MX chains: 1-D analog of CuD planes?

Physica B 163 (1990) 45X-462

North-Holland

MX CHAINS: 1-D ANALOG OF CUD PLANES?

J. TINKA GAMMEL. I. BATISTIC. A.R. BISHOP, E.Y. LOH. Jr. and S. MARIANER

Theoretical Division and Center for Non-Lineur Studies, Los iZiamos National Lahorutor):.

Los Alumos. New Mexico. USA

We study a two-band Peierla-Hubbard model for halogen-bridged mixed-valence transition metal linear chain complexes

(MX chains). We include electron-electron correlations (both Hubbard and PPP-like expressions) using several techniques

including calculations in the zero-hopping limit. exact diagonalization of small systems, mean field approximation, and a

CJutzwiller-like ansatz for quantum phonons. The adiabatic optical absorption and phonon spectra for both photo-excited

and doping induced defects (kinks. polarons. bipolarons and excitons) are discussed. A long period phase which occurs

cvcn at commensurate filling for certain paramctcr values may be related to twinning. The effect of including the

electron-phonon in addition to the electron-electron interaction on the polaron/bipolaron (pairing) competition is

especially interesting when this class of compounds is viewed as a 1-D analog of high-temperature superconductors.

1. Introduction

Halogen-bridged transition-metal linear chain com-

plexes (MX chains) have been of interest to chemists

for many decades as dyes and strongly dichroic materials [I]. However, they have only recently begun to receive detailed consideration in the physics communi- ty [2-51. A typical crystal of this material consists of an array of linear chains of alternating metal (M) and halogen (X) atoms; with ligands attached to the metals, and possibly counterions between the chains to give charge neutrality. A typical chain is shown schematically in fig. 1. The potential importance of MX chains arises because of:

(i) the increasing appreciation of strong, competing electron-electron and electron-phonon interactions in

low-dimensional materials and the consequent need to expand many-body techniques. The MX materials offer a rapidly expanding, near single-crystal. class of quasi-I-D systems which can be “tuned” (by chemistry, pressure, doping, etc.) between various ground state extremes: from strong charge-disproportionation and large lattice distortion (-15% distortion in PtCl chains) to weak charge-density-wave and small lattice distortion (-5% distortion in PtI chains), to magnetic and undistorted (a recently synthesized NiBr chain

Fl); (ii) the opportunity to probe doping- and photo-

induced local defect states (polarons, bipolarons. kinks, excitons) and their interactions in controlled environments and the same large range of ground states: and

t __-___ eo+2f3A J&

lb) - e,-2 PA

-

+.O -e. Fig. 1. (a) Schematic of the MX chain showing the model parameters and a CDW distortion; (b) the corresponding to = a = 0 energy levels.

0921-4526/90/$03.50 Q Elsevier Science Publishers B.V

(North-Holland)

J. T. Gammel et al. I MX chains: 1-D analog of CuO planes? 459

(iii) the similarities between models and theoretical

issues in these materials and the recently discovered high-temperature oxide superconductors [8], as well as the BaPbBiO compounds. The MX materials are also closely connected conceptually with mixed-stack charge-transfer salts and organic conductors.

Focusing on the similarity of the MX chains to the oxide superconductors, we note that they both can be described by a 3 -filled, two-band tight-binding Peierls- Hubbard model; though 1-D for the MX compounds and 2-D for the oxide superconductors. Intrinsic defects in both these materials are thought to be “polaronic” obtained via doping or photoexcitation. The electron-hole asymmetry has been experimentally observed in MX compounds [S] and is perhaps important to superconductivity. The model described below manifests long period (“superlattice”) phases, possibly observed in recent experimental measure- ments on the MX compounds [5], which may be related to twinning or real space pairing in the oxide superconductors.

The MX class, then, is important in its own right, but also as a 1-D testing ground for concepts and many-body, electronic structure techniques in strongly interacting (both electron-electron and electron- phonon) electronic materials.

2. The model

Focusing on the metal d,~ and halogen p, orbitals and including only near neighbor interactions, we use the following two-band model for the isolated MX chain [3]:

+ [t-l)‘% - MA, + A,- 1 >lc:,c,.,>

+CU,n,rn,l +KLlnl+,+vMM c n/n/-, I , I even

+ ; K 7 A; + ; K,, 7 (A,, + A,,+,)’

which includes as parameters the difference between metal and halogen electron affinities (2e,, = Ed - l x),

hopping (t,), (&,, &) inter-site (a) coupling, on-site U,) and

(V, V,,) repulsion, and

effective metal-halogen and metal-metal springs to the elements the structure

explicitly included. atoms sit even sites, atoms on sites. A, u, i - u, p, are lattice distortion momentum. For discussion here

set V,, 0. We also constrained sum of

displacements to zero (renormalizing We have not to a halogen-halogen

though there no conceptual in including The model are shown in fig.

At stochiometry are 3 per MX or j-filling. expect this to be to many To insure independent results have used number of techniques our investigation including Hartree-

approximation, perturbation (both weak strong coupling), diagonalization of

systems, quantum Carlo methods, molecular dynamics to investigate excitation, and approaches to quantum phonons. focus here the mean-field

adiabatic results, note that phonon corrections not important the heavy

considered here. have checked mean field against the results obtained a Lanczos procedure on sites [3] find essentially difference for to intermediate

3. Ground states

The values of K,, and /3x do not affect the CDW ground state, and we have set K,, = 0, &, = & = p, and U, = llx = U in the ensuing discussion of the ground states, to reduce the number of parameters and to explore the possibility of a BOW phase.

3.1. Long period

While Peierls’ theorem guarantees that a commensurate distortion is lower in energy than no distortion in one-dimensional e-p coupled systems, it does not rule out the possibility that another distortion will be even lower in energy. The /3 term drives a long period phase at exactly commensurate filling [4]. Con- sider the trivial zero-hopping limit (t,, = a = 0) where the electronic Hamiltonian is site-diagonal and the eigenstates are fully described by their site occupancy. The period 4 phase is then:

XMXMXMXM _=._ .20222022.

460 J. T. Gammel et al. I MX chains: 1-D analog of CuO planes?

Fig. 2. A long period distortion of roughly period 10. Shown arc the lattice distortion (solid) and charge density (dotted).

Parameter values are t,, = 1, (Y = 0. e,, = 0.5, p,,, = 0.7, and 3 = 0.5.

First consider U = V= 0. It is easily seen that the lowest energy state for small e,, phase separates into two regions, one of which has all the sites fully occupied and one of which has all the sites empty:

222.. ,222O.. .O.

The hopping drives the competing period 4 phase. A roughly period 10 distortion, lower in energy than the period 4 phase, is shown in fig. 2. Long range Coulomb effects clearly also disfavor such long period phases. In ref. [4] we investigate this phase using an unscreened Coulomb interaction plus an on-site ex- change, treating the hopping t,, in perturbation theory. Defining at $-filling the period 4n states Cm and Cc::

C : 222.. ,222 0.. .(I <I 3a sites LY sites ’

CL: 22...22 ll...ll

2o sites 2a sites ’

we find that for small I,, and fixed strength of the electron-electron correlations there is a sequence of

transitions through the states C,, C,, C,, , Ch,

Cb,,> 1 CL as p is increased. STM experiments to look for long period phases in MX and MMX materials are currently in progress [7]. We speculate that this tendency toward charge-clumping may be related to twinning (superlattice discommensurations), or real- space (bipolaronic) pairing in the 2-D extension of our model. For the rest of the discussion we restrict the ground state to be in the period 4 phase.

3.2. Period 4

In the ground state in the absence of e-e corela- tions, this problem can be analyzed analytically. The resulting phase diagram is rather featureless: for posi- tive p the lowest energy period 4 phase is nearly always a charge-density-wave on the M sites (CDW) 131. (We label the states by the M behavior in analogy with the one-band model notation [2].) This is in agreement with the fact that all known MX materials with structural distortion are in the CDW phase, and demonstrates one important difference between the two-band model and one-band models [2], where the

J. T. Gammel et al. I MX chains: 1 -D analog of CuO planes? 461

BOW phase is found for a substantial range of parameter values. It also implies there can never be an exact mapping to a one band model.

We have mapped out the phase diagram as a func- tion of U and V numerically. We find [3] (for K,, =

0) for small U that the system has a CDW with decreasing magnitude as U is increased, but for intermediate U the system switches over to a BOW, again with decreasing magnitude, and finally a SDW phase develops. The Hubbard V term lowers the transition from CDW to SDW [3].

4. Excitations and associated optical absorptions 0

We have studied polarons, bipolarons, kinks and polarexcitons in the CDW phase numerically [3]. We focus here on the results for static polarons. We stress that this model has no electron-hole symmetry even in the absence of correlations, and this is reflected in the fact that the electron and hole defects have slightly different absorptions. This asymmetry is not present in the one-band model [2], again emphasizing the neces- sity of using the full two-band model. We have investigated the parameter dependence of the optical absorption spectra for polarons at U = 0. Three distinct intragap absorptions are observed, which are histori- cally labeled as the C, A and B bands (in order of increasing energy). For small A the C peak is at lower energy and has larger amplitude than at large A. The B peak is lost at small A. The electron polaron is insensitive to e,, and PM, whereas the hole polaron absorptions are quite sensitive.

Fig. 3. The optical absorption spectra, with the IVCT scaled to 1, for the hole (solid) and electron (dotted) polaron (P) and bipolaron (BP) with PtCl parameters. Note the electron- hole asymmetry.

We have investigated the dependence of the optical absorption spectra on K,, and U,. We have scaled the parameters when including U,,, to keep the uniform structure bands and distortion constant; in keeping with the interpretation of the U,,, = 0 parameters as the effective mean-field values. Decreas-

ing KM, from infinity tends to move the B absorption

0.38 A, E,,,, = 2.5-3.0 eV, E,,I~ - E,, = 4.7 eV, yielding for the dimensionless parameters PtCl t, = 0.5, (~=0.5, e,=0.3, &=0.03, K=0.54 and A=

0.58. As we expect the ligands to strongly constrain the metal-metal distance, we used K,, = x. The defect peak locations were then calculated and com- pared with experiment; yielding good agreement. Ex- perimentally observed Raman resonances are observed at 1.3-1.4 and 1.9-2.1 eV enhancing a 263 cm-’ mode, 1.4-1.7 and 2.2-2.5 eV enhancing a 287 cm-’ mode, and 1.7-1.9 eV enhancing a 272 cm-’ mode, with a peak at 0.4eV observed in infrared

BP-- Qc^ c

to the gap edge and the A and C absorptions to the gap center, and a BOW roughly following the deriva- tive of the CDW amplitude develops. U, has little effect, and U, effectively increases the polaron A gap state absorption energy. The Hubbard V first delocal- izes the defect in the CDW phase, then drives the SDW phase where the defect is again localized.

BP++ 0

The spectrum in fig. 3 agrees fairly well with the experimentally measured spectrum for [Pt(en),] [Pt(en),Cl,] (CIO,), (en = NH,CH,CH,NH,) [5]. The parameters were derived by fitting the known uniform structural and band structure data: A =

Fig. 4. The lattice positions of the metal (circle) and halogen

(diamond), excess charge density (solid), and excess spin

density (dotted) for the defects of fig. 3, stressing the elec-

tron-hole asymmetry.

462 .I. T. Gammel ri al. i MX chains: 1 -D arzalog of CuO plams?

absorption [S]. The IVCT edge is at 2.5 eV. We iden- tify these peaks as the A and B peaks of the electron polaron; the A and B peaks of the hole polaron; a bipolaron absorption: and a polaron C absorption. respectively. We stress that this identification means that the separate absorptions for the electron and hole polaron are seen in the resonance Raman studies [5]. The excess charge density for these defects is shown in fig. 4. Note that the hole defect is more delocalized.

Acknowledgements

We would like to thank D. Baeriswyl. D.K. Campbell. R. Donohoe, R. Martin. S.R. Phillpot, J. Reichl, B. Swanson and S.M. Weber-Milbrodt for useful discussions. This work was supported by the US DOE.

References

M.B. Robin and P. Day, in: Advances in Inorganic

Chemistry and Radiochemistry, Vol. 10. H.J. Emeleus. ed. (Academic Press. New York, 1967) p. 247.

P. Day, in: Low Dimensional Cooperative Phenomena,

H.J. Keller, cd. (Plenum Press, New York, 1974) p. 191.

H.J. Keller in: Extended Linear Chain Compounds, Vol.

I. J.S. Miller. ed. (Plenum Press, New York. 19X2) p.

351.

K. Nasu. J. Phys. Sot. Jpn. SO (1981) 235, 52 (1983)

3865. 53 (19X4) 302. 53 (1984) 427. 54 (1985) 1933: J.

Lumin. 38 (19X7) 90.

K. Nasu and Y. Toyozawa, J. Phys. Sot. Jpn. 51 (19X2) 2098. 51 (19X2) 3111.

I31

141 [Sl

IhI

[71 181

A. Mishima and K. Nasu. Synthetic Metals 29 (1989)

F175. and unpublished.

Y. Ichinose, Solid State Commun. SO (19X4) 137.

Y. Onodera, J. Phys. Sec. Jpn. 56 (19X7) 2%). S. Kurita. M. Haruki and K. Miyagawa. J. Phy5. Sot.

Jpn. 57 (1988) 17X9.

S. Kurita and M. Haruki, Synthetic Metals 29 (19X0) F129.

L. Degiorgi. P. Wachter. M. Haruki and S. Kurita.

Synthetic Metals 29 (1989) F137.

A. Painelli and A. Girlando. Synthetic Metals 20 (1989)

FlSl.

I). Bacriswyl and A.R. Bishop, Physica Scripta 1‘19

(19X7) 239. J. Phys. (‘ 21 (1988) 339.

S.I>. Conradson et al., Solid State Commun. 6.5 (IYXX)

733.

A. Bishop, J.T. Gammel and S. Phillpot. Synthetic Met-

als 29 (19X9) FlSl.

J.T. Gammcl. S.M. Weber-Milbrodt. E.Y. Loh, Jr. and

A.R. Bishop. Synthetic Metals 29 (1989) F161.

J. Tinka Gammel, A.R. Bishop and S.R. Phillpot, un-

published.

J. Tinka Gammel. A.R. Bishop, I. Batistic. E.Y. Loh.

Jr.. S. Marianer, S.M. Weher-Milbrodt and J. Reichl,

unpublished.

A.R. Bishop, J. Tinka Gammel. E.Y. Loh. Jr.. S.R.

Phillpot and S.M. Weber-Milbrodt, Proc. NATO Ad-

vanccd Research Workshop on Interacting Electrons in

Reduced Dimensions, Torino. Italy, 3-7 Oct. 19XX

(Plenum. New York), to be published.

1. Batistic et al., to be published.

R.J. Donohoc. S.A. Ekberg, C.D. Tait and B.I. Swan-

son. Solid State Commun. 71 (1989) 4Y.

R.J. Donohoc. C.D. Tait and B.I. Swanson. Chem.

Mat.. submitted. K. Toriumi et al.. J. Amer. Chem. Sot. I II (lY89) 2341.

J. Weinrach, M. Holly and B.I. Swanson, unpublished.

.l.k. Hirsch and F. Marsigilio. Phys. Rev. B 39 (19X9)

11515.

Documents

MX chains: 1-D analog of CuD planes?