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Charge Transport in Antiferromagnetic Insulating Phaseof Two-Dimensional Organic Conductor λ-(BETS)2FeCl4

Shiori Sugiura, Kazuo Shimada, Naoya Tajima, Yutaka Nishio, Taichi Terashima,Takayuki Isono, Akiko Kobayashi, Biao Zhou, Reizo Kato, and Shinya Uji

J. Phys. Soc. Jpn. 85, 064703 (2016)

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Charge Transport in Antiferromagnetic Insulating Phaseof Two-Dimensional Organic Conductor λ-(BETS)2FeCl4

Shiori Sugiura1,2+, Kazuo Shimada3, Naoya Tajima3, Yutaka Nishio3, Taichi Terashima1,Takayuki Isono1, Akiko Kobayashi4, Biao Zhou4, Reizo Kato5, and Shinya Uji1,2

1National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan2Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan

3Faculty of Science, Toho University, Funabashi, Chiba 274-8510, Japan4Department of Humanities and Sciences, Nihon University, Setagaya, Tokyo 156-8550, Japan

5RIKEN, Wako, Saitama 351-0198, Japan

(Received February 5, 2016; accepted March 23, 2016; published online May 6, 2016)

Resistance and dielectric constants have been measured in the antiferromagnetic insulating phase of the quasi-two-dimensional organic conductor λ-(BETS)2FeCl4 to understand charge transport. Nonlinear current–voltage character-istics are observed at low temperatures, which are explained by a charge transport model based on the electric-fielddependent Coulomb potential between the thermally excited electron and hole. A small dip in the magnetic fielddependence of the resistance is found at 1.2 T, which is ascribed to a spin-flop transition. The large difference betweenthe in-plane and out-of-plane dielectric constants shows the two-dimensionality of the Coulomb potential, which isconsistent with the charge transport model. The angular dependence of the metal–insulator transition field is determined,which suggests that the Zeeman effect of the 3d spins of the Fe ions plays an essential role.

1. Introduction

Organic conductors, which are typical strongly correlatedelectron systems, have attracted much interest because oftheir fascinating electronic properties. Among variousorganic conductors, the two-dimensional salt λ-(BETS)2-FeCl4 [BETS = bis(ethylenedithio)tetraselenafulvalene] hasbeen extensively studied because of its unique magnetic field-temperature phase diagram, where strong electron correlationplays essential roles. The transfer integral between thehighest occupied molecular orbitals of the neighboring BETSmolecules results in a highly two-dimensional (2D) energyband in the BETS layer. Because of the dimerization of theBETS molecules, the conduction band is half-filled. In theFeCl4 anion, the 3d spins of the Fe3+ ion are in a high spinstate (S ¼ 5=2). A large exchange interaction between the πspin in the BETS layer and the localized 3d spin in the FeCl4anion, which is the so-called π–d interaction (J�d � 16K1)),makes the phase diagram fascinating. At high temperatures,this salt shows metallic behavior. However, the resistanceshows a marked up turn due to a metal–insulator (M–I)transition at ∼8K (TMI).2) The M–I transition is recognized asa Mott transition due to a strong on-site Coulomb repulsion.3)

The magnetic susceptibility in the metallic phase, which isdominated by the localized 3d spins, follows the Curie–Weiss law down to ∼10K and then steeply decreases belowTMI, showing an antiferromagnetic (AF) order.4) Theantiferromagnetic insulating (AFI) phase below TMI is brokenby a magnetic field of ∼10T, and the paramagnetic metallic(PM) phase is recovered. In this PM phase, the measurementsof Shubnukov–de Haas oscillations confirm the presence ofa 2D Fermi surface.5,6) In magnetic fields above 17 T, asuperconducting phase is induced when the magnetic field isapplied parallel to the conducting a0c plane.7) This field-induced superconducting phase is explained by the Jaccarino-Peter compensation mechanism, which is clear evidence ofthe strong π–d interaction. In addition, the existence of anovel superconducting phase, the so-called Fulde–Ferrell–

Larkin–Ovchinnikov (FFLO) phase, near the upper criticalfield (Hc2) has been discussed.8–10)

For λ-(BETS)2FeCl4, some anomalous phenomena havebeen observed by various experiments in a wide range oftemperatures and fields. In the PM phase, a large dielectricconstant is observed for TMI < T < 70K by microwaveresponse measurements at 44.5GHz, which suggests thatdielectric domains or stripes with less metallic conductioninhomogeneously emerge in the π electronic state.11) Theinhomogeneity is consistent with the observation of thesplitting of a Bragg reflection peak by synchrotron radiationexperiments12) and the broadening of the NMR lineshape.13,14) In the AFI phase, a large frequency dispersionin the microwave response is found, which is ascribed tosome collective modes associated with the charge degree offreedom of the π electrons.11) The polarization curves PðEÞobtained from in-plane dielectric constant measurementsshow a steep increase in the saturation value of P for�0H > 5T, suggesting a certain dielectric order.15) At TMI, itis known that a first-order structural phase transition takesplace2) but no detailed structural studies have been carried outyet.

As mentioned above, various anomalous features havebeen found in λ-(BETS)2FeCl4. Among them, the mechanismof the M–I transition is one of the central issues.Experimental5) and theoretical studies3) first suggested thatthe M–I transition (charge localization of the π electrons) wasinduced by an AF order of the 3d spins. However, after that,specific heat measurements clarified that the π spins showthe AF order but the 3d spins surprisingly remain in aparamagnetic state.16) The results force us to reconsiderthe mechanism of the M–I transition. So far, no reliableresistivity measurements in the AFI phase have been carriedout because the resistivity in the AFI phase is too high tomeasure by conventional techniques. The lack of data makesit difficult to discuss the charge transport in the AFI phase.

In this study, we focus on the charge transport in the AFIphase of λ-(BETS)2FeCl4. We successfully measured the

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resistivity and current–voltage (I–V) characteristics in a widerange of temperatures and magnetic fields. The anisotropy ofthe dielectric constants at low frequencies is also measured,which provides crucial information on the dimensionality ofthe Coulomb potential in the BETS layers. We propose acharge transport mechanism based on the dielectric constantanisotropy.

2. Experiments

Single crystals of λ-(BETS)2FeCl4 were synthesized by astandard electrochemical method. The I–V characteristics andresistivity were measured by a four-terminal method. Goldwires of 10 µm diameter were attached to crystals with carbonpaste. In the AFI phase, the resistance increases to 108Ω.Therefore, special care should be taken to measure theresistance. In the high-resistance region, the DC current wasapplied using a source meter (Keithley 2400) and the samplevoltage was detected by an electrometer (Keithley 6514)whose internal impedance (>2 � 1011Ω) is much higher thanthe sample resistance. In the low-resistance region, the ACcurrent was applied using a lock-in amplifier (StanfordResearch Systems SR830). For both AC and DC measure-ments, the currents were applied along the a0–c conductingplane. We checked that both AC and DC measurements forthe same samples give the same resistance values in theintermediate resistance region. The dielectric constants weremeasured using a lock-in amplifier at 1Hz–2 kHz. Coaxialcables were used to reduce the stray capacitance of theexperimental setup. The electrical contacts were made usingcarbon paste on the sides of the crystals. The AC voltage waskept at a low value of ∼0.1V. The crystals were slowlycooled to 1.6K at a rate of 1K=min in the 4He cryostat.

3. Results

3.1 Temperature and field dependences of resistanceThe temperature dependence of the in-plane resistance at

a low-bias voltage for sample #1 is shown in Fig. 1. In themeasurements, the voltage is kept small, where the I–Vcharacteristics are nearly linear. The broad peak at ∼100Kand the observation of the M–I transition (TMI ¼ 8:5K) areconsistent with previous studies.2) In the AFI phase, theresistance exponentially increases with decreasing temper-ature. In the Arrhenius plot (inset), we note that the linearbehavior R ¼ R0 expð�=2kBTÞ is seen only in a limitedregion as shown by dotted lines. The result shows that Δ istemperature-dependent in a wide temperature region fromTMI to ∼3K. This behavior is in sharp contrast to conven-tional charge order (CO) or Mott insulating phases, in which�ðTÞ becomes almost constant for T=TMI < 0:7.17–21) Themagnetic field dependences of the in-plane resistance at 1.6and 7K are shown in Figs. 2(a) and 2(b), where the magneticfield is applied along the c-axis. The resistance monotonicallydecreases with increasing field and then shows a rapid dropat the M–I transition [Fig. 2(a)]. The M–I transition isassociated with hysteresis. The transition field HMI dependson the field angle [Fig. 2(b)]; the HMI value for H k b� ishigher than that for H k c.

We measured the RðHÞ curves at various field directionsand obtained the anisotropy of HMI (Fig. 3). Here, we defineHMI at the criterion R ¼ 4Ω [dotted line in Fig. 2(b)], whichcorresponds to about ten times the R value in the PM phase.

Because of the hysteresis of the transition, HMI values areobtained from up- and down-sweeps at each angle. Note thatthe HMI values are slightly sample-dependent, e.g., HMI of#3 for H k b� is smaller than that of #4. Figure 4 showsthe resistance at low fields for H in the b�–c plane. We

Fig. 1. (Color online) Temperature dependence of the in-plane resistanceR at a low-bias voltage for λ-(BETS)2FeCl4. Inset: Arrhenius plot. The dottedlines show �=kB � 30K.

(a)

(b)

Fig. 2. (Color online) Magnetic field dependence of the in-plane resist-ance in the whole field region (a) and near the M–I transition field (b).

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successfully observed a small dip at ∼1.2 T for � ¼ 55°,associated with hysteresis. As the field is tilted from thisangle, the dip is suppressed and no dip is evident at � ¼ 90°.Since the magnetic torque measurements show that the spinflop (SF) transition occurs at 1.2 T for � � 55°,22,23) the smalldip can be ascribed to the SF transition.

3.2 I–V characteristicsThe I–V characteristics at different temperatures are shown

in Fig. 5(a). At high temperatures above 4.4K, the I–V

characteristics are linear in the whole voltage region. Atlower temperatures, the I–V characteristics are almost linearup to ∼0.2V and then show slightly upward curvature athigher voltages. At 1.6K, for instance, we see the power-lawbehavior I ¼ V� for V > 0:3V. The exponent α at highvoltages increases from 1 to ∼3 with decreasing temperature.The I–V characteristics in magnetic fields at 1.6K are shownin Fig. 5(b). In low magnetic fields of up to ∼6 T, the I–Vcharacteristics are almost linear up to ∼0.2V and then showupward curvature at higher voltages. The power-law behavioris seen above ∼0.3V. Above ∼7 T, the I–V characteristics arelinear in the whole voltage region. The nonlinear I–Vcharacteristics for λ-(BETS)2FeCl4 were first reported byToyota et al.24) They measured the I–V curves up toE ¼ 100V=cm at 4.2K, which is ∼30 times that in our case,and found negative differential resistance behavior. In thelow-electric-field region, power-law-like behavior is seen.The negative differential resistance was discussed in terms ofcarrier decondensation, although the microscopic origin is anopen question. We also attempted measurements at highervoltages but found kinks in the I–V curves, showing contactdamage. At such high voltages, we often observed hysteresisin the I–V curves, suggesting that the Joule heating of thesample is a serious problem. Therefore, we focus ourdiscussion on the data in the voltage region shown inFigs. 5(a) and 5(b).

(a)

(b)

Fig. 3. (Color online) Angular dependence of the M–I transition field(HMI) in the b�–c (a) and b�–a0 planes (b). The closed and open symbols aredetermined from the up- and down-sweeps, respectively.

Fig. 4. (Color online) Magnetic field dependence of the normalizedresistance at 1.6K. The inset shows schematic spin configurations of the πelectrons below and above the spin-flop transition field.

(a)

(b)

Fig. 5. (Color online) I–V characteristics at various temperatures (a) andmagnetic fields (b). The dotted curves show the calculated results for1:6 � T � 2:7K.

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3.3 Dielectric constantsFigures 6(a) and 6(b) show the frequency dependence of

the dielectric constants at various temperatures for the electricfield E parallel ("in) and perpendicular ("out) to the plane,respectively. We see large anisotropy of the dielectricconstants between the in-plane and out-of-plane electricfields. Both "in and "out decrease with increasing frequencyand show a 1=f 2 dependence in the low-frequency region.The extrinsic effect arising from contact resistance andcapacitance becomes evident at low frequencies in dielectricconstant measurements20) when the work function of themetal contact is larger than that of the semiconductingsample.25) Under realistic conditions, the total capacitance isdominated by the contact capacitance, following 1=f 2

dependence at low frequencies. Therefore, the residual part,which is almost flat at higher frequencies ( f > 100Hz),should be intrinsic (from the bulk sample). Above 100Hz, wenote that "in is 10 times larger than "out. Both "in and "outdecrease with decreasing temperature. A similar temperaturedependence is observed at 100 kHz.26)

Figure 7 shows the magnetic field dependence of "in and"out at 1 kHz and 1.6K. Both "in and "out gradually increasewith increasing magnetic field and then tend to diverge near8 T. Above 8T, reliable data are not obtained because of thelow impedance. The field dependence of "in has already beenmeasured at 1 kHz above 2.5K15) and shows a similar gradualincrease.

In dielectric constant measurements, a sample with alayered structure such as λ-(BETS)2FeCl4 can be modeled assimple electronic circuits with two different capacitors: aparallel circuit for in-plane measurements and a series circuitfor out-of-plane measurements.20) Assuming that the dielec-

tric constant of the BETS layer ("BETS) is much larger thanthat of the FeCl4 layer ("FeCl), we obtain the relations"BETS � "inðdBETS þ dFeClÞ=dBETS and "FeCl � "outdFeCl=ðdBETS þ dFeClÞ. Here, dBETS ’ 1 nm and dFeCl ’ 0:5 nm arethe thickneses of the BETS and FeCl4 layers, respectively. At1.5K, we have "BETS="0 � 1:8 � 10�3 and "FeCl="0 � 2:7 �10�5 at 1 kHz for �0H ¼ 0T.

4. Discussion

4.1 Charge transport modelA charge transport model to explain the nonlinear I–V

characteristics in charge-ordered and Mott insulating phaseswas first proposed by Takahide et al.17) The conductivity inthis model is based on the electric-field (E)-dependentpotential barrier �ðEÞ between the thermally excited electronand hole [Fig. 8(a)]. The total conductivity is given byJ=E ¼ �0 exp½��ðEÞ=2kBT�, where J is the current density.For λ-(BETS)2FeCl4, the transfer integral t is highlyanisotropic: the in-plane t is considerably larger than theout-of-plane t. Therefore, the excited electron–hole pairsremain in the same layer. In the AFI phase of λ-(BETS)2-FeCl4, since "BETS � "FeCl, the electric fluxes between thethermally excited hole and electron are confined in each

(a)

(b)

Fig. 6. (Color online) Dielectric constants as a function of frequency atvarious temperatures in the in-plane (a) and out-of-plane electric fields (b).

Fig. 7. (Color online) Magnetic field dependence of the in-plane and out-of-plane dielectric constants at 1 kHz for T ¼ 1:6K.

(a)

(b)

Fig. 8. (Color online) (a) Schematic picture of the charge excitation in theAFI phase. (b) Coulomb potential curves between the thermally excitedelectron and hole at zero and finite electric fields.

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layer. Then, the attractive Coulomb potential ’ðrÞ betweenthe electron and hole with a distance r has a 2D form,

’ðrÞ ¼ � 2e

4�"BETSdBETSln

r

2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidBETSdFeCl�

p� �

þ C

� �; ð1Þ

for dBETS r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidBETSdFeCl�

p, where � ¼ "BETS="FeCl and

C is the Euler constant.27) Thus, the Coulomb potential iswritten as U0 lnðr=aÞ, where r is shorter than the cutoff length� ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

dBETSdFeCl�p

. Here, a is a minimum length scale, whichwe take as the size of the BETS molecule (∼0.5 nm). TheCoulomb potential reaches the three-dimensional form 1=r ata longer distance. For simplicity, we take a constant Coulombpotential ’ðEÞ ¼ U0 lnð�=aÞ for r > � in the followingsimulation [Fig. 8(b)]. The activation energy �ðEÞ in theelectric field E is given by the maximum value of the ’ðEÞcurve, �ðEÞ ¼ U0 lnðU0=eEaÞ �U0 for U0=e� � E and�ðEÞ ¼ U0 lnð�=aÞ � eE� for U0=e� > E. Under our exper-imental condition (U0=ea � E), we obtain nonlinear I–Vcharacteristics, which follow the power law at high electricfields, U0=e� � E, J / E�ð� ¼ U0=2kBT þ 1Þ. In the low-electric-field region, U0=e� � E, �ðEÞ is almost independentof E, � � U0 lnð�=aÞ. Therefore, we obtain a linear I–Vcurve. The activation energy �=kB � 30K is determinedfrom the Arrhenius plot (inset of Fig. 1).

The dotted curves in Fig. 5(a) show the I–V characteristicscalculated by the above model for 1:6 � T � 2:75K. Thecalculations include only one parameter � � 100 nm. Notethat the experimental results are well reproduced. Thereasonably good agreement shows that the charge transportin the AFI phase of λ-(BETS)2FeCl4 can be characterized bythe energy gap Δ determined by the Coulomb potentialbetween the excited electron and hole. This energy gap iscompletely different from that of semiconductors, where Δ isgiven by the band gap. This model is valid only when Δ isconstant. The results in Fig. 1 show that Δ changes above3K, which indicates that the dielectric constant and λ changewith temperature. Such a change may be related to theanomalous behavior of the dielectric constant11) and chargedisproportionation.12)

Here, we compare the parameters obtained from theanalyses of the I–V characteristics with those for θ-(BEDT-TTF)2CsZn(SCN)4.17,21) As shown in Table I, the �=kBvalues are comparable to each other. However, the power-law exponent α at the base temperature shows a largerdifference. From the relation � � U0 lnð�=aÞ, the larger λ ofλ-(BETS)2FeCl4 gives a smaller U0. Therefore, we obtain asmaller α because � / U0.

From the "BETS and "FeCl values at 1.6K for f ¼ 1 kHz, weobtain the cutoff length � � 6 nm, which is shorter than theexperimental result (� � 100 nm) obtained from the I–Vcurve calculations. Similar differences have been found inother bulk crystals17–21) and are explained in terms of someinhomogeneities of the samples. To obtain the I–V character-

istics, the electric contacts are made in a small region(∼20 µm) on the flat surface of the crystal, but the dielectricconstant is measured for the bulk crystal (∼200 µm).Therefore, the dielectric constant could be more affected bymicrocracks, which might be induced in cooling. Thesecracks will strongly reduce the in-plane capacitance, whichleads to the underestimation of λ.

4.2 SF transitionAs shown in Fig. 4, a dip in the resistance is observed at

the SF transition. A resistance anomaly at the SF (ormetamagnetic) transition has been reported in various π–dsystems. In (EDT-DSDTFVSDS)2FeBr4, the resistance issemiconducting below 30K28,29) and shows a dip at the SFtransition field (HSF ¼ 1:8T) in the AF phase of the Fe 3dspins (TN ¼ 3:3K). In (DIETSe)2FeCl4, the π electrons showan incommensurate spin-density-wave transition30) at 10Kunder a pressure of 3.5 kbar. A small dip in the resistance isobserved at HSF (¼ 1:5T) in the AF phase of the Fe 3d spins(TN ¼ 4K). For κ-(BDH-TTP)2X, where X = FeBr4 andFeCl4, the resistances show steep decreases (not dips) at HSF

(¼ 2T) and at the metamagnetic transition field (HM ¼0:15T), respectively, in the AF phases of the Fe 3d spins.31)

For all these salts, the changes in resistance at HSF or HM areexplained by the magnetic scattering between the π and 3dspins via the π–d interaction. Among the above salts, the dipbehavior in (EDT-DSDTFVSDS)2FeBr4 is similar to theresult shown in Fig. 5; a small dip is superimposed on thenegative magnetoresistance. However, the crucial differencefrom the above π–d systems is that the π spins areantiferromagnetically ordered but the 3d spins are not forλ-(BETS)2FeCl4.

On the basis of the above electron–hole excitation model,we could qualitatively explain the dip at HSF. The spin statehas not been taken into account in the above model. However,in the AFI phase, an up (down)-spin electron must be excitedto a down (up)-spin site [Fig. 8(a)]. This means that thenumber of possible excited states (doubly occupied sites) ishalf of the total number of sites. Even for H > HSF, thesituation is the same. Since the π spin exchange interaction(J�� � 450K1)) is much larger than the Zeeman energy, theneighboring π spins are almost antiparallel to each other forH > HSF (inset of Fig. 4). For H � HSF, on the other hand,the spin state will be highly fluctuating between the two states.This situation will effectively increase the number of possibleexcited states, which leads to a resistance dip at HSF.

4.3 Angle dependence of HMI transition fieldIn the PM phase, the localized 3d spins are strongly

polarized but the π spins are hardly polarized. Therefore, thefree energy in the PM phase is approximately given byFPMðHÞ ¼ FPMð0Þ �M3dH, where FPMð0Þ corresponds to thefree energy of the π spins and M3d is the magnetization of the3d spins, hM3di ¼ g�BhSi. Therefore, the PM phase becomesstable with increasing field. If the Zeeman term M3dH has apredominant effect in the M–I transition, the anisotropy ofHMI is determined by that of the g-factor of the 3d spins.Therefore, HMI will have sinusoidal dependence as a functionof the angle, as shown in Fig. 3. At present, no systematicESR measurements of the 3d spins in the PM phase havebeen carried out, which will be a future work.

Table I. Parameters obtained from the analyses of the I–V characteristics.

Material λ-(BETS)2FeCl4 θ-(BEDT-TTF)2CsZn(SCN)417,21)

TMI (K) 8.5 20�=kB (K) 30 24α (at base temperature) ∼3 ∼8λ (nm) 100 23

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5. Conclusions

The nonlinear I–V characteristics in the AFI phase ofλ-(BETS)2FeCl4 are interpreted on the basis of the chargetransport due to the thermally excited electron–hole pairs inthe 2D Coulomb potential. In the RðHÞ curve, a small dip at1.2 T can be ascribed to the SF transition. This dip is likelycaused by the spin-dependent excitation of the charges basedon the above model. The dielectric constant at lowfrequencies is anisotropic; "in is 10 times larger than "out.This anisotropy is consistent with the presence of the 2DCoulomb potential. The HMI values in the b�c and b�a0

planes have sinusoidal behavior as a function of the fieldangle. The results suggest that the Zeeman effect of the 3dspins of the Fe ions plays an essential role.

Acknowledgement

This research was partially supported by Grants-in-Aid forScientific Research on Innovative Areas (Nos. 25400384,25287089, and 15H02108).

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