aa r X i v : . [ c ond - m a t . s t r- e l ] M a y Collective Charge Excitations below the Metal-to-Insulator Transition in BaVS T. Ivek, ∗ T. Vuleti´c, and S. Tomi´c
Institut za fiziku, P.O.Box 304, HR-10001 Zagreb, Croatia
A. Akrap, H. Berger, and L. Forr´o
Ecole Politechnique F´ed´erale, CH-1015 Lausanne, Switzerland (Dated: October 24, 2018)The charge response in the barium vanadium sulfide (BaVS ) single crystals is characterized bydc resistivity and low frequency dielectric spectroscopy. A broad relaxation mode in MHz rangewith huge dielectric constant ≈ emerges at the metal-to-insulator phase transition T MI ≈
67 K,weakens with lowering temperature and eventually levels off below the magnetic transition T χ ≈
30 K. The mean relaxation time is thermally activated in a manner similar to the dc resistivity.These features are interpreted as signatures of the collective charge excitations characteristic for theorbital ordering that gradually develops below T MI and stabilizes at long-range scale below T χ . PACS numbers: 71.27.+a, 71.30.+h, 72.15.Nj, 77.22.Gm
I. INTRODUCTION
A variety of condensed matter systems with reduceddimensionality and strong Coulomb interactions betweencharges, spins and orbitals, display rich phase diagramswith novel forms of ordering phenomena . These col-lective, broken symmetry phases like charge and spin-density waves, charge and orbital orderings have beenthe focus of intense scientific activity in recent years.Additionally, in transition metal compounds d -electronsexperience competing forces: Coulomb repulsion tendsto localize electrons, while hybridization with the ex-tended ligand valence states tends to delocalize them .The subtle balance makes these systems an excellentsource for studying diverse metal-to-insulator (MI) phasetransitions usually accompanied with drastic changes incharge, spin and orbital properties. In particular, the in-fluence of the orbital degeneracy and orbital ordering onelectrical transport and magnetic properties is rapidlybecoming a central issue . For example, in the classictransition metal oxide V O X-ray anomalous scatteringresults have given a direct evidence that the orbital occu-pancy plays a central role in the physics of this system .The spatial ordering of the occupancy of degenerate elec-tronic orbitals was shown to account for the anisotropicexchange integrals found in the antiferromagnetic insu-lator phase. Another outstanding issue is the questionof collective excitations in the orbital ordered state. Al-though no theoretical model has been worked out untilnow, it is expected that the orbital degrees of freedom caneither give rise to novel collective excitations, e.g. orbitalwaves, or can strongly renormalize other excitations .The perovskite-type sulfide BaVS represents an ex-ceptional system to study the aforementioned phenom-ena and as such has attracted much attention in the lastyears. Face sharing VS octahedra stack along the crys-tallographic c -axis and form the VS spin chains withone 3 d electron per V site. The chains are sepa-rated by Ba atoms in the ab planes, yielding a quasi-one-dimensional (quasi-1D) structure. The unit cell at room temperature (RT) is a primitive hexagonal withtwo formula units. At 240 K the structure transformsinto orthorhombic, but each chain keeps two equivalentV atoms per unit cell. The corresponding two electronsare shared essentially between two hybridized bands pro-duced by the crystal field splitting: a broad A g bandderived from d z orbitals overlapping along the c -axis,and a quasi-degenerate narrow E g band originating from e ( t g ) orbitals with isotropic interactions via V-S-S-Vbonds . The filling of these bands is controlled bythe on-site Coulomb repulsion U and local Hund’s rulecoupling J . The main effect is to bring the occupanciesof A g and E g orbital closer to one another, which in thelimit of strong correlations yields the occupancy for eachof these orbitals close to half-filling. The spin degreesof freedom of the localized electrons and the coupling ofconduction and localized electrons make the system ex-tremely complex. Their interplay results in the MI tran-sition at about 70 K and a magnetic transition at about30 K.In spite of a great deal of experimental efforts, no def-inite understanding has been reached yet on the detailednature of the MI phase transition and the ground state inBaVS . Diffuse X-ray scattering experiments have shownthat at T MI a commensurate superstructure with the crit-ical wave vector q c = 0 . c ∗ close to 2 k F ( A g ) sets in,preceded by a large fluctuation regime extending up to170 K . This behavior is reminiscent of a Peierls transi-tion into a charge-density wave (CDW) state. However,the nature of the ground state is certainly more compli-cated since 2 q c harmonic is found suggesting that the lo-calized e ( t g ) electrons are also involved in the transitionand order below T MI . Indeed, the related susceptibility,which follows the Curie-Weiss law from RT, exhibits anantiferromagnetic (AF)-like cusp at T MI and decreasesbelow . There is no sign of magnetic long-range orderdown to T χ ≈
30 K, where the incommensurate magneticordering is established . The next unusual result at T MI is a structural transformation from the orthorhombic tomonoclinic with internal distortions of VS octahedronand tetramerization of V chains . The modulationof V distances in the superstructure can be described asa superposition of a 2 k F and a 4 k F bond order waves(BOW), the latter component being primarily responsi-ble for the intensity change of the basic Bragg reflections.It is noteworthy that the tetramerization might be under-stood as an inherent feature of the 2 k F Peierls transition,which reveals that a dimerization gap at high tempera-tures is negligible and that the broad A g band could beregarded as effectively one-quarter filled band. Finallyand the most surprisingly, X-ray anomalous scattering atthe vanadium K -edge revealed no charge disproportion-ation in the ground state . A very intriguing interpreta-tion has been suggested involving the stabilization of twoout-of-phase CDWs from d z and e ( t g ) electrons, whichimplies an orbital ordering via an out-of-phase modula-tion of the occupancy of V sites by the d z and e ( t g )orbitals.In this paper, we address these important questionsconcerning the insulating state in BaVS . Our resultspresent a supporting evidence for an orbital orderedground state and that the MI Peierls-like transition isalso an orbital ordering transition. We find that a hugedielectric constant which arises in close vicinity of theMI transition dramatically decreases on cooling down toabout 30 K and levels off below. We argue that such abehavior might be rather well explained in terms of anorbital ordering which sets in at the MI transition anddevelops the long-range order below the magnetic tran-sition. II. EXPERIMENTAL AND RESULTS dc resistivity was measured between RT and 10 K.In the frequency range 0.01 Hz–10 MHz the spectra ofcomplex dielectric function were obtained from the com-plex conductance measured by two set-ups. At highfrequencies (40 Hz–10 MHz) an Agilent 4294A preci-sion impedance analyser was used. At low frequencies(0.01 Hz–3 kHz) a set-up for measuring high-impedancesamples was used . The employed ac signal level of50 mV was well within the linear response regime. Allmeasurements were done on single crystals along thecrystallographic c -axis. The typical crystal dimensionswere 3 × . × .
25 mm .An influence of extrinsic effects, especially those dueto contact resistance and surface layer capacitance, wasruled out with scrutiny. In order to determine the qual-ity of contacts we have performed dc resistance measure-ments in the standard 4- and 2-contact configurations.Taking into account the difference in geometry betweencontacts in these two configurations, the 4-contact re-sistance can be scaled and subtracted from the 2-contactresistance in order to estimate contact resistance ( R c ) vs. sample bulk resistance ( R s ). Our analysis clearly showsthat good quality contact samples whose dielectric re-sponse reflects the intrinsic features of the sample bulk Frequency (Hz)10 -1 e ( ) e '- e HF e '' 20 K35 K50 KBaVS FIG. 1: Real and imaginary parts of the dielectric functionof BaVS measured at three representative temperatures as afunction of frequency with the ac electric field applied alongthe c -axis. The full lines are from fits by the generalized Debyeexpression (see Text). can easily be distinguished from bad samples by featuringthe R c /R s ratio not larger than 5 in the metallic phaseand in the vicinity of T MI , and R c = 0 . R s in the wholerange of the insulating phase except close to T MI . In con-trast, bad samples displayed R c /R s ratio of the order of100–1000 in the metallic phase and in the vicinity of T MI ,indicating large contact resistances, which concomitantlyimply large contact capacitances throughout the wholemeasured temperature range. Consequently, the dielec-tric response registered in samples with bad quality con-tacts was a combination of the sample bulk and contactcapacitance influence, the latter becoming dominant withincreasing temperature. In this way, out of nine sam-ples studied, seven were discarded either due to bad con-tacts, or due to exceptionally low RRR at high pressureof 20 kbar. Two remaining good quality contact sam-ples with high RRR at high pressure have shown quali-tatively the same dielectric response, confirming that theobserved response comes from the sample bulk. In thispaper we present and discuss results obtained on one ofthese two single crystals.Fig. 1 shows frequency dependence of the complex di-electric response at three selected temperatures. A pro-nounced dielectric relaxation is observed. The screenedloss peak ε ′′ centered at τ − moves toward lower fre-quencies and smaller amplitudes with decreasing temper-ature. The main features of this relaxation are well de-scribed by the generalized Debye expression ε ( ω ) − ε HF =∆ ε/ (cid:2) iωτ ) − α (cid:3) , where ∆ ε = ε − ε HF ( ε and ε HF are static and high-frequency dielectric constant, with thelatter being negligible), τ is the mean relaxation timeand 1 − α is the symmetric broadening of the relaxationtime distribution function. T (1000/K)20 40 60 80 100 ρ ( Ω c m ) -3 d l n ρ / d ( / T ) ( K ) -50005001000150020002500 Temperature (K)300 67 30 20 15 1010 ∆ ε T MI T χ BaVS FIG. 2: Temperature dependence of the dielectric constant ofthe collective mode (upper panel), and dc resistivity and itslogarithmic derivative (lower panel) in BaVS . The arrowsindicate the MI and magnetic transition temperature. Our results clearly demonstrate that a huge dielec-tric constant ∆ ε is associated with the metal-to-insulatorphase transition (Fig. 2). On decreasing temperature, asharp growth of ∆ ε starts in the close vicinity of T MI andreaches the huge value of the order of 10 at T MI = 67 K(Fig. 2, upper panel). This T MI value corresponds per-fectly well to the phase transition temperature as deter-mined in the dc resistivity measurements, indicated bypronounced peaks at T MI in the logarithmic derivative ofresistivity (Fig. 2, lower panel).The observed dielectric relaxation would suggest acharge-density wave formation at T MI16 . The standardmodel of a deformable CDW pinned in a non-uniformimpurity potential accounts for the existence of twomodes, transverse and longitudinal . The former cou-ples to the electromagnetic radiation and yields an un-screened pinned mode in the microwave region. Unfor-tunately, no microwave measurements on BaVS havebeen done yet. The longitudinal mode couples to an elec-trostatic potential and mixes in the transverse responsedue to the non-uniform pinning resulting in an over-damped low-frequency relaxation at τ − due to screen-ing effects. The relaxation detected in our experimentsbears two features as expected in the standard model.The first is that the relaxation time distribution is sym-metrically broadened, 1 − α ≈ .
8. The second is thatthe mean relaxation time τ closely follows a thermallyactivated behavior similar to the dc resistivity τ ( T ) = τ exp(2∆ / k B T ) ∝ ρ ( T ) (see Fig. 3). τ ≈ ≈
500 K, as found in the spec- T (1000/K)20 40 60 80 100 r ( W c m ) -3 t ( s ) -9 -6 -3 Temperature (K)300 67 30 20 15 10
BaVS FIG. 3: The mean relaxation τ of the collective charge mode(points) and the dc resistivity (full line) in BaVS as a func-tion of the inverse temperature. tra of the optical conductivity . The dissipation can benaturally attributed to the screening due to single parti-cles originating from the wide A g band. However, ourdiscovery finds no consistent explanation within the stan-dard model , since the dielectric constant ∆ ε displays astrong decrease below T MI and levels off at temperaturesbelow about 30 K, a behavior which significantly devi-ates from the one expected for a CDW condensate den-sity n : ∆ ε ( T ) ∝ n ( T ). The decrease of ∆ ε on movingbetween the MI transition T MI and the magnetic tran-sition T χ is substantial and amounts to two orders ofmagnitude. One possible explanation for this discrep-ancy is the very nature of the standard model for the re-sponse of the conventional CDW to applied electric fieldsin which the long-wavelength collective CDW excitation s.c. phason keeps the prominent role. We remind thatthis model is worked out for the incommensurate CDWin a random impurity potential, whereas the CDW inBaVS associated with the observed lattice modulationis commensurate with the order of commensurability, i.e. the ratio of the CDW and lattice periodicity, N = 4.However, the order of commensurability is not too highto impose the commensurability pinning and forbid thephason excitations . Indeed, the experimental observa-tion of the broad relaxation, i.e. − α ≈ . . Our dc electric-field depen-dent measurements up to fields as high as 100 V/cm inthe temperature range between 15 K and 40 K have onlyrevealed a negligibly small non-linear conductivity, whichemerges from the background noise. III. DISCUSSION
Our results indicate that the long-wavelength CDWcollective excitations are frozen or strongly renormalizedand that the collective excitations of different kind shouldbe responsible for the observed dielectric relaxation. Inthe following we first address other possible causes andthen offer the most plausible scenario for our results.First, we verify if the observed behavior of the di-electric constant might be due to the hopping conduc-tion which is known to arise in disordered systems withlow dimensionality, where Anderson localization yieldsthe conductivity characterized by variable-range hopping(VRH) Mott law in dc limit, while in ac limit it fol-lows a power law dependence on frequency. AlthoughBaVS may be regarded as a quasi-1D system, the hop-ping scenario does not seem realistic for the followingreasons. First is that the frequency marking the on-set of the frequency-dependent transport is known tobe roughly proportional to the dc conductivity, i.e. tothe inverse of the dc resistivity . The dc resistivity ofBaVS at RT is about 10 − Ωcm and at lowest tempera-tures it is about 10 to 10 Ωcm. In the diverse systemswith dc resistivities of similar orders of magnitude, theac conductivity power law is observed only at frequen-cies above 1 MHz, whereas below 1 MHz an influence ofhopping on dielectric dispersion is detected only for dcresistivities much higher than 10 Ωcm.
Indeed, inthe case of BaVS a crude estimate for the crossover fre-quency yields values far above the frequency range wherethe dielectric response was observed . The second resultwhich excludes hopping comes from the observed opticalspectra . Namely, a simple indication for existence ofa hopping mechanism would be that the optical conduc-tivity is significantly enhanced in comparison with thedc conductivity, whereas in the case of BaVS the opti-cal conductivity, even at temperatures lower than T MI , isat best comparable to the dc conductivity.Next possible origin of the observed dielectric responsemight be associated with a ferroelectric nature of the MItransition. Simple space group considerations indicatethat below the MI transition the structure of BaVS isnoncentrosymmetric with a polar axis in the reflectionplane containing the VS chains. The symmetry of thislow-temperature superstructure is Im , implying that thedistortions of the two chains of the unit cell are out ofphase . Bond-valence sum (BVS) calculations of theseX-ray data have indicated some charge disproportiona-tion at low temperatures. However, it was recently ar-gued by P. Foury-Leylekian that the BVS method over-estimated the charge disproportionation due to severalreasons: a nonsymmetric V environment, thermal con-traction corrections which were not included and ratherimprecise atomic coordinates which were used. Taking allthis into account together with X-ray anomalous scat-tering result that showed negligible redistribution, notlarger than 0.01 electron below T MI14 , we conclude thatferroelectricity cannot provide an explanation of the di- electric response in BaVS .Finally, we address orbital ordering as a plausibleground state whose collective excitations might yield theobserved dielectric relaxation. First we list argumentsdeveloped by Fagot et al. who invoked an orbital or-dering associated with the MI phase transition in orderto consistently explain structural data of BaVS . Sup-porting results for an orbital ordering scenario at T MI arean almost non-existant charge modulation in the insulat-ing phase, together with a qualitative structural anal-ysis of the VS octahedron distortions, which revealsan out-of-phase modulation of the occupancy of V sitesby the d z and e ( t g ) orbitals. In particular, dominant E g and A g occupancies are proposed for V1 and V3sites respectively, while no definitive preferential occu-pancy was found for V2 and V4 sites. Furthermore,recent LDA+DMFT (local density approximation withdynamical mean-field theory) calculations performed inthe monoclinic insulating phase of BaVS have qualita-tively confirmed an orbital-ordering scenario showing aV-site-dependent orbital occupancy and only minor, ifany, charge disproportionation . However, these calcu-lations suggest quite different orbital occupancies: it ap-pears that the (V3,V4) pair forms a correlated dimer withmixed A g and E g occupancy, while the V1 and V2 ionsbear major E g occupancy and negligible coupling. Fi-nally, the overall study indicates that although the localenvironment of the V site does not change substantially,the electronic structure turns out to be rather sensitive tochange of temperature. The question arises what is thetemperature dependence of the order parameter of or-bital ordering which starts to develop below T MI and inwhat way it relates to the magnetic ordering. V NMRand NQR measurements also suggested an orbital order-ing below T MI that is fully developed only at T < T χ .The magnetic phase transition at T χ is preceded by long-range dynamic AF correlations all the way up to T MI and this phase bears features of a gapped spin-liquid-likephase. Mih´aly et al. suggested that the lack of magneticlong-range order between T MI and T χ might be the con-sequence of the frustrated structure of a triangular arrayof V chains, which also prevents the orbital long-rangeorder, so that the long-range spin and orbital orders candevelop only well below T MI . Finally, the AF static orderbelow T χ is not a conventional N´eel phase: an AF do-main structure is suggested by the magnetic anisotropymeasurements . The existence of domains seems to besupported also by the muon spin rotation ( µ SR) measure-ments, which showed an essentially random distributionof sizeable static electric fields below T χ indicating anincommensurate or disordered magnetism .Based on the considerations above we suggest the fol-lowing as the most plausible scenario. The primary orderparameter for the MI phase transition is 1D CDW in-stability and this CDW instability drives the orbital or-dering via structural changes involving a transformationfrom the orthorhombic to monoclinic with internal dis-tortions of VS octahedron and tetramerization of V chains. The orbital order is coupled with the spin de-grees of freedom and drives the spin ordering into anAF-like ground state below 30 K. In other words, the or-bital ordering transition happens at T MI , domains of or-bital order gradually develop in size with lowering tem-perature (concomitantly their number diminishes) andthe long-range order eventually stabilizes below T χ , al-beit domain structure persists. In this scenario we pro-pose that the collective excitations responsible for theobserved features of the dielectric relaxation are short-wavelength ones, like charge domain walls in the ran-dom AF domain structure. Similar short-wavelengthexcitations associated with domain structure have pre-viously been invoked as the origin of dielectric relax-ation in diverse systems . The relaxation happensbetween different metastable states, which correspond tolocal changes of the spin configuration. The spin con-figuration is intimately connected with the charge andthe orbital degrees of freedom as explained above. Sincethe dielectric constant is associated with the density ofcollective excitations, its anomalous temperature behav-ior below T MI indicates that the relaxation-active num-ber of domain walls decreases with lowering temperatureand eventually becomes well defined below T χ . In otherwords, the dynamics of domain walls becomes progres-sively more restricted as the temperature lowers and itbecomes constant below T χ . IV. CONCLUSION
In conclusion, we demonstrated the appearance of ahuge dielectric constant associated with the metal-to- insulator phase transition in BaVS followed by a dra-matic decrease on cooling down to the magnetic tran-sition and leveling off below. We argue that the col-lective excitations whose dispersion we detect as broadscreened relaxation modes are not CDW phason exci-tations; rather they represent short-wavelength excita-tions of an orbital ordering, which sets in at the metal-to-insulator transition and develops the long-range orderbelow the magnetic transition. Finally, BaVS repre-sents a beautiful example of the intricate interplay be-tween an orbital degeneracy on the one side, and spinand charge sector on the other side. This interplay needsto be taken into account in order to understand the ori-gin of the metal-to-insulator phase transition and low-temperature phases in the transition metal compoundsin general. Further work on the theoretical and experi-mental fronts is needed to demonstrate directly the ex-istence of an orbital order in BaVS and the associatedsuperstructure.We thank N. Bariˇsi´c, S. Bariˇsi´c, P. Foury-Leylekian,V. Ilakovac, M. Miljak and J. P. Pouget for useful discus-sions. This work was supported by the Croatian Ministryof Science, Education and Sports under Grant No.035-0000000-2836. The work in Lausanne was sponsoredby the Swiss National Science Foundation through theNCCR pool MaNEP. ∗ URL: http://real-science.ifs.hr/ ; Electronic address:[email protected] P. Fulde,
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