic contributions to the lat-

R

R

ν (cm -1

)

T (K )

0.4

0.8

FIG.1:(Color online)Upper panel:Reflectivity R of FeCr 2S 4vs.wave number for T =5K and 300K.A fit of the reflec-tivity for T =5K is indicated by the solid line.Lower panel:2D-contour plot of the reflectivity R vs.νand T generated by interpolation of 17spectra.The vertical lines are highlighting the maxima of the IR-active-phonons in R at 5K.

tice potential.31In contrast to the rather usual behavior in the paramagnetic regime,modes a and b soften for temperatures below T C ,while ωL and ωT increase to-wards lower temperatures in the case of modes c and d .These anomalous changes of the eigenfrequencies in the vicinity of T C suggest a correlation with the onset of magnetic order.However,it has to be stated that the size of the effect is different for the observed modes:∆ω=[ω(T =T C )−ω(T =0K)]/ω(T =0K)is of the order of +3%for the internal mode d , +1%for the bending mode b ,approximately −1.5%for the bending mode c ,and −1%for the stretching mode a .Longitudi-nal and transverse eigenfrequencies behave rather similar.The influence of magnetic order on phonons in magnetic semiconductors has been proposed by Bal-tensperger and Helman 32and Baltensperger 33more than 30years ago,and has recently been used by Sushkov et al.to describe the phonon spectra in ZnCr 2O 4.34Based on a model calculation,where superexchange interac-tion between the magnetic ions infers a spin-phonon cou-pling,relative frequency shifts up to 10−2have been pre-dicted.The order of magnitude of this effect corresponds nicely to the experimentally observed values in FeCr 2S 4and,therefore,Wakamura 29considered this mechanism