Journal ArticleThe temperature-dependent dielectric response and conductivity at =1010 Hz is reported for the title compound, (NMP)x(Phen)i-x(TCNQ), in the regime 0.50<-x<-0.59, spanning commensurate, bipolaron, and incommensurate regimes. The large and strongly temperature-dependent dielectric constant and o-(1010 HZ) are accounted for by a model based on the dynamics of pinned charge-density waves and the presence of relatively mobile charged bipolarons (confined soliton pairs) in the commensurate phase

Javadi, H. H. S.

Miller, Joel Steven

English

The University of Utah: J. Willard Marriott Digital Library

VOLUME 59, NUMBER 15 PHYSICAL REVIEW LETTERS 12 OCTOBER 1987 r --------------------------------------------_______ I'( Microwave Response of Confined Soliton Pairs (Bipolarons) in ,-I (N -MethylphenaziniunV x (Phenazine) I - x (Tetracyanoquinodimethanide) I~ \~ ,. H. H. S. Javadi Department of Physics. The Ohio State University. Columbus. Ohio 43210 Joel S. Miller Central Research and Development Department. E. I. DuPont de Nemours and Company. Inc .• Wilmington. Delaware 19898 -2~d.J :, r l(j(/n ltt-' ·~r:·" and A. J. Epstein Department of Physics and Department of Chemistry. The Ohio State University. Columbus. Ohio 43210 <Received 21 January 1987) The temperature-dependent dielectric response and conductivity at = 10 10 Hz is reported for the title compound, (NMP)x(Phen)l-x(TCNQ), in the regime 0.50 s x s 0.59, spanning commensurate, bipo-laron, and incommensurate regimes. The large and strongly temperature-dependent dielectric constant and <y(J 0 10 Hz) are accounted for by a model based on the dynamics of pinned charge-density waves and the presence of relatively mobile charged bipolarons (confined soliton pairs) in the commensurate phase. PACS numbers: 72.80.Le, 71.4S.Lr, 77.40.+i ,',:' Anomalously large and often strongly temperature-dependent microwave dielectric constants have been re-ported for many ID TCNQ salts of conduction-electron charge density of one electron per two TCNQ. For ex-ample, Buravov et al. and Shchegolev report 1,2 that the dielectric permeability, c, measured at 1.0 XI 0 \0 Hz of acridinium(TCNQ)2 was =700 at 4 K, increasing to = 3000 at 60 K. At higher frequencies, e.g., 3.84 x 10\0 Hz, c was reduced somewhat (for example, = 700 and 1500 at 4 and 60 K, respectively, for this compound). A localized-electron model based upon the electric-field-induced admixture of an excited state was proposed 2 to explain the data. The conductivity, a, at microwave fre-quencies was shown to be nearly identical to adc for tem-peratures T?:' 100 K and larger than adc for lower T. The crossover temperature was dependent upon the com-pound studied. A similar model was applied to dielectric data for Qn (TCNQh (Qn for quinolinium).3 It was in-dependently proposed 4 that randomness in the orienta-tion of the asymmetric donors would lead to localization in these ID systems. A T=O dielectric constant was cal-culated by Bush 5 in the limit of strong localization (to less than three sites). However, this model cannot ac-count for the temperature dependence of c. 6,7 It was al-ternatively noted 8 that a model of linear metallic strands interrupted by insulating lattice defects could account for a dielectric constant of several thousand in the mi-crowave regime. A generalization of this model to in-clude a random barrier height between conducting seg-ments was successful at fitting the real and imaginary parts of the conductivity of Qn(TCNQh over a wide range of frequencies and temperatures. 9 A common per-spective in all of these studies is that disorder localiza-tion and barriers dominate the physics of these materials. An alternative approach to these systems is based on the suggestion \0 that these systems are (Peierls) semi· conductors. It was later shown that Qn(TCNQh and the related (NMP>X (Phen) I -x(TCNQ) (0.50:s x :5 0.64) undergo a structural instability with one-dimen· sional 4kF precursor effects. II ,\2 For the latter com-pound, the number of conduction electrons per TCNQ is determined by the fraction of sites in the donor chain occupied by the NMP+ molecule. 12,13 The temper-ature-dependent Peierls gaps of Qn(TCNQ)2 13 and (NMP)x(Phen)l-x(TCNQ) 14 were later directly ob-served via optical techniques. NMR studies 15 of (NMP)x (Phen) I - x (TCNQ) demonstrated that CYdc(T) was not solely determined by temperature-dependent electron mobility in contrast to the earlier conclusion of the Qn(TCNQh NMR experiments. 16,\7 It was predict-ed 18,19 and shown 13,14,20 that addition of a small num-ber of conduction electrons to the commensurate (NMP)o.5(Phen)o.5 TCNQ (for 0.50 < x:5 0.56) resulted in the formation of pairs of solitons of charge - el2 (confined by the cation potential to form bipolarons 2o of charge - e for each electron added. For x?:' 0.58, an in-commensurate Peierls semiconducting ground state is formed. 12,13 In this Letter we report the temperature and micro-wave frequency behavior of dielectric constant and con-ductivity of (NMP)x(Phen)l-x(TCNQ) for 0.50:5x :5 0.59. This range of samples allows the study of the real and imaginary dielectric responses as a quasi one-dimensional system is varied from commensurate (x =0.50), to commensurate with bipolarons added through chemical doping (0.50 < x:5 0.56), to incom-mensurate (x?:' 0.58). At low temperature, T < 40 K, the real part of the dielectric constant, c, is = 200- 300 1760 © 1987 The American Physical Society VOLUME 59, NUMBER 15 PHYSICAL REVIEW LETTERS 12 OCTOBER 1987 near commensurability, increasing to =600 for x =0.53, then decreasing to = 300 for x > 0.56. For all samples, t increases with increasing T, tending to level off or de-crease at high T. The CTJ1w (T) is similar in magnitude and temperature dependence to the dc conductivity for samples with x =0.50 and x> 0.58 for T> 100 K, and (J~w > CTdc below = 100 K. An excess contribution to CTJ1w is observed to room temperature for samples of x=0.53 (the composition with the larger dc conductivity). We suggest that these data reflect the peculiarities of the evolution of a charge-density wave (COW) system from that of a pinned commensurate COW with thermally generated bipolarons (x=0.50), to that of a pinned commensurate COW system with chemically doped and thermally generated bipolarons (0.50 < x:5 0.56), to that of a pinned incommensurate COW system. The ,: large and strongly T-dependent dielectric constant for I compositions that are commensurate with thermally gen-erated (and chemically doped) dipolarons is proposed to originate from the polarization of these charged bipola-rons within the confines of the coherence length of the CDW, similar to the origin of the high dielectric con-stant within the interrupted-strand model. The generali-zation of these concepts to the dielectric properties of other charge-transfer salts is indicated. Samples were prepared by the previously described 'method. 21 The relative NMP composition is accurate to ± 0.015, so that the composition with minimum NMP ... prepared, i.e., x =0.49, is most likely x =0.50. The real and imaginary components of the dielectric constant were measured with the cavity perturbation technique of : Buravov and Shchegolev. 22 The data were acquired with II 10 o (NMP)o49 (Phen)o.OI TeNO o (NMP)005 (Phen)o •• TCNQ 000000000% B '" b 6 x \J.J 4 2 + (NMP)059 (Phen)o., TCNO 000 00 c5J (]!) o o 0 0 o o o 0 K 300 FIG. I. c(T) at 6.5 x 109 Hz for representative (NMP)x-r (Ph,,), -, (TeN Q) ",mpou,d<, l a Hewlett-Packard model 8350B sweep generator and 6.5-GHz (TMolO) and 1O.5-GHz (TEoll ) cavities, with a Janis Supervaritemp Oewar for T control. Measurement of change of cavity frequency and Q, together with an estimated depolarization factor, allows the calculation of E and CT. 22 Potential error bars are indicated in the figures. . The real part of E vs T for representative samples is shown in Fig. 1, with the variation of E at low tempera-ture with composition, x, given in Fig. 2. It is observed that at low T, E = 200 for x =0.50, increasing with x to nearly 600 for x=0.53 then decreasing to =300 for x> 0.56. The ratio Emax [the maximum value of E(T) measured] to EL (the value of E at low T) has its largest value at x =0.50, decreasing with increasing x. The microwave conductivity, at 6.5 GHz, normalized to the dc value at room temperature is shown in Fig. 3 (a) together with the dc conductivity 13,19 (uncertainties in the depolarization factor prevent determination of a more accurate absolute value for CTJ1w ) , for a sample representative of the intermediate regimes. A plot of 10gCT vs T -I of a typical commensurate COW (x =0.50) as well as an incommensurate COW (x> 0.59) is in Fig. 3(b). In all cases the CTJ1W is larger than CTdc for T < 100 K, the largest CTJ1w/CTdc for samples in the intermediate (x=0.53-0.56) regime. As T increases toward room temperature, the CTJ1w (T) is the same as CTdc(T) within experimental error, except for samples in the intermedi-ate regime, where CTJ1w indicates the presence of an addi-tional conduction mechanism. The dielectric response on (NMP) x (Phen) 1 - x-(TCNQ) and the related Qn(TCNQ)2 (earlier shown 11,20,23 to be similar to the subject compounds with x =0.54) can be understood in the context of a Peierls ground state and bipolarons/solitons. It is assumed that the dielectric constant can be decomposed into a sum of 16 o 40 K T + 70 K + '" b /'J:-~" J I "-/ +" / ~ " / iF": \ / \ 12 x \J.J R / . \ / \ / \ r A- \, .± // bel --- ...... ~ .1 / / ~'-/ / '-4' / "'" n l J ~/ ," I I--~ -O~ O~ O~ O~ O~ Offi X I·.;: FIG. 2. (3 VS x for T=40 K and T=70 K (the dashed curves are guides to the eye). 1761 ILUME 59, NUMBER 15 PHYSICAL REVIEW LETTERS 12 OCTOBER 1987 t ---~ o 1.2r---,----,-------,---,---1.0 08 o 65 GHz + DC . r·· .. ' o o b ~06 N o b 04 02 10' o o O~ o o o t \ 0 t 0 1e 0 + 00 ++ 0 + 0 + 0 + 0 065 GHz + DC (a) I,.·.· t 0 '_\ ,J + + " .,' + + + + + o + + :' + o Q .. o + (b) o 104~---~~---~~---~ o 001 002 0.03 liT (K-1) ,1 FIG. 3. dc and 6.5-GHz conductivity for representative (NMP)x(Phen)l-x(TCNQ) samples. The microwave data are normalized to their dc counterparts. (a) a vs T, x =0.56; (b) loga vs T -I, x =0.49. contributions: f = 1 + Csc + fb (nb, T,w) + fCDW, (I) where fsc is the contribution due to activation across the energy gap (hwg ) of the 1D semiconductor, fsc = t (wt/wi), 24,25 fCDW that due to the pinned charge-density wave,24 fCDw=nt/(wl-w 2) (nt is the pin-ned-mode oscillator strength and Wt the pinning frequen-1762 cy), and Cb (nb, T, w) is that due to nb bipolarons (see below). For x < 0.60, the plasma frequency h wp =0.7 eV,26 and hwg =O.1 eV,14 yielding csc=33, too small to account for the measured dielectric constants. The dielectric constants of pinned incommensurate CDW systems such as (TTF) (TCNQ) 25 and related compounds 27 are 4000 ± 2000 for T < 20 K, often in-creasing at higher temperatures as the pinning frequency decreases.27 The f(T) we report for the incommensurate (NMP)0.59(Phen)0.41 (TCNQ) is consistent with this be-havior. The much larger pinning frequencies expected for the commensurability-2 (NMP)0.5(Phen)0.5(TCNQ) implies that the CCDW for this system should be much less than that for the incommensurate x =0.59 system. However, for 0.50 < x < 0.56, a substantial contribution due to chemical-doped and thermally generated confined soli-ton-antisoliton pairs (bipolarons) is possible: fb(nb, T,w) =nbfg+ cb(nb, T,w). (2) Here d represents the electronic polarizability of bipola-rons and fb the dielectric response of bipolarons diffusing a length L ( < coherence length of pinned commensurate CDW) in the presence of the applied oscillating electric field. An upper bound on cg can be estimated if we as-sume a (field-induced) dipole moment of (e)h, where h is the length of each bipolaron (= 11 TCNQ-TCNQ spacings or 20 =42 A) and an excitation energy of h wg /2. This yields nb d = ISO for a concentration of one bipolaron per 100 TCNQ molecules. This cg is too small to account for the magnitude, frequency, and T dependence of the experimental f at all but the lowest temperatures. Disorder prevents 3D ordering of the CDW's and leads to a finite coherence length L of the CDW'S.12 Bi-polarons, especially thermally generated bipolarons, 20,28 are expected to be only weakly pinned within the coher-ence length L of a CDW, because of the large dielectric constants and the bipolaron's large spatial extent along the chain. 20,29 For x> 0.51, the effective pinning will be dramatically reduced as the average separation of the pinning sites (excess NMP + beyond the ordered x =0.50 composition) on the four donor chains surrounding each TCNQ chain is less than the bipolaron length. The rap-id increase in f for T= 180 K for the x =0.49 samples suggests that this is the pinning energy for the commen-surate system in excellent agreement with theoretical es-timates. 29 The rapid rise in c(T) at 70 K for x =0.56 may reflect the reduction in pinning energy with x indi-cated above. If we assume a classical model for a rotat-ing dipole to represent the motion of unpinned bipolaror. within L, the dielectric response for nb bipolarons per unit length confined to the length L is 'I VOLUME 59, NUMBER 15 PHYSICAL REVIEW LETTERS .. ;:' 12 OCTOBER 1987 where A is the cross sectional area per TCNQ chain, and r represents the time to polarize the bipolarons within L. If w r« 1, L = 100 A,30 and T = 100 K, if we assume two bipolarons per L (as a result of thermal generation 20 or doping) then fb = 50000, larger than that measured at 10\0 Hz for these materials but approximately equal to that reported 9 for Qn(TCNQ)2 at 100 K for w/27r < 1.25 xl 0 8 Hz. As w is increased to w/27r =9 xl 0 9 Hz, f decreases, suggesting that the (1 +w 2r2) -I term is important at higher frequencies. These earlier lower-frequency feW, T) results 9 for Qn(TCNQ)2 are likely representative for (NMP)x (Phen)l- x (TCNQ) in the bi-polaron regime (0.50::; x <0.56) as well. Hence, the model of moving bipolarons can readily account for the T-dependent high dielectric constants. The u(J 0 \0 Hz) exceeds Udc for T < 100 K in all composItIons. This result for the incommensurate (NMP)0.59(Phen)oAI (TCNQ) is in accord with similar experiments on other incommensurate CDW systems 25,27 and may be related to charge hopping among coherent CDW regions. The larger nb(T) and shorter L for the samples of 0.53 < x < 0.56 may lead to more pronounced frequency behavior even as T approaches room tempera-ture. In summary, the variation of dielectric response as a function of commensurability, bipolaron concentration, and temperature reveal a systematic variation of f and ul'W with x. A proposed model based on the dynamics of pinned charge-density waves and relatively mobile bipo-larons in the commensurate phases can account for the data. One of us (A.J.E,) acknowledges discussions with E. M. Conwell, S. Kivelson, and J. P. Pouget. 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Orbach, and A. Zettl, Phys. Rev. B 24, 7474 (1980. lOA. J. Epstein and E. M. Conwell, Solid State Commun. 24, 627 (1978). IIJ. P. Pouget, Chern. Scr. 17, 85 (1980. 12A. J. Epstein, J. S. Miller, J. P. Pouget, and R. Comes, Phys. Rev. Lett. 47,741 (J981). 13A. J. Epstein, J. W. Kaufer, H. Rornrnelmann, I. A. Ho-ward, E. M. Conwell, J. S. Miller, J. P. Pouget, and R. Comes, Phys. Rev. Lett. 49, 1037 (1982). 14A. J. Epstein, R. W. Bigelow, J. S. Miller, R. P. McCall, and D. B. Tanner, Mol. Cryst. Liq. Cryst. 120,43 (1985). 15L. J. Azevedo, J. S. Miller, and A. J. Epstein, Mol. Cryst. Liq. Cryst. 120,67 (1985). 16F. Devreux, M. Nechtschein, and G. Gruner, Phys. Rev. Lett. 45, 53 (1980). 17W. G. Clark, K. Glover, M. D. Lan, and L. J. Azevedo, J. Phys. (Paris) Colloq. 44, C3-1493 (1983). 18M. J. Rice and E. J. Mele, Phys. Rev. B 25, 1339 (J 982). 19A. J. Epstein, J. W. Kaufer, H. Rommelmann, J. S. Miller, R. Comes, and J. P. Pouget, J. Phys. (Paris) Colloq. 44, C3-1479 (1983). 20E. M. 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I.r.. 1763 

Microwave response of confined soliton pairs (Bipolarons) in (N-Methylphenazinium) x (Phenazine) 1-x (Tetracyanoquinodimethanide)

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Microwave response of confined soliton pairs (Bipolarons) in (N-Methylphenazinium) x (Phenazine) 1-x (Tetracyanoquinodimethanide)

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