Phonon anomalies and charge dynamics in Fe_{1-x}Cu_{x}Cr_{2}(3)

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 fit 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 influence 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 influence 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 36confirms the above interpretation.In FeCr 2S 4the interpretation of the effect 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 fluctuations of the Fe spins,in agree-ment with the strong influence 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 finds 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 complex behavior than in CdCr 2S 4,indicating a significant influence of the iron sublattice and the additional effective exchange coupling between Fe-Fe and Fe-Cr ions on these modes.

Additionally,we want to mention the large increase in intensity (about 20%)for mode d (close to 120cm −1)when cooling from room temperature to 5K (see Fig.1).The intensity remains almost constant above 200K,while a linear increase with decreasing temperature is observed below 200K.At this temperature,maxima appear in the temperature dependence of the damping constants,sug-gesting a correlation of the two phenomena with regard to the spin-fluctuation scenario discussed above.

When adopting the overall interpretation of the data in terms of spin-phonon coupling,one has to consider,how-ever,that e.g.the appearance of the cusps in the damp-ing constants may be connected to domain reorientation processes visible in the ac susceptibility 24and anoma-lies detected by ultrasonic investigations.25Although the absence of significant changes of the phonon frequencies contradicts the scenario of a structural phase transition at 60K driven by orbital ordering as suggested in Ref.25,it becomes clear that the complex mechanisms dominat-ing the damping effects demand further theoretical stud-ies to single out the important contributions in detail.Having discussed the phonon properties of pure FeCr 2S 4we now turn to the temperature dependence of the phonon modes for Fe 1−x Cu x Cr 2S 4.Figure 3shows the FIR reflectivity for x =0.2(upper panel)and x =0.5(lower panel)for temperatures 5K and 300K each.The