Magnetoelectrodynamics of a three-dimensional organic conductor: Observation of cyclotronresonance ind2†1,1;0‡-„DMe-DCNQI …2Cu

S. Hill and P. S. SandhuNational High Magnetic Field Laboratory, 1800 E. Paul Dirac Drive, Tallahassee, Florida 32310

M. E. J. Boonman, J. A. A. J. Perenboom, and A. WittlinResearch Institute for Materials and High Field Magnet Laboratory, University of Nijmegen, Toernooiveld 1, 6525 ED, Nijmegen,

The Netherlands

S. UjiNational Research Institute for Metals, Tsukuba, Ibaraki 305, Japan

J. S. BrooksNational High Magnetic Field Laboratory, 1800 E. Paul Dirac Drive, Tallahassee, Florida 32310

R. Kato, H. Sawa, and S. AonumaInstitute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan

~Received 13 June 1996!

We have used an amplitude- and phase-sensitive millimeter-wave technique, in combination with a resonantcavity configuration, to observe cyclotron resonance in the three-dimensional organic conductord2@1,1;0#-~DMe-DCNQI!2Cu. The data obtained in this way are simple to analyze and serve as an extremelyclear illustration of the electrodynamic response of an organic conductor in a high magnetic field. A cyclotronresonance mass of~3.3560.2!me is obtained, in agreement with the effective mass deduced from de Haas–vanAlphen measurements. This result suggests that Coulomb correlations between the three-dimensional chargecarriers in this material are not important and that the large effective mass is simply a result of the hybridiza-tion between a narrow Cu 3d band and the pp band due to the DMe-DCNQI molecules.@S0163-1829~96!01944-3#

I. INTRODUCTION

Over the past decade, organic conductors have attractedconsiderable interest due, in part, to their unique physicalproperties and also because of the versatility of these systemsfor the study of band formation.1–5 Until recently, much ofthe activity has centered on the low-dimensional charge-transfer salts based on the organic donor molecules2,4

tetramethyltetraselena-fulvalene~Refs. 1, 2, and 4! andBEDT-TTF @bis~ethylenedithio! tetrathia-fulvalene#.1,3,4 Al-though there have been many developments in the synthesisof these materials, their electronic structures remain low di-mensional. In this work, we look at a molecular conductorthat shows truly three-dimensional~3D! behavior.

Recently, an organic conductor containing Cu ions~DMe-DCNQI!2Cu ~DMe-DCNQI denotes 2,5-dimethyl-N,N8-dicyanoquinone-diimine! has been synthesized.6 Theplanar DCNQI molecules are stacked in one-dimensionalcolumns along the tetragonalc axis and are interconnectedby tetrahedrally coordinated Cu ions.7,8 A 1D Fermi surfaceis formed by the overlappingpp orbitals of the stacked DC-NQI molecules. The Cu ions, meanwhile, which form a sev-enfold diamondlike lattice, are found to be in a mixed va-lence state9 between Cu1 and Cu21, indicating that the Cu3d level lies close to the Fermi energy. Consequently, a 3Denergy band is expected in addition to the 1Dpp energyband.7,9 Recent de Haas–van Alphen~dHvA! studies by Uji

et al.10,11 have confirmed the existence of a 3D Fermi sur-face, in agreement with band-structure calculations.7,12,13

Various studies of deuterated and undeuterated alloys,~DMe12xMeBrx-DCNQI!2Cu, reveal a complex low-temperature phase diagram,9–11,14–16as shown in Fig. 1. Inparticular, the partially deuteratedd2@1,1;0#-~DMe-DCNQI!2Cu compound shows reentrant metal-insulator-metal (M -I -M ) phases.16 The I phase is believed to

FIG. 1. Schematic of the experimentally determinedtemperature-pressure phase diagram for~DMe-DCNQI!2Cu ~Refs.9–11 and 14–16!; arrows indicate the positions of the deuteratedsalts~d2 andd4! with respect to the undeuterated (h) salt.

PHYSICAL REVIEW B 15 NOVEMBER 1996-IVOLUME 54, NUMBER 19

540163-1829/96/54~19!/13536~6!/$10.00 13 536 © 1996 The American Physical Society

arise from a static ordering of the Cu ions~ . . . Cu1Cu1Cu21 . . . !. A steep enhancement of the elec-tronic specific-heat coefficient~g! close to the insulatingphase has been interpreted by some groups as evidence thatCoulomb interactions drive theM -I and I -M transitions.15

However, other groups fail to observe this enhancement ofg~Ref. 17! and, so, the issue as to whether Coulomb interac-tions are significant is still controversial.

dHvA measurements in the metallic phase for both deu-terated and undeuterated~DMe-DCNQI!2Cu single crystalsyield rather large effective-mass values (m*.3me).

10,11

These results could be interpreted as a further indication thatCoulomb interactions lead to an enhancement ofg ~propor-tional to the effective mass!. However, band-structure calcu-lations do indeed predict such large effective masses due tothe hybridization between a narrow Cu 3d band and theppband due to the DMe-DCNQI molecules;7,12,13 i.e., this pic-ture is consistent with the mixed valence character of the Cuions in the metallic phase. Furthermore, similar effectivemasses are found for both deuterated and undeuteratedsamples;10,11 i.e., g shows no enhancement on approachingtheM -I phase boundary.

The present study is motivated by several factors: First,any renormalization of the quasiparticle effective mass, dueto Coulomb interactions, is expected to be energy and wave-vector dependent;18 therefore, different measurements shouldyield different effective-mass values. In the language ofstrongly interacting fermions,18 thermodynamic measure-ments yield the quasiparticle effective massm* , which in-cludes contributions from band-structure, electron-phonon,and electron-electron interactions. In contrast, cyclotronresonance~CR!, which couples to the center-of-mass motionof an electronic system,19,20 probes the dynamical massml

and is insensitive to Coulomb interaction effects.18–20There-fore, a comparison between thermodynamic~dHvA! and CRmasses would be a natural way to settle the argument overthe role of Coulomb correlations in the title compound. Sucha comparison is particularly important in view of the fact thattight-binding band-structure calculations~as in Refs. 7, 12and 13! only predict the ratios of effective masses corre-sponding to different Fermi surface sections; i.e., they do notproduce absolute values.21

Second, recently there have been a number of reports ofCR in some of the quasi-two-dimensional~2D! BEDT-TTFsalts.20,22–24In each case, there is a difference between theeffective masses deduced from CR and those determinedfrom thermodynamic and/or magnetotransport measure-ments,20,22–24suggesting that Coulomb correlations may playan important role in the quasi-2D organic conductors. Inview of this, it is interesting to compare these findings withmeasurements on a 3D organic conductor.

Finally, existing optical data on the organics have beendifficult to interpret due to the rather weak features attributedto CR. Matters are further complicated by the highly aniso-tropic conduction in these metals; this is particularly so inthe quasi-2D salts. An understanding of CR data in thesematerials relies heavily on a good knowledge of certain fac-tors such as the conductivities and relaxation times, togetherwith any anisotropy in these quantities. We will show thatthe data obtained by our experimental technique can be suc-

cessfully modeled, giving rise to an accurate determinationof the CR mass.

II. EXPERIMENTAL CONSIDERATIONS

A millimeter-wave vector network analyzer25 ~MVNA !was configured to monitor the reflected phase and amplitudeof millimeter wave radiation coupled to a resonant cavitycontaining the samples. The MVNA allows measurements ina very extended frequency range~8–350 GHz!; the measure-ments reported here were performed in the 70–130-GHzrange~l;2–4 mm! where the MVNA has a dynamic reservein excess of 90 dB. Partially deuteratedd2@1,1;0#-~DMe-DCNQI!2Cu samples were chosen for thisstudy because of their reentrantM -I -M behavior.9–11,14–16

The use of resonant cavities offers many advantages inthis frequency regime, particularly in the case of small me-tallic crystals, where the radiation wavelength is comparableto the sample dimensions.26,27 Under these conditions, thesample acts as a perturbation of the electromagnetic fielddistribution within the cavity.26,27Due to the resonant natureof the problem, the resonance condition is very sensitive tosmall changes in the sample conductivity. Another advantageof this technique is that, by carefully positioning the samplewithin the cavity, one can excite ac currents in any desireddirection within the sample.26 Furthermore, it is possible toselectively couple to either the electric or magnetic dipolefields within the cavity.26

The so-called ‘‘cavity perturbation’’ technique has beenused by several groups to study organic conductors,26,28–30

however, there are relatively few reports combiningthis technique with high magnetic fields.24 Polisskiiet al.24 have observed CR in the quasi-two-dimensionala-~BEDT-TTF!2NH4Hg~NCS!4 salt; a rectangular cavity isemployed and the transmitted amplitude is monitored for afew frequencies between 50 and 105 GHz. In this work, weutilize the full vector capability~i.e., phase and amplitude! ofthe MVNA, enabling a precise understanding of the couplingbetween our conducting samples and the microwave fields inthe cavity. Furthermore, we have developed a technique thatallows measurements to be performed at many closelyspaced frequencies over a fairly extended frequency range.

A detailed description of our experimental setup is re-ported elsewhere.31 An oversized cylindrical copper cavitywas employed~diameter 12.5 mm, height 20 mm!, providingmany resonant modes in the desired frequency range. Foursmall needlelike d2@1,1;0#-~DMe-DCNQI!2Cu samples~length;3 mm, width;200mm! were inserted into a thinslice of styrofoam so that theirc axes ~needle axis! coin-cided. The measurements were then performed with the dcmagnetic field applied parallel to these needles. By excitingtransverse electric modes, we can assume that there is anelectric field antinode at a distancel/4 above the bottom ofthe cavity; this electric field acts in a plane perpendicular tothe axis of the cavity. With this in mind, the styrofoamsample holder was placed close to the bottom of the cavity insuch a way as to excite currents in the samples in a planeperpendicular to the applied dc magnetic field, i.e., in theabplane.

An oversized cylindrical waveguide was used to pass ra-diation from the spectrometer, through our cryostat, and into

54 13 537MAGNETOELECTRODYNAMICS OF A THREE- . . .

the bore of the magnet. Smooth conical transitions were in-serted wherever changes in the waveguide diameter mightlead to impedance mismatches, thereby minimizing unneces-sary reflections. The radiation was then coupled to, and from,the cavity via a 1.4-mm~;l/42l/2! aperture centered onthe top of the cavity. Discrimination between the incidentand reflected radiation was achieved by means of an opticalbeam splitter. The samples and the cavity were maintained at1.2 K and placed at the maximum magnetic field positionwithin a 20-T resistive magnet. Once cooled, the frequencysweeping capability of the MVNA could be used to identifyresonant modes of the loaded cavity. All measurements werethen performed at a fixed frequency, while sweeping themagnetic field. A quartz-locking frequency counter stabilizedthe source frequency to the cavity resonances.

III. ANALYSIS

In analyzing our data, we shall consider the surface im-pedance of the sample,Zs5Rs1iXs , whereRs is the surfaceresistance andXs is the surface reactance.26 This is a com-mon approach for good conductors in the so-called ‘‘skindepth’’ regime, where the skin depth is much smaller thanthe sample dimensions and, therefore, the ac electromagneticfields are not uniform within the sample. The surface imped-ance is given by the expression

Zs5S im0v

s12 is2D 1/2, ~1!

wheres~5s12is2! is the complex conductivity,v/2p thefrequency, andm0 the free space permeability. Solving forRsandXs in terms ofs1 ands2, we obtain

Rs5V~11a!1/2, Xs5V~12a!1/2, ~2!

where

V5F ~m0v!2

4~s121s2

2!G1/4

, a5s2

~s121s2

2!1/2.

To demonstrate that a good single crystal of~DMe-DCNQI!2Cu is in the skin-depth regime when micro-wave radiation is coupled to the sample in this geometry, weestimate the skin depth@d5(p fs1m0)

21/2# to be about 1mm, assuming a value ofs1 of 33104 V21 cm21 in the abplane and at 1 K;32 this is small when compared to the small-est sample dimension.

With the dc magnetic field applied parallel to thec axis,only a single dHvA oscillation is observed,10,11 correspond-ing to a single closed orbit ink space; this is thea orbit. Byexciting ac currents in theab plane, it should, in principle,be possible to observe CR due to thea orbit. The complexconductivity will then be given by

s51

2

ne2t

maF 11 i ~v2vc!t

11~v2vc!2t2

111 i ~v1vc!t

11~v1vc!2t2G , ~3!

wherevc ~5eB/ma! is the cyclotron frequency andt is therelaxation time;ma is the CR mass due to thea orbit, n is

the carrier density, andB is the applied dc magnetic field.Both resonant~left-hand term in square brackets! and non-resonant~right-hand term in square brackets! contributions tothe ac conductivity are considered in the above expression;this is due to the fact that the radiation everywhere in thecavity may be separated into left and right circularly polar-ized components. No special considerations are made aboutthe exact shape of the Fermi surface; i.e., Eq.~3! is derivedfor a free electron gas.

Changes in the sample conductivity and, therefore, its sur-face impedance, result in the following changes in the cavityresonance parameters:26

DG

2 f 05 1

2D~1/Q!5jDRs ,D f

f 05jDXs . ~4!

In the above expressions,DG is the change in the width ofthe resonance,D f is the change in the resonance frequencyf 0, Q is the quality factor, andj is a geometrical factor.26

Therefore, on application of a dc magnetic field, we can re-late changes in these quantities~Q, f 0, etc.! to changes in thesurface impedance of the sample.

In our experiment, changes in the resonance frequencyf 0will result in changes in the phase of the radiation reflectedfrom the cavity, while changes in the resonance quality fac-tor ~Q or G! will lead to changes in amplitude.25,31 Moreprecisely,

Df}D f

f 0}DXs ,

1

DA}DG}DRs , ~5!

wheref andA are the reflected phase and amplitude, respec-tively. Here we see the virtue of the vector capability of theMVNA, which allows us to extract both components of thesurface impedance with a single measurement.

IV. RESULTS

Figure 2 shows typical results for several frequencies be-tween 83.87 and 125.24 GHz; the temperature is 1.2 K ineach case. Also included in Fig. 2 are fits to the data accord-ing to the above analysis. In order to achieve good fits, acomplex linear term was subtracted from the raw data, whichwe attribute to several external factors, e.g., magnetoresis-tance in the waveguide and variations in the coupling be-tween the spectrometer and the cavity; the latter is a result ofstanding waves in the waveguide and mechanical changes inits length caused by thermal fluctuations. The reason for theapparent increase in noise as the frequency is increased isdue to two factors:~i! the dynamic range of the MVNAdecreases with increasing frequency, and~ii ! the cavity be-comes overcoupled at higher frequencies resulting in a re-duction in the cavityQ factor. For these reasons, no scale isassigned to the vertical axes in Fig. 2 since the noisier curveshave had to be expanded by up to a factor of 20 for the sakeof clarity. Furthermore, the geometrical factorj appearing inEq. ~4! cannot be determined in this experiment; i.e., Fig. 2displays qualitative changes inRs andXs .

From fits to the data, an average CR mass value ofma5(3.3760.2)me is obtained and, in every case, a scatter-

13 538 54S. HILL et al.

ing rate oft215231010 s21 gave the best results. Agreementbetween experiment and analysis is remarkably good overthe entire field and frequency range. Similar results wereobtained at many other frequencies in the range 70–130GHz. By plotting the magnetic field value above which thephase begins to increase sharply~see Fig. 2!, as a function offrequency, we obtain an independent estimate of the CRmass; such a plot, together with a linear fit, is shown in Fig.3. Using this method, we obtain a value for the CR mass ofma5(3.3460.2)me , which is fully consistent with the ear-lier estimate. What is more, to within experimental errors,these values of the CR mass agree with the effective massdeduced from dHvA studies,10 i.e.,ma5(3.3–3.4)me .

33

V. DISCUSSION

The fact that exactly the same values forma are obtainedfrom dHvA and CR measurements seems to rule out strongCoulomb correlations between carriers on the 3D Fermi sur-face in d2@1,1;0#-~DMe-DCNQI!2Cu. This result, coupledwith the dHvA results, which indicate thatma is the same fordeuterated and undeuterated salts,10,11suggests that Coulombcorrelations between the 3D carriers play no significant role

in the entire~DMe-DCNQI!2Cu family. Therefore, we con-clude that the largema is simply a result of the hybridizationbetween a narrow Cu 3d band and thepp band due to theDMe-DCNQI molecules.

One then has to ask why correlations apparently play animportant role in some of the quasi-2D organicconductors.20,22–24One possibility is that the reduced dimen-sionality of the quasi-2D systems leads to an enhancement ofthe Coulomb interactions. However, the BEDT-TTF and~DMe-DCNQI!2Cu systems differ in many other respects5

~i.e., not just dimensionality!, so there may be many otherexplanations.

Since CR and dHvA measurements probe only the 3DFermi surface, one cannot rule out the possibility that Cou-lomb correlations between carriers on the 1D Fermi surfaceare significant. One way to verify this would be to look forsignatures in the surface impedance for quasi-1D CR. Thispossibility was first suggested by Gor’kov and Lebed’34 andhas been discussed elsewhere.35,36 In order to do this, a dif-ferent experimental configuration should be devised and fur-ther work in this direction is currently in progress.

The form of the amplitude and phase variation in Fig. 2 isnot typical for CR; it is more usual to observe a Lorentzianresonance line shape as seen, e.g., in doped semiconductors.The reason for this is because, in the present case, we aredealing with a highly conducting sample in a resonant cavityand, under these conditions, it is the boundary condition be-tween the sample surface and the surrounding vacuum thatdetermines the cavity response@see Eqs.~2!–~5!#. This typeof result has been observed previously in experiments onsemimetallic bismuth involving a resonant microwave bridgetechnique.37,38 In a semiconductor, however, electromagneticradiation will penetrate the entire sample~quasistatic ap-proximation! and, therefore, its bulk dielectric response~«5«11i«2! dictates the CR line shape;«1 and«2 are directlyrelated tos2 ands1, respectively, thereby accounting for aLorentzian line shape@see Eq.~3!#.

Figure 4 shows the predicted field dependence of thephase and amplitude, in the ‘‘skin depth’’ regime, for severaldifferent values ofvt. It is interesting to note the entirelydifferent field dependence ofRs in the case ofvt.1 andvt,1. In the limitvt!1, the well-known ‘‘Hagen Rubens’’limit is reached whens1@s2 andRs'Xs @see Eq.~1!#. In

FIG. 2. ~a! Change in the surface resistance(DRs}1/DA), and ~b! the surface reactance~DXs}Df!, as a function of the applied dc mag-netic field for several different frequencies; thetemperature is 1.2 K in each case. The smoothcurves through the data have been fitted accord-ing to the analysis described in the text. Thehigher-frequency data have been expanded forthe sake of clarity.

FIG. 3. A plot of the resonance field positions against fre-quency. The straight line fit may be used to make an accurate de-termination of the CR effective mass.

54 13 539MAGNETOELECTRODYNAMICS OF A THREE- . . .

this limit, the transport properties of the sample are probed,which can be seen, to a certain extent, in Fig. 4~d! whereRs

andXs begin to resemble the magnetoresistance of a typicalmetal. By extending our measurements to lower frequencies,it should be possible to observe this crossover. For the datashown in Fig. 2,vt;10, therefore, it would be necessary togo below 10 GHz in order to check this. Alternatively, mea-surements on less pure samples~shortert! could access thisregime.

In view of the above, we comment briefly here on some ofthe results obtained by Pollisskiiet al., for ac coupling to thehighly conducting planes of the quasi-2D organic metala-~BEDT-TTF!2NH4Hg~NCS!4, with the magnetic field ap-plied normal to these planes, i.e., a similar geometry to theexperiments reported here. They plot absorption versus mag-netic field for a frequency of 50.3 GHz: A broad peak isobserved at low fields, corresponding to a CR mass 1.8me ,while at higher fields the absorption starts to increase sharplyin identical fashion to the behavior ofRs shown in Fig. 4~b!.The authors comment on this behavior, but make no assign-ment of this feature of their data. The broad peak seen atlower fields is also observed for ac coupling in the interplane~low conductivity! direction, when radiation will penetratethe entire sample; hence this fairly symmetric peak is attrib-uted to CR. Due to anisotropy in the BEDT-TTF conductors,it is far easier to excite ac currents in the interplane directionthan within the highly conducting planes.39 Therefore, wesuggest that the results in Ref. 24, for the in-plane geometry,include effects due to both intraplane and interplane currents.For the inplane currents, their data implyvt,1, while forthe interplane currents,vt must be greater than unity in or-der to observe CR. This raises the question as to whethert ishighly anisotropic in these materials, or whether these twofeatures of the data are of a different origin. Furthermore, acomparison between their data andRs in Fig. 4~d! indicatesthat a larger cyclotron mass may be appropriate, thus ac-counting for the apparent difference between CR and mag-netotransport measurements.

VI. SUMMARY

We have observed CR in the 3D organic conductord2@1,1;0#-~DMe-DCNQI!2Cu. We obtain a CR mass that is inagreement with the effective mass obtained from dHvA mea-surements. This rules out the possibility that correlations be-tween the 3D carriers play an important role in these mate-rials. Therefore, we suggest that the large effective mass issimply a result of the hybridization between a narrow Cu 3dband and thepp band due to the DMe-DCNQI molecules.

In this work, we have studied, by far, the simplest geom-etry for the~DMe-DCNQI!2Cu system. We have been able toneglect the quasi-1D character associated with this materialalong itsc axis.7,12 Clearly, much work remains to be donein understanding the magnetoelectrodynamics of these, andother, highly anisotropic organic conductors. We also notethat, in many of the organic conductors that are currently ofinterest, sample quality is such that typical scattering ratesare comparable to the frequencies used in this study, i.e.,vt;1. Therefore, this general experimental area offers greatpotential in understanding the electrodynamics of these ma-terials in high magnetic fields. We conclude by emphasizingthe power of the vector measurement technique in combina-tion with a resonant cavity configuration. The data obtainedin this way are simple to analyze and serve as an extremelyclear illustration of the electrodynamics of an organic con-ductor in high magnetic fields.

ACKNOWLEDGMENTS

This work was supported by the National Science Foun-dation under Grant No. NSF-DMR 95-10427. The work inNijmegen was part of the research program of the ‘‘Stichtingvoor Fundamenteel Onderzoek der Materie,’’ which is finan-cially supported by the ‘‘Nederlandse Organisatie voorWetenschappelijk Onderzoek’’ and has been supported bythe European Commission under Contract No. CHGT-CT93-0051. The authors would also like to thank P. Goy of ABmmfor his advice and expertise and Dr. A. Polisskii for usefuldiscussion.

FIG. 4. Predicted field depen-dence @normalized to the cyclo-tron resonance field (mv/e)# ofthe surface resistance (Rs) andsurface reactance (Xs) for differ-ent values ofvt.

13 540 54S. HILL et al.

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54 13 541MAGNETOELECTRODYNAMICS OF A THREE- . . .