Phonon anomalies and charge dynamics in Fe_{1-x}Cu_{x}Cr_{2}S_{4} single crystals

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

a r X i v :c o n d -m a t /0506052v 1 [c o n d -m a t .s t r -e l ] 2 J u n 2005

Phonon anomalies and charge dynamics in Fe 1?x Cu x Cr 2S 4single crystals

T.Rudolf,1K.Pucher,1F.Mayr,1D.Samusi,2V.Tsurkan,1,2R.Tidecks,3J.Deisenhofer,1and A.Loidl 1

1

EP V,Center for Electronic Correlation and Magnetism,University of Augsburg,86135Augsburg,Germany

2

Institute of Applied Physics,Academy of Sciences of Moldova,MD 2028,Chisinau,Republic of Moldova

3

Institute of Physics,University of Augsburg,86135Augsburg,Germany

(Dated:February 2,2008)

A detailed investigation of phonon excitations and charge carrier dynamics in single crystals of Fe 1?x Cu x Cr 2S 4(x =0,0.2,0.4,0.5)has been performed by using infrared spectroscopy.In FeCr 2S 4the phonon eigenmodes are strongly a?ected by the onset of magnetic order.Despite enhanced screening e?ects,a continuous evolution of the phonon excitations can be observed in the doped compounds with x =0.2(metallic)and x =0.4,0.5(bad metals),but the e?ect of magnetic ordering on the phonons is strongly reduced compared to x =0.The Drude-like charge-carrier contribution to the optical conductivity in the doped samples indicates that the colossal magneto-resistance e?ect results from the suppression of spin-disorder scattering.

PACS numbers:72.15.-v,72.20.-i,78.30.-j,75.30.Vn

Keywords:infrared spectroscopy,optical spectra,chalcogenide spinel,colossal magnetoresistance

I.INTRODUCTION

The discovery of colossal magnetoresistance (CMR)in perovskite-type manganites has attracted considerable attention.1,2,3,4,5Double-exchange (DE)mechanism,6,7strong electron-phonon coupling,7phase separation scenarios 8or a Gri?ths singularity 9were suggested to clarify the origin of the CMR e?ect,but a conclusive mi-croscopic model has not yet been established.Ever since,the occurrence of CMR e?ects has been reported for vari-ous other classes of materials,such as pyrochlores,10rare-earths based compounds like GdI 2,11and ternary chalco-genide spinels A Cr 2S 4.12These CMR materials have been classi?ed in terms of spin-disorder scattering and a universal dependence of the magnetoresistence vs.carrier density has been suggested on theoretical grounds.13,14Ramirez et al.drew attention to the spinel system Fe 1?x Cu x Cr 2S 4in 1997.12In polycrystalline FeCr 2S 4with T C =170K,the CMR e?ect reaches values compa-rable to those observed in perovskite oxides.The substi-tution of Fe by Cu increases T C to temperatures above room temperature,and the CMR e?ect remains relatively strong (～7%).12In addition,solid solutions of the ferri-magnetic semiconductor FeCr 2S 4and the metallic ferro-magnet CuCr 2S 4show a number of puzzling properties:From the very beginning,a controversial discussion has been arising whether the Cu ions are mono-or divalent for x ≥0.5.15,16,17For x <0.5it was established that only monovalent and hence diamagnetic (d 10)Cu exists in the mixed crystals.18Moreover,Fe 1?x Cu x Cr 2S 4shows two metal-to-insulator transitions as a function of x ,as the room-temperature resistivity reveals two minima at x =0.2and x =1and concomitantly the Seebeck co-e?cient changes sign two times.15,19Additionally,band-structure calculations predicted that the Fe 1?x Cu x Cr 2S 4system should exhibit a half-metallic nature.17,20,21

Recent experimental investigations of Fe 1?x Cu x Cr 2S 4single crystals indicated a strong dependence of their

magnetic and magneto-transport properties on hy-drostatic pressure suggesting a strong magneto-elastic coupling.22,23Measurements on the ac susceptibility in pure FeCr 2S 4exhibited a cusp in the low-?eld magneti-zation and the onset of magnetic irreversibilities at 60K was explained by domain-reorientation processes.24Later on,ultrasonic studies indicated an anomaly in the tem-perature dependence of the shear modulus close to 60K,and it was suggested that the onset of orbital order in-duces a structural distortion at this temperature.25This result,however,is hardly compatible with the observa-tion that orbital order is established in polycrystals close to 10K,while an orbital glass state is found in single crystals.26

Optical spectroscopy simultaneously probes the lattice and electronic degrees of freedom and is,therefore,ide-ally suited to investigate structural phase transitions and to clarify the importance of electron-phonon coupling for the CMR e?ect.27Earlier infrared (IR)studies in polycrystalline FeCr 2S 4reported,in accordance with the crystal-lattice symmetry F d 3m ,the existence of four IR-active phonons,which strongly depend on temperature near and below T C .28,29We performed measurements of the optical properties of single crystals of Fe 1?x Cu x Cr 2S 4(x =0,0.2,0.4and 0.5)to shed light on the interplay of structural and electronic properties in these compounds.Since the optical properties of the samples with x =0.4and x =0.5were found to be very similar,we only show and discuss the corresponding data for x =0.5in the following.

II.EXPERIMENTAL DETAILS

Single crystals of Fe 1?x Cu x Cr 2S 4were grown using a chemical transport-reaction method with chlorine as transport agent and the ternary polycrystals as start-ing material.Details of the sample preparation are de-

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

2

scribed elsewhere.17No indication for the existence of secondary phases was found by x-ray di?raction analysis of powdered single crystals.X-ray single-crystal anal-ysis con?rmed 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 re?ectivity 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 re?ectivity 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 ?t assuming frequency-dependent damping constants to account for the asym-metry of the phonon peaks.This ?tting 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 re?ectivity down to 100cm ?1very well,with-out assuming an additional contribution of free charge carriers.A representative result of these ?ts is shown by the solid line in the upper panel of Fig.1for T =5K.The detailed temperature dependence of the re?ectivity 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: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 complex behavior than in CdCr 2S 4,indicating a signi?cant in?uence of the iron sublattice and the additional e?ective 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-?uctuation 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 signi?cant 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 e?ects 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 re?ectivity for x =0.2(upper panel)and x =0.5(lower panel)for temperatures 5K and 300K each.The

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

4

R

ν (cm-1)

FIG.3:(Color online)Re?ectivity R vs.wave number for

Fe1?x Cu x Cr2S4with x=0.2(upper panel)and x=0.5

(lower panel)at T=5K(open circles)and T=300K

(open triangles).The dashed lines represent results of?ts as

described in the text.

results for x=0.4are very similar to those obtained

for x=0.5and,hence,only the data for x=0.5is

shown and discussed.The re?ectivity of both samples,

x=0.2and0.5,shows a Drude-like contribution due

to the presence of free charge carriers,while FeCr2S4can

be described as an insulator.The highest Drude-like con-

ductivity is found for x=0.2and the phonon modes are

on the verge of being fully screened.For both compounds

the internal mode d at～120cm?1(see Fig.1for the

pure compound)can hardly be detected.Focusing on the

group of external modes,a new mode e appears close to

350cm?1,while on increasing Cu concentration x mode

a at380cm?1becomes considerably reduced in intensity.

Without an accompanying lattice dynamical calculation

one cannot decide,if this new mode represents an im-

purity mode due to the doping with Cu or a symmetry

change.There are reports in literature15,38claiming the

reduction of symmetry to F

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

5

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 in?uence of spin?uctuations and spin-phonon coupling on the phonon properties in FeCr2S4,Cu-doping seems to reduce these features sig-ni?cantly.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-?lled d-shell is present in the system17,39and the system becomes almost mag-netically isotropic as it was con?rmed by ferromagnetic resonance experiments.23

B.Dynamic conductivity and electronic excitations When the re?ectivities 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 signi?cant 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 re?ectivity spectra to higher energies. The room-temperature re?ectivities 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 re?ectivity of insulating FeCr2S4. For the Kramers-Kronig analysis of the smoothed re?ec-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 in?uenced in the relevant energy range be-low20000cm?1.The use of a Hagen-Rubens extrapola-tion is justi?ed 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,speci?cally for the sample with x=0.5.However, the best?ts of the re?ectivity at room temperature,even in the limited spectral range,yielded dc conductivities of 150(?cm)?1for x=0.2and35(?cm)?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 de?ned electronic transi-tion is observed close to2000cm?1and a further tran-sition appears close to20000cm?1(≈2.5eV).On sub-

R

σ

1

(

?

-

1

c

m

-

1

)

ν (cm-1)

FIG.5:(Color online)Upper panel:Semi-logarithmic plot of the room-temperature re?ectivity 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 re?ectivity spec-tra.

stituting iron by copper,metallic behavior shows up and for Fe0.8Cu0.2Cr2S4the dc conductivity is of the order 150(?cm)?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 partly?lled e band at the Fermi level.Correlation e?ects 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

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

6

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-?eld.The expected crystal-?eld 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-?eld transitions as mea-sured for diluted Fe2+in CdIn2S4.Here a crystal-?eld 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-de?ned 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 di?erent 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 constant?∞=10.6for x=0.2,which is close to the value?∞=11.5for x=0.For x=0.5we used ωp=5000cm?1and an enhanced dielectric constant ?∞=15.5.The enhanced?∞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 in?∞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 be?tted 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

σ

d

c

(

?

-

1

c

m

-

1

)

γ

(

1

3

c

m

-

1

)

T (K)

FIG.6:(Color online)Upper panel:Temperature dependence of the dc conductivity of Fe1?x Cu x Cr2S4as determined from ?ts to the re?ectivity(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 e?ects,which appear much weaker in the high-frequency(>100cm?1)derived op-tical data.That localization e?ects are most signi?cant 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 e?ects dominate already at higher temperatures.This may be attributed to a signi?cant 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.

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

7

Finally,we want to draw attention to the tempera-ture dependence of the relaxation rateγ(lower panel of Fig.6).In the magnetically ordered state below T C,the relaxation rates become signi?cantly reduced,e.g.the re-duction amounts to almost50%for x=0.2.We recall that the plasma frequency has been kept constant for each compound as a function of temperature.This indi-cates that the increase of the conductivity just below the magnetic ordering temperature results from the freezing-out of disorder scattering and not from a change of the carrier density via band-structure changes at the onset of ferrimagnetic order.Taking into account the classi?-cation of chalcogenide spinels A Cr2S4as systems where CMR originates from spin-disorder scattering,13the ob-served reduction of the relaxation rate below T C has to be regarded as direct evidence of such a scenario:In external?elds the onset of ferrimagnetic order shifts to higher temperatures.Concomitantly,a reduction of the scattering rate and the anomalous increase of the con-ductivity arise.As a consequence,maximal CMR e?ects will show up just below T C as a function of an external magnetic?eld.A similar scenario has been reported for GdI2,where the magnetic and magneto-transport prop-erties have been described successfully in terms of spin-?uctuations and their suppression by external magnetic ?elds in the vicinity of T C.44,45We would like to point out,that at low temperatures the relaxation rates for x=0.2and x=0.5are of the same order of magnitude ～104cm?1,indicating a similar level of disorder for the Cu doped compounds.

IV.SUMMARY

In summary,we investigated the optical properties of Fe1?x Cu x Cr2S4single crystals for Cu concentrations x=0,0.2,0.4and0.5.Phonon excitations and dynamic conductivity for x=0.4are very similar to the results for Fe0.5Cu0.5Cr2S4and were not discussed separately. The phonon excitations were measured as a function of temperature between5K and room temperature.Pure FeCr2S4shows clear anomalies in the eigenfrequencies at the transition from the paramagnetic to the ferromag-netic state,which can be explained by spin-phonon cou-pling.Concerning the complex behavior of the damping constants,spin?uctuations in the vicinity of T C may de-scribe many of the anomalous changes,but further the-oretical studies are necessary to corroborate this inter-pretation.The in?uence of magnetic order on the eigen-modes is reduced with increasing x,and the appearance of a new phonon mode close to350cm?1is attributed to an impurity mode rather than to a symmetry reduction due to A-site order.

Morover,the charge dynamics of Fe1?x Cu x Cr2S4were investigated.FeCr2S4is an insulator,but becomes metal-lic when slightly doped with Cu.The conductivity of the free charge carriers can be described by a normal Drude-type behavior.The dc conductivity for x=0.2is en-hanced by a factor of four in comparison to x=0.5.The temperature dependence of the optically derived dc con-ductivity for both doped compounds is is in good agree-ment with resistivity measurements,but localization ef-fects at lowest temperatures appear weaker in the op-tical measurements.The corresponding behavior of the scattering rate,which shows a strong decrease below the ferrimagnetic phase transition,evidences the freezing-out of disorder scattering below T C.In accordance with the proposed classi?cation of the ternary chalcogenide spinels as spin-disorder magnetoresistive materials,the reduc-tion of the relaxation rate corroborates such a scenario and makes clear that spin-disorder has to be considered a necessary ingredient towards a theoretical description of this fascinating class of materials.

Acknowledgments

It is a pleasure to thank H.-A.Krug von Nidda, J.Hemberger,and Ch.Hartinger for fruitful discus-sions.This work was partly supported by the DFG via the Sonderforschungsbereich484(Augsburg),by the BMBF/VDI via the Contract No.EKM/13N6917/0,by the U.S.Civilian Research&Development Foundation (CRDF)and by the Moldavian Research&Development Association(MRDA)via Grant No.MP2-3047.

1R.M.Kusters,J.Singleton,D.A.Keen,R.McGreevy, and W.Hayes,Physica B155,362(1989).

2Z.Jir´a k,S.Krupiˇc ka,Z.ˇSimˇs a,M.Dlouh´a,and S.Vratislav,J.Magn.Magn.Mater.53,153(1985).

3R.von Helmolt,J.Wecker,B.Holzapfel,L.Schultz,and K.Samwer,Phys.Rev.Lett.71,2331(1993).

4K.Chahara,T.Ohno,M.Kasai,and Y.Kozono, Appl.Phys.Lett.63,1990(1993).

5S.Jin,T.H.Tiefel,M.McCormack,R.A.Fastnacht, R.Ramesh,and L.H.Chen,Science264,413(1994).

6C.Zener,Phys.Rev.82,403(1951).

7A.J.Millis,P. B.Littlewood,and B.I.Shraiman,

Phys.Rev.Lett.74,5144(1995).

8M.Mayr,A.Moreo,J.A.Verg´e s,J.Arispe,A.Feiguin, and E.Dagotto,Phys.Rev.Lett.86,135(2001).

9M. B.Salamon,P.Lin,and S.H.Chun, Phys.Rev.Lett.88,197203(2002).

10Y.Shimakawa,Y.Kubo,and T.Manako,Nature379,53 (1996).

11C.Felser,K.Ahn,R.K.Kremer,R.Seshadri,and A.Si-mon,J.Solid State Chem.147,19(1999).

12A.P.Ramirez,R.J.Cava,and J.Krajewski,Nature386, 156(1997).

13P.Majumdar and P.Littlewood,Nature395,479(1998).

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

8

14G.Gomez-Santos,S.Fratini,and F.Guinea, Phys.Rev.B70,184420(2004).

15F.K.Lotgering,R.P.Van Stapele,

G.H. A.M.Van Der Steen,and J.S.Van Wierin-

gen,J.Phys.Chem.Solids30,799(1969).

16J.B.Goodenough,J.Phys.Chem.Solids30,261(1969). 17E.Z.Kurmaev, A.V.Postnikov,H.M.Palmer,

C.Greaves,St.Bartkowski,V.Tsurkan,M.Deme-

ter, D.Hartmann,M.Neumann, D. A.Zatsepin, V.R.Galakhov,S.N.Shamin,and V.Tro?mova,J.Phys.: Condens.Matter12,5411(2000).

18V.Tsurkan,M.Demeter,B.Schneider,D.Hartmann,and M.Neumann,Solid State Commun.114,149(2000).

19G.Haacke,and L.C.Beegle,J.Appl.Phys.39,656(1968). 20W.E.Pickett,and J.S.Moodera,Phys.Today54,39 (2001).

21M.S.Park,S.K.Kwon,S.J.Youn,and B.I.Min, Phys.Rev.B59,10018(1999).

22V.Tsurkan,I.Fita,M.Baran,R.Puzniak,D.Samusi, R.Szymczak,H.Szymczak,S.Klimm,M.Klemm,S.Horn, and R.Tidecks,J.Appl.Phys.90,875(2001).

23V.Fritsch,J.Deisenhofer,R.Fichtl,J.Hemberger,H.-

A.Krug von Nidda,M.M¨u cksch,M.Nicklas,D.Samusi,

J.D.Thompson,R.Tidecks,V.Tsurkan,and A.Loidl, Phys.Rev.B67,144419(2003).

24V.Tsurkan,J.Hemberger,M.Klemm,S.Klimm,A.Loidl, S.Horn,and R.Tidecks,J.Appl.Phys.90,4639(2001). 25D.Maurer,V.Tsurkan,S.Horn,and R.Tidecks, J.Appl.Phys.93,9173(2003).

26R.Fichtl,V.Tsurkan,P.Lunkenheimer,J.Hemberger, V.Fritsch,H.-A.Krug von Nidda, E.-W.Scheidt,and

A.Loidl,Phys.Rev.Lett.94,027601(2005).

27Ch.Hartinger, F.Mayr,J.Deisenhofer, A.Loidl,and T.Kopp,Phys.Rev.B69,100403(R)(2004).

28H.D.Lutz,G.Waschenbach,G.Kliche,and H.Haeuseler,

J.Solid State Chem.48,196(1983).

29K.Wakamura,Solid State Commun.71,1033(1989).

30D.W.Berreman and F.C.Unterwald,Phys.Rev.174, 791(1968).

31K.Wakamura and T.Arai,J.Appl.Phys.63,5824(1988). 32W.Baltensperger,and J.S.Helman,Helv.Phys.Acta41, 668(1968).

33W.Baltensperger,J.Appl.Phys.41,1052(1970).

34A.B.Sushkov,O.Tchernyshyov,W.Ratcli?,S.W.Cheong, and H.D.Drew,Phys.Rev.Lett.94,137202(2005).

35K.Wakamura,T.Arai,and K.Kudo, J.Phys.Soc.Jpn.41,130(1976).

36J.M.Wesselinowa and A.T.Apostolov,J.Phys.:Condens.

Matter8,473(1996).

37P.Bruesch,and F.d’Ambrogio,Phys.Status Solidi(b)50, 513(1972).

38H.M.Palmer,and C.Greaves,J.Mater.Chem.9,637 (1999).

ng,C.Felser,R.Seshadri,F.Renz,J.-M.Kiat,J.En-sling,P.G¨u tlich,and W.Tremel,Adv.Mater.12,65 (2000).

40A.Abragam and B.Bleaney,Electron Paramagnetic Res-onance of Transition Ions,Clarendon,Oxford,1970.

41S.Wittekoek,R.P.van Stapele,and A.W.J.Wijma, Phys.Rev.B7,1667(1973).

42G.Haacke, A.J.Nozik,Solid State Commun.6,363 (1968).

43P.Lunkenheimer and A.Loidl,Phys.Rev.Lett.91,207601 (2003).

44I.Eremin,P.Thalmeier,P.Fulde,R.K.Kremer,K.Ahn, and A.Simon,Phys.Rev.B64,064425(2001).

45J.Deisenhofer,H.-A.Krug von Nidda,A.Loidl,K.Ahn, R.K.Kremer,and A.Simon,Phys.Rev.B69,104407 (2004).

本文来源：https://www.bwwdw.com/article/36pe.html