We discuss the consequences of both electron-phonon and electron-electron
couplings in 1D and 2D multi-band (Peierls-Hubbard) models. After briefly
discussing various analytic limits, we focus on (Hartree-Fock and exact)
numerical studies in the intermediate regime for both couplings, where unusual
spin-Peierls as well as long-period, frustrated ground states are found. Doping
into such phases or near the phase boundaries can lead to further interesting
phenomena such as separation of spin and charge, a dopant-induced phase
transition of the global (parent) phase, or real-space (``bipolaronic'')
pairing. We discuss possible experimentally observable consequences of this
rich phase diagram for halogen-bridged, transition metal, linear chain
complexes (MX chains) in 1D and the oxide superconductors in 2D.Comment: 6 pages, four postscript figures (appended), in regular Te

Bishop, A. R.

Gammel, J. T.

Roeder, H.

Saxena, A.

Yonemitsu, K.

English

arXiv

We discuss the consequences of both electron-phonon and electron-electron couplings in 1D and 2D multi-band (Peierls-Hubbard) models are discussed. After a brief discussion of various analytic limits, we focused on (Hartree-Fock and exact) numerical studies in the intermediate regime for both couplings, where unusual spin-Peierls as well as long-period, frustrated ground states are found. Doping into such phases or near the phase boundaries can lead to further interesting phenomena such as separation of spin and charge, a dopant-induced phase transition of the global (parent) phase, or real-space (``bipolaronic``) pairing. Possible experimentally observable consequences of this rich phase diagram for halogen-bridged, transition metal, linear chain complexes (MX chains) in 1D and the oxide superconductors in 2D are discussed

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IA-UR- 92-3242TitleAuthor(s).LosAlamosNATIONAL LABORATORYELECTRON-PHONON DRIVEN SPIN FRUSTRATION INMULTI-BAND HUBBARD MODELS: MX CHAINS ANDOXIDE SUPERCONDUCTORSWUF+-92-3242DZ93 003697J. Tinka Gamrncl* llF.c Q : ;!.vpK. YoncmitsuSzlll~c:ic MedJ Jourd - Proceedings of International conferenceon Synthetic Metals (ICSM 92), GdtdxxE, sw~en, August 12-1g!1992*Code 573, Materials Research Branch, NCCOSC RDT&EDivision (NRaD), San Diego, CA 92152-SM.M●*phygika]ishcs InstitUt Bayrcuth, W-8580 Bawuth, Ge~anYELN!TRON-PHC)FJON DRJVEN SPIN FR~=ON IN MULTI-BANQHUBBARD MODELS: MX CH AIVS AND OXIDE SUPERCONDUCTOR~J. ‘Tinka GAMMEL,I”) K. YONEMITSU,(~) A. SAXENA,(~l A.R. Bishop,(b) and H. ~derf’~(o) Code 573, Materials Research Branch, NCCOSC RDT&E Division (NRaD), San Diego, CA 92152-5000, USA(b) Theoretical Division and Centers for Non.lineti Studies and Materials Science, Los AlamosNational Laboratory:’ Los Alarms, New Mexico 87545, USA(c) physi~sheg ~stittit, Univereit5t Ba~euth, W-8580 Bayreutlq GermanyABSTRACTWe discuss the consequences of both electron-phonon and electron-electron couplings in ID and2D multi-band (Peierla-Hubbard) models. After briefly discussing wuiouo analytic limits, we focuson (Hartr*Fock and exact) numerical studies in the intermediate regime for both couplings, whereunusual spin- Peierls a well aa Iongperiod, frustrated ground etatee are found. Doping into suchphaws or near the phase boundaries can lead to further intereating phenomena such aa separationof spin and charge, a dopant-induced phaae transition of the global (pwent) phase, or real-space(Ubipolaron.ic” ) ptiring. We discuss possible experimentally observable consequences of this rich phasediagram for halogen-bridged, transition metal, linear chain complexee [MX chains) in ID and the oxidesuperconductor in 2D.INTRODUCTIONThe MX chain CICWUof materials [1] and oxide high-temperature superconductors (HTS) are strik.ing simi.k from the parapective of strong competitions for broken-symmetry ground etates — bond-order-wavea (BOW), chuge (CDW) or spin- (SDW) density -wavea or mtiferromagnetlsm (AF), orboth bond- and spin- distortions (spin-Poierla, SP) – and the properties of doping- and photo-inducedlocal defect etat- (kinkn, polaronr, bipoh.rona, axcitorm, breathers, efc. ) within the same wide varietyof novel g-round statea. It is becaning LncreMingly apparant that to correctly model these materials,not only must one take into account both alectron-electron (e-e) and electron-phonon (*p) Interactions,but alno that multi-band smd/or multl-nrbital effects ue critically important.Experimentally, the remarkable tunability of the hfX cbs, along with the e~a of oynthe.sis ofsin~le crystals, is a major advantage allowing systematic investigation between small and large po-laron regima, th~ influence of dimensionalJty, and the competition with non-adiabatic and irnpu.rity/localization effects. Intrinsic defectn (seM-trapped local defect ataten or bags) in both HT3 and lviXchain materialn are tuought to be polaron.ic in nature, and can be created via doping or photoexcitation,Electron-hole asymmetry, 1 hlch haa been propooed az a driving mechanhm for suparconductlvity (SC),ha been experimentally observed in MX compound- [2], Racent evidence in PtBr ouggestc bipoiamndhociation and polaronJc trapping u temperature is varied [3]. Mormver, the model described IIOIOWmanifests long-period (LP) ( “superlat tice” ) phases [4], possibly observed in recent experiments on NIX .compounds, and may be related to twi.lning or real space pairing in th” cuprate HTS. Importantly,SC is be~eved to occur at the regions of “melting” between various broken symmetry ground statesand correlated metals. Thus we anticipate the possibility of SC, or one dimensional ( lD) precursors ofSC, in MX materials when we are near metal-insulator boundaries, where bipolarons are extended andoverlapping, competing with a correlated metal state. Here also the tunabdity of the MX class canbe utilized, leading to our current strategy of studying PtI and Pd=Nil-=Br to tune into weak CDWand SDW regimes. Recent unusual results on PtI in high magnetic fields [5] may indicate such a lDprecursor.Theoretically, MX materials ZI.Mclearly a lD template [6] for the same many-body methods andparameter determinations one must employ in 2D cuprate and 3D bismuthate HTS models when non-binding orbitals are neglected. Particularly all are hybridized, multi-band materials. The appearanceof superlattice CDW ordering in MX materials [4] may be similar to observations in many HTS ma-terials. In other words including a microscopic driving force for finite scale “twinning” textures andintegrating electronic degreea of freedom yield an effective enharmonic lattice dynamico. Indeed, i~ themodel described below the superlattices arise from ordering of ‘bipolaronic” def~ts with respect tothe period-4 CDW, correapmding to a “melting” of the broken symmetry state (cf. llal-. PbzBi03),Polaron pairing into bipolarone is a common ingredient of many current ee and ep theories of HTSmaterials. Further, both MX chine and (with M=CU, X=O) CuOa planea (and chains), can bedescribed by essentially the same multi-band, tight-binding extended Peierls-Hubbard Hswniltonian(PHH), demribecl briefly below, although a 3/4-filled, 2-band (2B) lD model for the MX compoundsor a CUO chain, and a 5/6-fl.lled, 3-band 2D model for the CUO planea. This same model can beconsidered a 3/4-filled analog of the the organic conductor polyacetylene, model charg~transfer saltssuch aa TTF-TCNQ, or be used to investigate neutral-ionic transitions [7]. Mathematically, one canconsider the two orbitala to be on the same site, and thus this Hamiltonian is also related to the KondoHamiltonian used to describe heavy fermion materials.MULTI-BAND MODELOur model ID, 2B, PHH f~cueing on the d,a and p, orbitals and inc.ludinq only the nearestneighbor interactions is [8,9]{H = ~ (+ + CIq(clacl+l,e+C)+,,ac,,e) + [c,- P,(fi + h,)]+b1,0 } (1;1)+ ~{ulwlnll + Vwnl. +1+ ;If(61 -ao)a ,1where (c, L3,U) f=(c, @,U)M,X and cM-{x=2e0. For a tncre detailed description of the parameters, themethods of molution, and general properties of thisHamiltonian, me Ref.o [8] and [9). The reoults herewere obtained by exact diagonalization (ED) of the many. body PHH on small oyetemo.‘runing eo, 10,UM, and UX is ementied.ly a lD analog of the theoretical discusdons in 2D wl)irhfocus on the Pd hybridization in KTS mater!ds, There, m here, these pararrwtere determine thi!atoichiometric ground state broken eymmetry order, and the nature of electron or hole doping into tho~rground states. Indeed, the similarity is even stronger because the mmdnal band flUiLIgis ementially thesame in both MX and HTS materials - 3/4- ftllIng of 2 bands and 5/&tWing of 3 bands, rcspectiv!’ly,Furthermore, both strongly AF and C12W stoichiometric compound~ exist for both HTS and MX, \VIIatrem the MX cl-s hu the advantage 01’eeeential.iy continuous tunability between these extremes,ExaIninhg trends in ralated materlah often yields insi~hts that a Sinmln matdd fnrit. Ril-ht.,..:I,~4 I I \ \ \ \n ‘+,oCDW\& _\ \> /=2\ %m \ \Q MAT? \ \ 1A1-0 I I I I liJIJ0 5 ‘JM/eo 10Fig. 1. The to=O phase diagram for ~x/~M=Ux/UM=l. The dashed line is the slice used for FiE. 4and + the point in Fig. 3. Note changin’g P translates into moving along a line through the origin:Table 1. The period-4 phasee, occupancies, distortions, energies, -d effective J Ecaling in the to-Olimit. Here u~,==UM,X/q, b~,==(~M,X)2/(KeO), and 6(n)= dx(coe ~-sin “~) -d~(cos ~+sin ~)defines X(M) sublattice distortion order parameters dx(dM) with the first h md (X-M) being short,(constant or (- 1)” terms just renonnalize tiI and co). For non-period-4 phaa~ * Ref. [4]. For to#O,the unpaired spins are antiferromagneticly correlated.phasa XMXM dM dx 2E~/(qN) J“u—CDW u=.=~-l- B~lK u=-l+um/2-bmBOW ●=U-I-U= DxO/K u=/2-b=+u~+lMIX T=l-UO”l- BM~(2ff) 0x{(2K) u=/2-b=/4+um/2-bm/4 JM,yCCt~MAP ll-T-l-l- U=-: 3hfMCXt$XAF T-Tl-l-ll- 0 0 Um+l .?Xxatf——miss. Finally, we note that competition between ~p and ee coupling is especially important for fordoping statea and can induce strong 10CO1LD even in a strongly magnetic background [9,10],ANALYTIC LIMITING CASESIn the LD CDW cam typhl of muiy MX chah, a first approximation 1s to approach the materialae decoupled X= M=X ttiara and M monomers. lnd~d, Pt Cl chain absorption are very close to themonomers smd tri.mera In aolutioa. Conversely, when e-e interactions Me dominant and the qdittlngbetween the baads 1s large (1B Undt), one expectsa SP phase in ID (11], with u effective AF couplingbetween M sites given by JMM = &M/UM, where thf~ is the h4-M hopping h the effective lB model.We discuss here the ~=0 lh.nit, whkh capturee the essential fcaturea of the matmlal in both theselimits. Another analythl.ly tractablo lhdt (U=O) wu d.hcuased in detail In Ref. [8].The dhtortion and energh of the period-4 (P4) phua for to=a=fl, U-ted in Table 1, arc: twoundistorted configurations with unpahd electrons on the M (MAF) or X (XAF) eltes, cne phamwith both LD and unpahd spins (MIX) and 2 diamagnetic phaees with the M (BOW) or X (CllW)eublattice distortod ~d a charge-denclty-wave on the opposite sublattlcei The phwe diagmn forp~amaters we expect to be relemt to MI or NIX materials, is shown In Fig. 1. The pham diagramis more complex for UX, PY 2 UM#Ml where the hybridization-drivencompetition IS meet efl@iv@’The BOW (XAF) phase ia only found for lPx/OMl (~,Y/~M) larger than the cam $hown (though *tto/eO w 2, or smaller with a>O, ● BOW phaae 10found nummicalJy near the MAF phaa~ boundary forthem p~amcters).SPIN-PEIERLS AND FRUSTRATED PHASESWhen tosO, all spin excitations are isoenergetic. For to#O, AF correlations develop and one cantreat the problem in terms of an effective spin model [12]. kVithout coupling between the two bands,the lower, X-like (for co>()) band is full and non-magnetic, while the upper (M-like) band is I/2-fullwith one electron per M site (when e-e repulsion is dominant). The on-site e-p coupling ~ leads ta asplitting of the upper band which competes with an AF ordering of the spins caused by the etiective AFcoupLing (JMM) (a in the effective IB case), When hybridization between the two bands is allowed,the lower band is not completely fuU, and now there is an effective AF coupling between neighboringhalide sites (JX.V, dominant when UX is dominant) = well = M and X sites (JMX), no: present in lBmodels. In fact, when the splitting due to the e-p coupling 0 is on the order of U and eo, the AF statewith neighboring M-X pairs singly occupied can become the ground state, = shown in Fig. 1, Note thisimplies, in contrast to the lB ewe, that the combination of e-e and e-p coupling in the 2B model drives,in addition to the non-magnetic CDW and BOW phases, three (competing) SP phases: one on theX-sublattice (XAF), one on the M-sublattice (MAF), and one involving MX pairs (MIX), Since J.wM,JXX, and JMX are all AF couplings (J > O), they obviously ;annot aU be simultanm.rsly satisfiedand the system is frustratw.1, u shown in Fig. 2. It is straightforward to derive from fourth-orderperturbation theory in the large U hit am effective t, JMX, JMM, Jxx model, though the expressionsfor the J’s are cumbersome and phase dependent [12], The resultant to dependencies of the J’s arelisted in Table 1, When to is small and one is in a regime where only one of the J’s is important, onecan numerically check this estimate by comparing the energies of the singlet and triplet ground states(at fixed LD), Fig. 3 shows thG to dependence is correctly predicted. Note the CDW ph~e h~ anentirely e-p driven AF component,In Fig. 4 we show the total energy md average lattice distortion for parameters similar to thoseused in the 2D model for CUO planea [10] (in hole notation, eo=to/2-UM/4, @=O, ( ~/to=3, “V/to= 1,cr2/Kto=2, and the M-M distance WMheld constant) with analogous resultg, For small UM, the groundstate is a CDW, as expected [8,9], As UM increases, the X no longer symmetrically distort ( BOW innotation of Ref. [10]), then a LP phaae develops, and finally the SDW ph~e expected at large [l~f SCI,Sin. In corttrat to the 2D c~e, the SP ph~e is not seen, though a metastable SP regime is found, ~ls isclearly seen from the figure, the “melting” of the CI)W phMe takes place through a LP il~termediary[13]. SC is believed to occur at the regions of ‘melting” between various broken eymmetry groundstates and correlated metals. While SC is not expected in the 1D materiala, unusual results on Pt 1 inhigh magnetic fields [5] may be ● lL) precursor.Upon doping, the phasa dl~arn becomet even richer. As hu also been men in the 2D version ofthe PIIH [10], doping into, e.g., the SDW ph~e can lead to polaronic defects with local CDW character,and uice-wrsu. An emraple of this for our ID model wan reported in R,efi [9] for f’J!parameters, Similarresults have recently been reported in ● 2D model for the HTS [10]. Further, near the phase boundary,wc have dao found re~ons where doping Into tho SDW ground state can cause a CDW defect in (1(,’I!)W tmckgmund (and vice-versa) - i,c, the doplmt h~ altered not only it’s local environment, huItho background ph~e as well. WhUe clearly finite-nize effects will be importamt for this enerfiy bdxrr(’~,one can ~Mily find par~meter regjone where the “finite size” ig M large M typical correlation tongths illthe rwd materiafs, Ar.fdithmalfy, In the “zero-hopping” limit where the many-body PHI{ in anaIytirrdlvtrmctable, one ran show that ouch phMe rewind upon doping ran occur even In the lnflnitrvsy~t mlimit. Indeed, the nmrrow (~DW phme men near l/Htll ~l~q]ingin the La bsaed HTS compoun(l~ II)~IyIw rclatwl to this phenomw-mn,‘rho rroseover from P4 CI.)W to 1’4 MAF may HJaobe acrmmpanicd by LP muperlattlce ph,n-w[1{]. Such euprwlattlce ph”as have rmwntlv hemr tnun~ in . I)rI ,ct .--J-I --r IJ*e -- II , 1 , , 1 , 10 1 2to/%Fig. 2 (left). Schematic er.ergy level diagram in the strongly correlated limitshowing frustration of theeffective amtiferromag-netic couplings caused by MX hybridization.Fig. 3 (right). The to dependence of the dHerence iu singlet a.ud triplet energies for the CDW, MIX,and MAl? phases at the + in Fig. 1, For small to, this corresponds to excitations of the effectivespin-Hamiltonian H = 4JSiSi+j with energy 4JMM in the MAF phiue ad 4JMX in the MIX ph=e,whereae in the CDW phase this reflects the Peierla gap,-0.6eda-0.8u 1- (a) ‘“%.1 1 1\,.0 “---3X;/,,; ,. \’“\“\‘\o2 ‘ # b 1 1‘(b) -. --!19ot -J-a ---- ---.*8.L.9●●.-. —0-. -.0Fig. 4. (a Total energy and (b) lattice distortion amplitude u a function of UM for CDW (-), BOW(. .), ~P ( . ..) SDW(-.), aud LP (- -) phaeea. Parameter consiatmt with CUO were used.including interuite e-p coupling, We mtlcipate the same behavior in our MX model when intersitee-p coupling ,0 included. Such superlatticee may be viewed u u ordered array of discommensurationdefects with reaped to a nearly stable commensurate order (e.g., P4). In view of the effective J’sdiscumed above, it may be natural to model ouch statea in term of AI’4NN1.i.ikemodels, where nearestand longer range couplings compete, leading to frustration and aaeociated complexity phenomena -mtdtitimeecale rehtation, hysteresis, metaatability, etc. In the context of the MX clam, it will heparticularly integrating to investigate m~teriala in, or nem, this crossover regime - e.~ PtI -- and toIfurther control the croeeover with pressure, magnetic field (5], doping, impurities, etf ndeed dopiflginto 1itic complax regime nhouJd be hlghiy mnsitive to the softness and competltiol ,~fthe phru,m:This may well be an axcdent regime to study pairing tendenciaa and metallizatiou. ‘$,,,,CONCLUS1ONSWe stress that the Ill, 213, PHH, wldle simple to write down, is rcpreeentative of a very Iargcvari~ty of 1ow-D electrordc materials. This mxhty ia mirrored in thg model’n richnees, especially i]lterms of doping near phwe boundarlen whore noval pairing mechedsmt exe found (incluoion of e-p ina 2D 3B model leads to coexletence of CDW and SDW phaeee - “CIMUKCIbuo” - M --” ~“*apm-’:-*.-are important only in the neighborhood of defects [10]), or a dopant-induced transition [l;] of theglobal phase may exist, besides the USU4 plethora of doping and photoinduced non-linear excitations.The MX class of compounds are uniquely important as a testing ground for many-body modeling andmaterials design strategy in strongly correlated, low-D materials (in particular the oxide HTS). Apartfrom pure and mixed-hdide NIX materials we are also beginning to explore mixed-metal (M=M~_=X)and bimettic (MMX) systenls, as well as effect,s of magnetic fields (especially on the weak CDW/SPLVground state materials). We feel that experimental investigations of the pressure dependence and high(magnetic) field behavior of pure and doped materials in the LD/AF crossover regime, such m PtI,NiBrl or their mixed-metal or -halide analogs, wili continue to yield interesting in ,ights into the natureof multiband effects and the competition between e-e and e-p interactions.~cknowledaementq. We acknowledge important discussions with X.2. Huang, L.A. }Vorl, R. Dono-hoe, and B.I. Swanson, J. Shi, among others, and thank E.Y. Lob, Jr, for help in writing the ED code.ARB, KY, and AS were supported by the US DOE, HR by the Deutsche Forschungsgemeinschaftthrough SFB 213, anti JTC by a NRC-NRaD Research Associateship through a grant from ONR,Supercomputer access was through the ACL at LANL. HR and JTG are grateful to the hospitality ofLANL, where this work was begun.REFERENCES1 The structure and chemistry of MX chains, [MLa][ML2Xz].Y4 (M: Pt,Pd,Ni; X: C1,Br,I; L,Y:various Ugands, counterions), has been reviewed by H.J, Keller, in J .S. Miller (cd.), Eztemhf LinearChain Compounds, Vol. 1, Plenum, New York, 1982, p. 357. For a sampling of the physics literaturesee, e.g, Proc. of the I.nt. Conf. on the Sci. and Tech. of Synth. Metals, ICSM ’90, Tubingen,Germany, Sept. 2-7, 1990 [S@h hfetafs 41-43, ( 1991)], or Ref.s [8] and [9] and references therein.2 J.T, Ga .~mel e; aL, Phys. Rev, B, 42 (1990) 10566,3 R.J. Donohoe et al,, J. Phyu. C, ( 1992), in press.4 1. Batistid, J.T. Gammel and AR. Bishop, Phys. Rev. B, 44 (1991) 13228.5 M. Haruki and P, Wachter, Phya. Rev, B, 43 (1991) 6273.6 D. Baeri.swyl and A.R, Bishop, Physics Scnpta, T19 ( 1987) 239; S,D, Conradeon et al., SofidState Commun., 65 ( 1988) 723; J.T. Gammel et al., Physics B, 163 ( 1990) 458.7 A. Painelli and A, Girlando, S@h. Metdu 29 ( 1989) F181,8 J,T. Gammel et al., Phy8, Rev, B, 44 ( 1992) 6408.9 SM. Weber-Miibrodt et aL, Phys. Rev, B, 45 ( 1992) 6435.10 K. Yonemitsu et al,, to be published in the Proc. of the Int. Conf. on Lattice Effects in High T,,Superconductors, S~te Fe, New Mexico, Jan. 13-15, 1992 (World Scientific).11 J,E. Hirech, Phys. Rev. Lett,, 51 ( 1983) 296.12 J, Shi, R. Bruinnma, and A.R. Bishop, preprint 1992.13 There are many m.cst~table LP phases, and the LP energies Bhould he treated u upper bounds,From Fig, 4 there is cledy a region where the LP phase is favored over any period-4 phue, “~hisintermediate LP re~ion is seen in ED, MFA, and the 2D model. [t is not an artifact,14 Intermediate ph~eo can be driven by the competition between to, [j, a, long-range (’oulombfields, and/or the effective short range J’s, Such intermediate phaues can be P4, M expected fromccirnmensurability effects, or LP, Note that the large-~) Lp phase discusoed in Ref. [4], tholl~hrelated, is somewhat different than the frustration driven, magnetic LP ph~e discussed here or,in ‘./D, in Ref. [10] (for large a), Similar to the ANNNI model, no e,,plicit long range tmns arl’needed w frustration drives M’ective long range interactions,15 J. Reichl, unpublished and S. Marianer, unpubiJnhed.

Electron-Phonon Driven Spin Frustration in Multi-Band Hubbard Models: MX Chains and Oxide Superconductors

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