single-particle excitations in one-dimensional mott-hubbard insulator

VOLUME 80, NUMBER 14 P H Y S I C A L R E V I E W L E T T E R S 6 APRIL 1998

7-22-1,

Single-Particle Excitations in One-Dimensional Mott-Hubbard Insulator NaV2O5

K. Kobayashi, T. Mizokawa, and A. FujimoriDepartment of Physics, University of Tokyo, Bunkyo-ku, Tokyo, 113, Japan

M. Isobe and Y. UedaMaterials Design and Characterization Laboratory, Institute for Solid State Physics, University of Tokyo, Roppongi

Minato-ku, Tokyo, 106, Japan(Received 2 September 1997)

We have made an angle-resolved photoemission study of NaV2O5 at room temperature, i.e., in theparamagnetic phase well above the spin-Peierls transition temperature. The obtained results reflectthe one dimensionality of the electronic structure. The lower binding energy side of the V3d bandshows a clear momentum-dependent modulation with the periodicity ofp, indicating the existence ofantiferromagnetic correlations or holon excitations in the one-dimensional Mott insulator. We comparethe results with recent theoretical works on the one-dimensional Hubbard andt-J models and discussconsistency between model parameters. [S0031-9007(98)05765-2]

PACS numbers: 71.10.Pm, 71.27.+a, 75.20.Ck, 79.60.– i

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Recently, quantum-spin systems in low dimensioncompounds such as spin-Peierls [1,2], spin-ladder, Hdane, and frustrated Heisenberg systems have attracconsiderable interest. The most basic but far frotrivial among them is the one-dimensional (1D) antiferromagnetic (AF) Heisenberg chain and its excitation spectTheoretical works on its excitation spectra based on tHubbard model ort-J model have shown signs of spin-charge separation: as a result of one dimensionality, tdegrees of freedom of an electron are decoupled into splike and chargelike elementary excitations called “spinonand “holon,” respectively [3]. Parameters appearingthose models are the transfer integralt between nearestneighbors, the exchange coupling constantJ (. 0) and theon-site Coulomb energyU. Exact diagonalization andanalytical studies [3–7] have shown that the singleparticle spectral function has spinon and holon dispersiofor momentumk , py2. The energy scale of the holonexcitation is given byt, while that of the spinon excitationis given byJ. In the photoemission spectra, fromk 0to py2 the holon excitations disperse towards the chemicpotential and beyondk py2 disperse back. In the caseof the U ! ` (J ! 0) 1D Hubbard model [3], whichcan be solved analytically, the holon dispersion has twbranch cuts atEskd E0 1 2jtj sink andE0 2 2jtj sink,between which there exist continuum excitations. Thspinon band is located atEskd E0 (k , py2) andhas no dispersion becauseJ ! 0. Observation of adispersional width of,t is therefore an indication of spin-charge separation. Experimentally, an angle-resolvphotoemission spectroscopy (ARPES) study has beperformed for a 1D charge-transfer type insulator SrCuO2

[8], and the spectra agree well with calculations on the 1t-J model with parameters appropriate for this compounexhibiting such spinon and holon excitations. Because tt-J model is an effective low-energy Hamiltonian of themore realistic but complicatedp-d model for the Cu-O

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chain, it is natural to ask whether simpler Mott-Hubbard(MH) systems [9] can be described by the Hubbard mode

In this Letter, we report on an ARPES study ofa0-NaV2O5, typical 1D MH-type insulators in the paramag-netic phase. We focus on a dispersive feature of V3dcharacter in the lower Hubbard band. We compare our results with the theoretical results on the 1D Hubbard [3,4and t-J [6] models. a0-NaV2O5 is the second exampleof inorganic spin-Peierls (SP) compounds [10] discoveredfollowing CuGeO3 [1]. As shown in Fig. 1 [11], it con-sists of layers (ab planes) of VO5 square pyramids iso-lated by interlayer Na ions. The V atoms are in a mixedvalent state of V41:V51 1:1 and are charge ordered inone-dimensional rows: V41 (d1, S 1y2) and V51 (d0)chains are alternatingly running along theb axis. TheVO5 pyramids are sharing corners along the chain direction. As a result, this compound is expected to behavas an ideal 1D-AF system (1D half-filled MH system)with nearest-neighbor exchange interaction, being mucsimpler than CuGeO3 [12]. Indeed, the magnetic suscep-tibility xsTd is well fitted to the characteristic curve forthe 1D-AF Heisenberg chain (the Bonner-Fischer curve[13]) with J , 560 K above the SP transition temperatureTSP 34 K [10]. Below TSP , xsT d decreases rapidly.Here, we restrict ourselves to the paramagnetic phase

FIG. 1. Crystal structure ofa0-NaV2O5. The V41O5 andV51O5 pyramids running along theb axis are shown by thewhite and shaded square pyramids, respectively.

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room temperature. In fact, severe charging effect prohibited us from doing measurements at lower temperatures

Single crystals of NaV2O5 with typical sizes,1 3

0.5 3 4 mm3 were prepared by the melt growth methodusing NaVO3 as a flux [14]. The crystals could be cleavedparallel to theab plane. ARPES measurements weremade using the HeI resonance line (hn 21.2 eV) and ahemispherical analyzer. The angular resolution was61±

and the energy resolution was set80 100 meV. Mea-surements were done for several cleaves to confirm threproducibility. Here, we present reproducible results o“good cleaves” as judged from laser reflection. The baspressure in the spectrometer was below1 3 10210 Torr.

Figure 2 shows ARPES spectra in the entire valenceband region. The upper panel shows spectra with momentum parallel to theb axis (k k b), and the bottompanel those with momentum parallel to thea axis (k'b).The prominent features at binding energies (EB) from 3to 8 eV are the O2p band, while the weaker structuresbetween 0.5 and 3 eV are the V3d band. The spec-tra are normalized to the area of the O2p band. Thek k b spectra in the upper panel clearly show dispersivO 2p features as marked by the dashed curves. Arounk 0 (take-off angleu 0±) the spectra have three dis-tinct peaks. The top of the O2p band appears to belocated aroundk p. In contrast, thek'b spectra inthe bottom panel are nearly independent of angles. Th

FIG. 2. ARPES spectra of NaV2O5 for various take-off anglesu. Upper panel:k k b axis. Lower panel:k'b axis. Thedashed lines indicate the dispersions of the O2p bands.

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supports the view that NaV2O5 has a highly anisotropicelectronic structure with sizable dispersions only alonthe b axis. This is not obvious from the crystal structure alone, however, because it has a two-dimensionV-O network in theab plane (see Fig. 1). Presumablythe dispersions of the O2p bands are predominantlycaused by hybridization with V3d states, which are ar-ranged in the one-dimensional way.

The V 3d band located betweenEB 0.5 and 3 eVis broad and shows no spectral weight at the Fermi lev(EF), reflecting its insulating behavior. The broad peacentered atEB , 1.5 eV, which has also been observedin other vanadium oxides such as insulating LaVO3 [15],metallic SrVO3, and CaVO3 [16,17], would be attributedto the lower Hubbard band or its remnant feature separafrom the upper Hubbard band by the Coulomb repulsioenergyU. Looking at both thek k b and k'b spectrain Fig. 2, we notice that the intensity of this peak takea minimum around the normal emission (u 0±). If theoccupied V3d orbital hasxy symmetry lying in theabplane [18], normal emission from this orbital is forbiddendue to a selection rule [19]. The weak but finite intensitfor the normal emission can be explained by the tilting othe VO5 pyramid from theab plane [11].

In Fig. 3, we show the spectra of the V3d bandnormalized to the peak height atEB , 1.5 eV. Forthe k k b spectra shown in Fig. 3(a),u was varied from219± to 53±, corresponding tok 20.7p to 1.8p

FIG. 3. (a)k k b spectra in the V3d band region. Theyare normalized to the peak height aroundEB 1.5 eV. Thevertical lines indicate the inflection points. (b) The intensityplot. The dashed lines are contours. (c)k'b spectra in the V3d band region and (d) the intensity plot.


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along theb axis. The line shape of the lower bindingenergy side (EB 0.5 1.2 eV) shows a weak but cleark dependence. The inflection points obtained from tsecond derivative of the spectra are marked with verticbars in the same figure while this dispersion seemsoverlap the stronger feature centered atEB 1.5 eV.The intensity plot in theE-k plane on the grey scaleshown in Fig. 3(b) indicates that the lower binding energside of the lower Hubbard band disperses with thperiodicity of p , half of the reciprocal lattice vectork 2p . In fact, the spectra atk 2py2, py2, and 3y2p

have shoulders aroundEB 0.5 1.2 eV. It thus appearsthat the spatial periodicity is effectively doubled for thelectronic structure of the V3d states. On the contrary,the higher binding energy side (EB 1.8 2.5 eV) showsno sign of periodicityp , and the result seems consistenwith the periodicity of2p as in the O2p band, reflectingthe periodicity of the crystal structure (although we counot check the2p periodicity within ourk range,2p).The structure centered atEB , 1.5 eV itself does notseem to disperse. We show thek'b spectra in Fig. 3(c)with their inflection points marked by vertical lines, whichsigns no dispersive feature. The intensity plot in Fig. 3(also does not show any detectablek modulation on thelower binding energy side of the lower Hubbard band.

To perform more quantitative analysis, we have maa line-shape analysis betweenEB 20.1 and2.1 eV onthe assumption that each spectrumI can be decomposedinto two components and an appropriate backgroundI IA 1 IB 1 Ibg [see Fig. 4(a)]. Here,IA and IB areassumed to be Gaussian and represent the dispersiveture on the lower binding energy side of the,1.5 eV peakand that of the nondispersive feature at,1.5 eV, respec-tively, although actual line shapes may be more compcated [3,4,6,7]. Ibg is assumed to be~E2

B. The peakposition and the width of GaussianA were treated as fittingparameters, while those ofB were assumed to bek inde-pendent. (TheB peak position may be weakly dependenon k, but when it was allowed to vary withk, we could notobtain reasonable convergence in the least-squares fittThe origin ofB shall be discussed below.) In Fig. 4(b)we have plotted the peak position ofA as well as the inflec-tion points. The figure shows that the momentum depedence of the peak position ofA, which is consistent withthat of the inflection point, seems to have the periodiciof p , fully supporting our observation discussed abovIn Fig. 4(c), we show the result of the analysis of thek'bspectra, indicating no detectablek dependence.

Now, we consider two possible causes for the obsvation of the doubled periodicity along theb axis: short-range order and spin-charge separation in the 1D systPossible short-range order in NaV2O5 is due to SP fluctu-ations or due to AF fluctuations. Such fluctuations woucause a weak “shadow band” atk . py2 in the exci-tation spectra. The observed shadow band is, howevstrong. On the other hand, the one dimensionality mlead to a spin-charge separation which gives rise to the

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FIG. 4. (a) Line-shape analysis of an ARPES spectrum. Thmeasured spectrum is plotted with dots,I, IA, andIB with solidcurves, andIbg with a dot-dashed curve. (b) Peak positions forthe k k b spectra obtained from the line-shape analysis (closecircles and the inflection points) and the inflection points (opencircles). (c) Peak positions for thek'b spectra.

pearance of the spinon and holon bands in the excitatiospectra [20]. A similar interpretation to that performedfor SrCuO2 [8] would be possible for NaV2O5. Concern-ing the SP versus AF fluctuations, Augieret al. [6] haveshown by exact diagonalization of thet-J model that theARPES spectra of NaV2O5 calculated for the SP chain isquite similar to the results for the undimerized chain because of sizable AF correlations.

Now we compare our results with the prediction ofthe Hubbard model.J for NaV2O5 has been estimatedto be 560 K (,0.05 eV) from the Bonner-Fischer typemagnetic susceptibility [10]. On the other hand,U isknown to be 2 4 eV for vanadium oxides [17,21,22].With relationshipJ 4t2yU, t is estimated to be 0.15–0.25 eV, which should give the dispersional width2t 0.3 0.5 eV of the upper holon band (with the total holonband width being,4t) [4]. In fact, the experimentaldispersional width of the V3d band 0.06–0.12 eV issmaller but still in the same range as that2t value. Inthis sense, our result well reflects the nature of the 1DAF quantum system and indicates spin-charge separatiorealized in this system. On the other hand, the spinon banwhose spectral weight should remain large, is not identifiein the present spectra. In addition, the holon band shouconsist of two branch cuts while in our spectra the highebinding energy part seems to be buried under the intensfeature (B) aroundEB , 1.5 eV. A possible reason forthe discrepancy is that the finite temperature effect maresult in the weight redistribution and the broadening othe holon band. In fact, our measurements have bee

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done at T , 300 K, which is as large as,Jy2. Asto the weight redistribution, Tohyama and Maekawa [4have calculated the excitation spectra of thet-J modelat finite temperatures by exact diagonalization and fouthat at T , Jy2 the spectra become broader and loomore symmetric with respect tok py2 with the holonband being smeared out and at the same time the spinband being obscured in going fromk , py2 to k .

py2. Similarly, Penc and Serhan [23] have shown thin such a strongly correlated 1D system finite temperture causes a transfer of spectral weight from the spinband to the holon band over a wide energy range oft(¿T ) rather than ofT . On the other hand, in regardto the broadening of the holon band, Tsunetsugu [2have obtained the temperature dependence of the scorrelation length (js) for the 1D Hubbard model andestimatedjs to be a few lattice spacings atTyt , 0.2.This short correlation length causes broadening of the baby ,1yjs along thek direction, which may have obscuredthe k dispersion and lead to the reduction of the apparedispersional width2t. Besides these two possibilitiest might be effectively reduced from,0.2 eV estimatedabove by a polaronic effect caused by the strong electrophonon coupling neglected in the Hubbard model. Ift iseffectively as small as,0.05 eV, which means thatt , J,the excitation spectra should again look symmetric wirespect tok py2 [6], making the spinon band hardlyidentifiable.

So far we have focused on thek-dispersive feature (A)of the V 3d band, which appears relevant to the uppebinding energy part of the holon branch cuts. As for thintense feature (B) aroundEB , 1.5 eV, a very similarfeature has been observed in the spectra of 3D vanadiand titanium oxides with3d1 configuration and has beeninterpreted as the “incoherent part” of the spectral functioaccompanying the quasiparticle excitation at lower bindinenergies [16,17,25]. The position of structureB is almostindependent ofk and has almost the same width as thaof the 3D compounds [16,17,21]. The origin of thisincoherent part is not known at present but is presumabdue to effects which are not included in the Hubbarmodel such as electron-phonon interaction and long-ranCoulomb interaction [26]. This remains to be clarified ifuture studies.

In summary, we have performed an ARPES studythe 1D MH-type insulator NaV2O5. The lower Hubbardband in thek k b spectra has ak-modulated feature withthe periodicity ofk p , implying an effective doublingof the unit cell while the higher binding energy part of thV 3d band rather reflects the lattice periodicity. Whilethe feature with periodicityp might be qualitativelyexplainable as a shadow band due to short-rangeor SP order, we have analyzed the experimental resubased on theoretical works on the 1D Hubbard ant-J models. Possible causes of the discrepancies betwtheory and experiment, namely, the smearing out of tspinon band and the existence of the large incohere

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part, have also been discussed. Those possibilities maytested by performing ARPES measurements by changintemperature. Further ARPES studies on other dimerizeand undimerized 1D systems as well as 2D quantum-spsystems will shed more light on the properties of the lowdimensional quantum-spin systems.

We would like to thank T. Tohyama and S. Maekawafor providing the results of exact diagonalization stud-ies prior to publication and for fruitful discussion andH. Shiba, C. Kim, and H. Suzuura for informative dis-cussions. One of us (K. K.) acknowledges support by thJapan Society for the Promotion of Science for YoungScientists. This work is supported by a Grant-in-Aid forScientific Research from the Ministry of Education, Sci-ence and Culture.

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exist in theU ! ` limit, i.e., J ! 0 [3], the holon bandshould be distinguished from the shadow band of the AForigin while for an intermediateU value both the AFcorrelation and holon excitation contribute to the observedispersion of periodicityp.

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single-particle excitations in one-dimensional mott-hubbard insulator

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