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

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:Re?ectivity R of FeCr 2S 4vs.wave number for T =5K and 300K.A ?t of the re?ec-tivity for T =5K is indicated by the solid line.Lower panel:2D-contour plot of the re?ectivity 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 e?ect is di?erent 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 in?uence 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 e?ect corresponds nicely to the experimentally observed values in FeCr 2S 4and,therefore,Wakamura 29considered this mechanism

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

3

T (K)

ΓL , ΓT (cm -1

)

ωL , ωT (c m -1

)

FIG.2:(Color online)Temperature dependence of the longi-tudinal (transverse)resonance frequencies ωL (ωT )and damp-ing constants ΓL (ΓT )obtained by a 4-parameter ?t for the four IR-active phonons in FeCr 2S 4as described in the text.All solid lines are drawn to guide the eye.

to dominate the phonons’behavior for T T C .Sub-sequently,Wakamura and coworkers 31,35discussed the sign of the relative frequency shift in terms of nearest-neighbor FM exchange and next-nearest-neighbor AFM exchange for CdCr 2S 4,which exhibits phonon modes with a similar temperature dependence as FeCr 2S 4.Moreover,they could show that these anomalous changes in the phonon frequencies are absent in non-magnetic CdIn 2S 4,further corroborating their approach.35Thus,the positive shift of modes a and b would indicate that FM exchange (Cr-S-Cr)dominates in accordance with a strong in?uence of the (Cr-S)force constants on these modes,and,correspondingly,the negative shift of modes c and d favors AFM exchange (Cr-S-Cd-S-Cr)with a strong in?uence of the (Cd-S)force constants.Note that a more rigorous theoretical treatment of anhar-monic spin-phonon and phonon-phonon interactions in cubic spinels by Wesselinova and Apostolov 36con?rms the above interpretation.In FeCr 2S 4the interpretation of the e?ect of magnetic ordering on the IR active phonon modes becomes even more complicated,because there exist,besides FM nearest-neighbor Cr-S-Cr bonds,addi-tional exchange paths via AFM Fe-S-Fe and Fe-S-Cr-S-Fe bonds.Nevertheless,the overall temperature behavior of the phonon frequencies in FeCr 2S 4is similar to CdCr 2S 4and may be well interpreted,accordingly.Note,however,that a critical discussion of the above approach is given by Bruesch and d’Ambrogio.37

A straightforward interpretation of the temperature dependence of the damping constants (right panel of Fig.2)is not obvious at all.Again,considering only the anharmonicity of ionic non-magnetic crystals,the damp-

ing is expected to show some residual low-temperature value and a quasi-linear increase in the high-temperature limit,just as observed for the longitudinal damping con-stants of modes a and b for T >T C .29However,the temperature dependence of ΓL and ΓT in general devi-ates from such a behavior:In the case of mode d both damping constants show a broad maximum just above T C and a steep decrease towards lower temperature for T <T C .Mode c follows a similar temperature depen-dence for T <T C ,but the reduction of the damping constants is slightly smaller,and in the paramagnetic regime ΓL and ΓT remain almost constant in contrast to the results of Wakamura.29The behavior of modes a and b for T T C appears even more complex,but one can identify the onset of enhancement damping close to T C =170K followed by broad cusp-like maxima close to 100K,except for ωT of mode a that increases linearly with decreasing temperatures.

Wakamura 29argues that the maxima of mode d (and c )are due to spin ?uctuations of the Fe spins,in agree-ment with the strong in?uence of the corresponding force constant on this mode according to Bruesch and d’Ambrogio.37Furthermore,long range spin order as-sumingly leads to the anomalous changes of the damping constants for all modes below T C .In comparison to the temperature dependences of the damping constants in CdCr 2S 4,one ?nds that modes c and d behave similar to the case of FeCr 2S 4.31On the other hand,modes a and b in FeCr 2S 4clearly reveal a more co …… 此处隐藏：5933字，全部文档内容请下载后查看。喜欢就下载吧 ……