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Tuning dimensionality in low-dimensional electronic materials
19 June 1998
Chemical Physics Letters 289 Ž1998. 559–566
Tuning dimensionality in low-dimensional electronic materials Geoffrey F. Strouse a,) , Brian Scott b, Basil I. Swanson b, Avadh Saxena c , Ivo Batistic d , J. Tinka Gammel c , Alan R. Bishop c b
a Department of Chemistry, UniÕersity of California-Santa Barbara, Santa Barbara, CA 93106, USA Chemical Science and Technology DiÕision, Los Alamos National Laboratory, Los Alamos, NM 87545, USA c Theoretical DiÕision, Los Alamos National Laboratory, Los Alamos, NM 87545, USA d Institute of Physics of the UniÕersity, P.O. Box 304, 41001 Zagreb, Croatia
Received 3 December 1997; in final form 8 April 1998
Abstract We demonstrate how dimensionality can be tuned in complex low-dimensional electronic materials via small perturbations in competing molecular forces. The delicate balance between molecular level forces on observed dimensionality in materials is illustrated by the 1-d to 3-d structural reorganization following deuteration of the ancillary ligands in the halogen-bridged transition-metal charge-transfer complex wPtŽen. 2 I 2 xwPtŽen. 2 xI 2 ŽPtI. where en denotes ethylenediamine. Specifically, the impact of competing forces on dimensionality is clearly demonstrated by the temperature-dependent phase transitions in perdeuterated PtI ŽD-PtI., where small changes in inter- and intra-sheet interactions drive mesoscopic structural changes. q 1998 Published by Elsevier Science B.V. All rights reserved.
Dimensionality in complex electronic materials is governed by a variety of competing subtle influences such as a competition between cell forces, e.g. hydrogen bonding, Coulomb and van der Waals forces, and competition between inter- and intra-chain effects w1–20x. The importance of dimensionality for low-dimensional electronic materials, such as mixed-stack charge-transfer salts ŽTTF-TCNQ w1–3x, Bechgaard salts w4,5x., high-temperature superconductors ŽLa x CuO, YBCO. w6–9x, organic conductors with hydrogen bonding w10–12x, conducting polym e r s Ž p o ly a c e ty le n e , p o ly d ia c e ty le n e , polyphenylenevinylene. w13x, colossal magnetoresistance materials ŽCMR. w14–16x and the halogen-
)
Corresponding author. Fax: q1-805-893-4120.
bridged transition-metal ŽMX. chains w17–19x, is well documented in the literature. The common underlying themes of dimensionality and strongly coupled spin–charge–lattice degrees of freedom lead to a rich variety of phenomena controlled via structural and external perturbations, for example competing ground states, polarons and excitons, multiscale intrinsic textures and dynamics, metal–insulator transitions, strongly correlated metals and non-Fermi-liquid behavior, and so forth. Controlling these properties is fundamentally important technologically, e.g., in gap states for light-emitting polymer devices, for the control of optical, transport and directional properties in nonlinear- and electrooptics, and local polarizability and charge transfer at complex interfaces, blends and heterostructures. Modulating the electronic properties by tuning the effective dimensionality requires an understanding of the microscopic perturbations
0009-2614r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 0 4 7 6 - X
560
G.F. Strouse et al.r Chemical Physics Letters 289 (1998) 559–566
arising from subtle competitions in crystal packing forces on dimensionality in the solid state. Quasi-1-d metal halogen chain materials ŽMX. offer the unusual opportunity to directly probe dimensionality effects by correlating the changes in the strength of the charge-density-wave broken-symmetry state with optical and structural changes in the material. Peierls distortion and competition between electron–electron and electron–phonon forces are the dominant and competing mechanisms that open semiconductor-like energy gaps in the MX materials. Inter-chain interactions are influenced by changes in the hydrogen bonding network and inter-chain forces ŽCoulomb. that couple the chains. These microscopic effects drive the mesoscopic textures and their structural, electronic, optical and magnetic consequences. The tuning of dimensionality by subtle crystallog ra p h ic c h a n g e s is m o st strik in g in wPtŽen. 2 I 2 xwPtŽen. 2 xI 2 ŽPtI., where en denotes ethylenediamine, due to instabilities arising from weak hydrogen bonding and Coulomb interactions in the solid state. The remarkable feature is that mere deuteration of the ancillary ligand is sufficient to tip the delicate balance between Coulomb Žthrough charge-density-wave ŽCDW.. and van der Waals Žthrough H-bonding. forces resulting in novel 2-d and 3-d ordering of the material. D-PtI is a unique material from the viewpoint of its extreme sensitivity to isotopic chemistry resulting in global crystal packing effects. In PtI with normal isotopic distribution, the structure is comprised of weak inter-chain H-bonding between incoherent chains Ž‘D’-type. lacking CDW phase registry which gives rise to the observation of disorder of the halide position about the centroid between adjacent Pt atoms w21,22x. This disorder is a common structural feature for virtually all MX solids. Upon perdeuteration of the ancillary ethylenediamine ligands in D-PtI, a peculiar structural polymorph is observed consisting of sheets of phase coherent Žhalide-ordered. chains Ž‘O’-type. interleaved with sheets of phase incoherent chains Ž‘D’-type. in the C 2rm space group ŽFig. 1. w23–26x. An unexpected strengthening of intra-chain H-bonding in the lattice over the non-deuterated parent complex drives this structural peculiarity. In the O-sheet, Coulomb forces result in ordering of the chains along the a-axis Žinter-sheet interactions.. This registry results in ex-
treme Coulombic frustration in the D-sheets arising from the unfavorable Coulombic interactions with the next nearest neighbor O-type sheet. This result suggests that the structure of PtI is not explicitly dominated by electronic interactions, but rather by subtle cell packing forces. The subtleties of packing and systematic strengthening of interactions are essential for understanding and predicting the phase transitions. Both types of D-PtI chains exhibit disorder for the en ancillary ligands w23–26x. The D chain is distinguished by the crystallographic observation of partial occupation of the I position along the 1-d axis arising from a lack of phase registry between chains within the D sheet; while the O chain crystallographically shows single site occupation due to complete phase-registry within the O sheet ŽFig. 1b.. In the unit cell the crystallographic axes define specific interactions in the cell packing forces. The a-axis defines the inter-sheet interactions, predominantly Coulomb forces, the b-axis defines intra-chain forces, the CDW strength and the c-axis defines intra-sheet interactions, predominantly H-bonding Ži.e., van der Waals forces.. There exists a distinct difference in the CDW strengths Ž r . for the two chains D Ž r s 0.862. and O Ž r s 0.874. at room temperature arising from the subtle differences in competing interchain forces Žhydrogen bonding networks. within a sheet and between dissimilar sheets 1 w23–26x. The CDW strengths of the two chains exhibit temperature dependence, showing shifts in their respective CDW strengths as the temperature is lowered corresponding to a compression of the cell lattice w24,26x. Temperature-dependent studies in D-PtI suggest two phase transitions, a first-order phase transition and a peculiar phase transition associated with a change in space group from C 2rm to C 2 w27x. The first-order phase transition at 150 K results in a 2-d ordering Ždirectionality. within the D-sheet, accom-
1
The hydrogen bonding in D-PtI is comprised of two distinct interactions, NH–O and CH–O. The H-bonding in the O sheet is ˚ . from the en on dominated by strong NH–O bonding Ž3.01Ž3. A the PtŽIV. centers to the perchlorate counterions linking chains Žinterchain. within the sheet. In contrast, on the D-sheet the ˚ .. CH–O intrachain NH–O bonding is more significant Ž3.02Ž3. A hydrogen bonding in the D sheet is significant in the D-PtI ˚ .. structure Ž3.15 A
G.F. Strouse et al.r Chemical Physics Letters 289 (1998) 559–566
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Fig. 1. Ža. Projection of the crystallographic packing for D-PtI along the ac-plane at 298 K. D and O represent the two chain types observed in the crystal. Žb. Schematic representation showing the packing geometry for the O- and D-type D-PtI chains.
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G.F. Strouse et al.r Chemical Physics Letters 289 (1998) 559–566
Fig. 2. Temperature-dependent Raman of D-PtI between 150 and 10 K at an excitation wavelength of 960 nm Ž2 mW.. The fit curves are least- squares fits to three guassians. The dashed line represents the new O-type chains.
panied by a distortion of the c-axis in a C 2rm cell w10,11x. Coupled to the first-order phase transition, a continuous phase transition associated with weakening of the CDW strength of the D-chain Ž r s 0.923. and a slight increase of the CDW strength for the O-chain Ž r s 0.866. is observed by X-ray diffraction and temperature-dependent vibrational spectroscopy w24,26x. X-ray data at 170 K give rise to a surprising result, the structural phase transition is associated with a change in the CH–O bonding in the D-sheet, resulting in a ligand ordering transition, in which one conformer of the en is favored. The ordering of the en’s on the D-chains occurs in the C 2rm cell, doubling the c-axis, and resulting in a gauche conformer for the en’s on the Pt centers w24,26x. This suggests the H-bonding in the D-sheet is potentially more significant than in the structurally ordered O-sheet, consistent with stronger Coulombic coupling in the O-sheet. An important feature observed in the Raman spectrum with regards to the D-sheet is that the n 1 Raman active mode for the D-chain at 104 cmy1 Ž150 K. is extremely broad Žfwhm s 55 cmy1 ., suggesting significant dynamic disorder for the CDW strength between chains within
the D sheet 2 ŽFig. 2.. This dynamic disorder is not observed for the O-sheet. This disorder suggests an instability or a ‘frustration’ in the CDW strength, arising from intersheet Coulomb forces. The second structural transition at 120 K associated with a lowering of cell symmetry ŽC 2rm to C 2 . is more complex, neither a first- nor second-order phase transition, as observed by changes in acoustic modes Že.g., in resonant ultrasound ŽRUS.. and the optical phonon modes Žresonant Raman spectroscopy. w24,25x. The loss of centricity correlates with 3-d domain structures in the material, resulting in the D-PtI structure not being a single phase until below 4 K. Due to the domain structure, neutron diffraction studies have proven to be insufficient in describing the 3-d ordering transition w27x. Temperature-dependent Raman studies provide insight into the 3-d domain ordering of the separate chain types in D-PtI. Two main features in the Raman data
2 The Raman data was fit to a series of Gaussians. Peak positions for the Gaussian were fixed and the Gaussian intensity and width minimized using a Marquadt–Levenburg routine.
G.F. Strouse et al.r Chemical Physics Letters 289 (1998) 559–566
below 160 K ŽFig. 2. are evident: a sharpening of the band at 104 cmy1 ŽD-chain. and the growth of a new feature at 112 cmy1 corresponding to a loss of intensity for the 114 cmy1 band ŽO-chain.. We speculate that the observed sharpening of the 104 cmy1 band below 120 K arises from chain-to-chain phase-registry within the D-sheet due to loss of dynamic CDW disorder. Curve resolution of the 112 and 114 cmy1 bands indicate two competing mesoscale structures for the O-sheet below 120 K. Based upon the coupled changes for the intensity of the Raman bands observed at 112 and 114 cmy1 , we assign these bands as different structural types for the O-sheets. The increase in intensity for the 112 cmy1 band nearly corresponds with the sharpening of the n 1 band Ž104 cmy1 . for the D-sheets, suggesting that ordering of the D-sheet directly perturbs the structure of the O-sheet. The appearance of a weaker CDW strength for the new phase in the O-sheet is consistent with increased Coulombic inter-sheet interactions between the D- and O-sheets. This is interpreted as local intersheet reordering, lowering Coulombic repulsion terms with a coupled decrease in CDW strength for the chains. The proteo and deutero PtI materials exist at the boundary between different CDW phase types dictated by differences in the strength of competing Coulomb ŽMadelung. and van der Waals Žhydrogen bonding. energies for the two structures. We model hydrogen bonding here as the interaction between charge fluctuations Žwithin the CDW. on two neighboring chains, i.e. via van der Waals forces. At room temperature, the model parameters associated with the PtI structures predict van der Waals and Coulomb forces with the same order of magnitude w20,26x. Thus a small change in parameters can make one interaction dominate over the other and can result in a phase transition from one type of CDW ordering to another. This is experimentally observed not only for the two isotopic structures, but also within the deutero-structure. The Coulomb interaction ŽMadelung energy. term between the two CDW chains in a sheet is V Mad s Ý Vn l Q nŽ1. Q lŽ2. , n, l
where we take
Ž 1a .
Vn l s
563
e2
(c q Ž br4. Ž n y l . 2
2
2
.
Ž 1b .
Here a, b and c denote the unit cell lattice parameters of D-PtI, e is the electronic charge, Q nŽ1. is the total charge on the nth ion on chain one and Q lŽ2. is the total charge of the lth ion on chain two. The charges Q nŽ1. and Q lŽ2. are calculated using a tight-binding unrestricted mean-field approach in which charge and lattice structure vary from site to site to achieve self-consistent distributions w26x. The above Madelung energy is evaluated using first-order perturbation theory. The contribution from the van der Waals interaction on two neighboring chains in a sheet is calculated within second-order perturbation theory w28,29x. VvdW s D E s y Ý n
<² n < V <0:< 2 En y E 0
.
Ž 2a .
If we denote by eg , f lŽ1. the single particle energies and the corresponding wavefunctions for the first chain and by ´a , cnŽ2. the single particle energies and the corresponding wavefunctions for the second chain, then D Esy
1
Ý a) ´ F) b
D ´ab q D egd
g) ´ F) d
=
Ý Vnl cnŽ a .)cnŽ b .f lŽg .f lŽ d .)
,
Ž 2b .
n, l
where ´ F is the Fermi energy and D ´a b s ´a y ´b . We estimated this energy using small cluster and small dipole approximations. Within this model, using a reasonable set of model parameters for the PtI materials, we find that DV Mad s V Žin-phase. y V Žout-phase. s 5 = 10y3 eV and DVvdW s V Žinphase. y V Žout-phase. s y7.8 = 10y3 eV w26x. Thus, we expect in-phase CDW ordering at room temperature. If the magnitude of the van der Waals forces is stronger the materials are predicted to be at a boundary between the phases, and a structural frustration would lead to phase-disorder as observed in the proteo case. In the deutero material, the structure rearranges increasing the van der Waals forces, leading to ‘in-phase’ ordering of the CDW on the O-sheet. The D-sheet remains disordered, either due
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to frustration in the CDW amplitude, or due to weaker van der Waals forces resulting in a lack of phase order as observed in the proteo material. We emphasize that the present results are not based on ab-initio total energy calculations, which are unfeasible for such large unit cells. The Raman observations can be interpreted in terms of changes in the competition between interacting forces, dominated by Coulombic interactions in the D-sheet. Two simple models for the intrasheet ordering of the D-sheet for the 120 K phase transition can be proposed ŽFig. 3.. Both models require a doubling of the b-axis to fulfill the symmetry constraints for a C 2 space group. The first model ŽFig. 3a. is optimized for van der Waals interactions; while the second model, with alternating 2–4 Pt ions is optimized for Coulombic terms. Based on theoretical predictions the second case is predicted to be the most energetically favorable. Lifting of the frustration in the CDW for the D-sheet results in the observed behavior with temperature, i.e., increased CDW strength coupled to an increase in Coulomb interactions. If there is a 2-d ordering of CDW in the D-sheets at low temperatures, then such an order will create an extra Coulomb force on the sheets, resulting in sliding of sheets and a strengthening of interaction of rA over r B Žwhere rA and r B denote
Fig. 3. Projection of D sheet ordering in the bc-plane at 120 K phase transition for: Ža. a van der Waals favored structure and Žb. a Coulomb favored structure. The numbers 2 and 4 refer to the nominal charge at the Pt ion.
Fig. 4. Ža. Sliding interaction projected in ab-plane minimizing inter-sheet Coulomb interactions as predicted from theoretical models, where rA and r B denote distances between Pt ions. Žb. Molecular projection of D-sheet to O-sheet ordering in the abplane below 120 K. The numbers 2 and 4 refer to the nominal charge at the Pt ion.
distances between Pt ions. ŽFig. 4a., producing the sheet-to-sheet ordering predicted in Fig. 4b. It is energetically favorable for the CDW on the O-sheet to slide with respect to the D-sheets at low temperatures. The reason is that sliding reduces Coulomb repulsion between X–M II –X clusters and increases Coulomb attraction between a X–M IV –X cluster and the M II ion. The sliding transition can be expected to proceed by a mesoscopic domain growth, as observed in the Raman data, and exhibits an increase in the polar nature of the crystal, as observed in the SHG data w28,29x. Based on the combination of theoretical predictions of competing interactions, crystallographic symmetry constraints and experimental data, we propose that the structural phase transition at 120 K is governed by mesoscopic domain growth ŽFigs. 3 and 4.. Initially, an incommensurate to commensurate phase transition occurs, resulting in inter-D-sheet ordering in a Coulombically favored arrangement ŽFig. 3b.. The ordering phenomenon within the sheet
G.F. Strouse et al.r Chemical Physics Letters 289 (1998) 559–566
sets up domains of different CDW strengths for both the D- and O-chains. As the structure compresses and Coulombic forces dominate the interactions, the structure begins 3-d ordering ŽFig. 4. with subsequent domain wall motion and inter-D-sheet registry in the cell. The actual order of the single phase is not known. The 3-d ordering occurs in a C 2 space group. It is not possible to order both chains in the C 2 cell without doubling the b-axis. This was not observed at the lowest temperature neutron diffraction spectrum Ž20 K. w27x. However, our results, as well as symmetry considerations, strongly suggest a doubling of the b-axis must occur. We are continuing investigations of the results by measuring the cell below 20 K by X-ray diffraction, and using pair distribution function analysis of temperature-dependent neutron studies and anomalous X-ray scattering studies to probe the local structural changes w30x. In conclusion, complex electronic materials increasingly teach us that we need to probe a combination of structural, electronic, optical and magnetic properties to understand and control dimensionality. The MX class of materials is very rich in terms of the breadth of physical properties that may be obtained by simply changing chemistry, including the hydrogen bonding as demonstrated above through deuteration w17–19x. Based on the change in the total ŽMadelung plus van der Waals. energy and the experimentally known variation of lattice distortion we were able to model the ‘in-phase’ to ‘phase-disordered’ crossover in the CDW on D-PtI chains within the sheets Ž2-d ordering.. We also studied the 3-d ordering of D-sheets at low temperature within the same model. At present we have neglected explicit configurational entropy contributions in the modeling. As more experimental data become available, the model will be refined to study quantitatively the various structural transitions observed in these weak CDW materials. The above interchain coupling and intra-sheet ordering is very reminiscent of ordering transitions known in TTF-TCNQ and related mixed-stack charge-transfer salts, but with two notable differences: Ž1. The CDW is commensurate in D-PtI while it is incommensurate in TTFTCNQ and Ž2. both types of sheets are of the same material ŽD-PtI. in the MX case while they are of different materials ŽTTF and TCNQ. in TTF-TCNQ w1–3,26x. At least two structural transitions are known
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in both materials. The contrast with chainrsheet ordering in D-PtI with TTF-TCNQ is particularly instructive from the perspective of competing energies. It is essential that the CDW strength is weak in PtI for the effect observed: otherwise the strong lattice commensurability energy will dominate and the CDW deformation would be pinned. MX materials offer the opportunity to probe the question of dimensionality in low-d materials by specific molecular level engineering of the interactions dictating dimensionality in materials, i.e. Coulomb forces, van der Waals forces and H-bonding interactions. We believe that a greater control over the CDW strength in pure and mixed-halide MX solids will contribute to our understanding of the underlying physics of these and other low-dimensional electronic materials. The success of this level of modeling in conjunction with synthesis and elaborate characterization of these materials is allowing us to make quantitative predictions for more complex geometries and materials, thus enabling us to explore systematically their potential for applications. We believe that these studies will likely have a profound effect on our ability to predict and control microstructure, self-assembly and functionality in complex electronic materials, in both one- and higher dimensions.
References w1x J.P. Pouget, Semicond. Semimet. 27 Ž1988. 88. w2x P. Bak, V.J. Emery, Phys. Rev. Lett. 36 Ž1976. 978. w3x R. Comes, S.M. Shapiro, G. Shirane, A.F. Garito, A.J. Heeger, Phys. Rev. Lett. 35 Ž1975. 1518. w4x L.P. Gorkov, J. Phys. I 6 Ž1996. 1697. w5x J.P. Pouget, S. Ravy, J. Phys. I 6 Ž1996. 1051. w6x J.M. Tranquada, J.B. Sternlieb, J.D. Axe, Y. Nakamura, S. Uchida, Nature 375 Ž1995. 561. w7x J.M. Tranquada, D.J. Buttrey, V. Sachan, J.E. Lorenzo, Phys. Rev. Lett. 73 Ž1994. 1003. w8x A.W. Sleight, Science 242 Ž1988. 1519. w9x Y. Bar-Yam, T. Egami, J. Mustre de Leon, A.R. Bishop ŽEds.., Lattice Effects in High Tc Superconductors, World Scientific, Singapore, 1992. w10x O.M. Yaghi, H.L. Li, T.L. Groy, J. Am. Chem. Soc. 118 Ž1996. 9096. w11x G.R. Desiraju, Mol. Cryst. Liq. Cryst. 211 Ž1992. 63. w12x V.A. Russell, M.D. Ward, J. Chem. Mater. 8 Ž1996. 1654. w13x J.L. Bredas, R.R. Chance ŽEds.., Conjugated Polymeric Materials: Opportunities in Electronics, Optoelectronics, and
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w22x B. Scott, S.R. Johnson, B.I. Swanson, Acta Crystallogr. Žin preparation.. w23x B. Scott, B.L. Bracewell, S.R. Johnson, B.I. Swanson, J.F. Bardeau, A. Bulou, B. Hennion, Chem. Mater. 356 Ž1995. 207. w24x G.F. Strouse, B. Scott, M. Berkey, S. Johnson, T. Darling, A. Migliori, B.I. Swanson, J. Synth. Met. 86 Ž1997. 1919. w25x T. Darling, A. Migliori, G.F. Strouse, S. Johnson, B.I. Swanson, M.F. Hundley, J.D. Thompson, J. Synth. Met. 86 Ž1997. 1922. w26x G.F. Strouse, B. Scott, B.I. Swanson, A. Saxena, I. Bastic, T. Gammel, A. Bishop, Phys. Rev. B Žin preparation.. w27x J.-F. Bardeau, A. Bulou, B.I. Swanson, B. Hennion, Acta Crystallogr. B - Struct. Sci. 52 Ž1996. 854. w28x S. Barisic, A. Bjelis, J. Phys. Lett. 44 Ž1983. L327. w29x A. Bjelis, S. Barisic, J. Phys. Coll. 44 Ž1983. C34–1539. w30x T. Egami, S. Billinge, A. Eberhardt, G.F. Strouse, B.I. Swanson, work in progress.
Chemical Physics Letters 289 Ž1998. 559–566
Tuning dimensionality in low-dimensional electronic materials Geoffrey F. Strouse a,) , Brian Scott b, Basil I. Swanson b, Avadh Saxena c , Ivo Batistic d , J. Tinka Gammel c , Alan R. Bishop c b
a Department of Chemistry, UniÕersity of California-Santa Barbara, Santa Barbara, CA 93106, USA Chemical Science and Technology DiÕision, Los Alamos National Laboratory, Los Alamos, NM 87545, USA c Theoretical DiÕision, Los Alamos National Laboratory, Los Alamos, NM 87545, USA d Institute of Physics of the UniÕersity, P.O. Box 304, 41001 Zagreb, Croatia
Received 3 December 1997; in final form 8 April 1998
Abstract We demonstrate how dimensionality can be tuned in complex low-dimensional electronic materials via small perturbations in competing molecular forces. The delicate balance between molecular level forces on observed dimensionality in materials is illustrated by the 1-d to 3-d structural reorganization following deuteration of the ancillary ligands in the halogen-bridged transition-metal charge-transfer complex wPtŽen. 2 I 2 xwPtŽen. 2 xI 2 ŽPtI. where en denotes ethylenediamine. Specifically, the impact of competing forces on dimensionality is clearly demonstrated by the temperature-dependent phase transitions in perdeuterated PtI ŽD-PtI., where small changes in inter- and intra-sheet interactions drive mesoscopic structural changes. q 1998 Published by Elsevier Science B.V. All rights reserved.
Dimensionality in complex electronic materials is governed by a variety of competing subtle influences such as a competition between cell forces, e.g. hydrogen bonding, Coulomb and van der Waals forces, and competition between inter- and intra-chain effects w1–20x. The importance of dimensionality for low-dimensional electronic materials, such as mixed-stack charge-transfer salts ŽTTF-TCNQ w1–3x, Bechgaard salts w4,5x., high-temperature superconductors ŽLa x CuO, YBCO. w6–9x, organic conductors with hydrogen bonding w10–12x, conducting polym e r s Ž p o ly a c e ty le n e , p o ly d ia c e ty le n e , polyphenylenevinylene. w13x, colossal magnetoresistance materials ŽCMR. w14–16x and the halogen-
)
Corresponding author. Fax: q1-805-893-4120.
bridged transition-metal ŽMX. chains w17–19x, is well documented in the literature. The common underlying themes of dimensionality and strongly coupled spin–charge–lattice degrees of freedom lead to a rich variety of phenomena controlled via structural and external perturbations, for example competing ground states, polarons and excitons, multiscale intrinsic textures and dynamics, metal–insulator transitions, strongly correlated metals and non-Fermi-liquid behavior, and so forth. Controlling these properties is fundamentally important technologically, e.g., in gap states for light-emitting polymer devices, for the control of optical, transport and directional properties in nonlinear- and electrooptics, and local polarizability and charge transfer at complex interfaces, blends and heterostructures. Modulating the electronic properties by tuning the effective dimensionality requires an understanding of the microscopic perturbations
0009-2614r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 0 4 7 6 - X
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G.F. Strouse et al.r Chemical Physics Letters 289 (1998) 559–566
arising from subtle competitions in crystal packing forces on dimensionality in the solid state. Quasi-1-d metal halogen chain materials ŽMX. offer the unusual opportunity to directly probe dimensionality effects by correlating the changes in the strength of the charge-density-wave broken-symmetry state with optical and structural changes in the material. Peierls distortion and competition between electron–electron and electron–phonon forces are the dominant and competing mechanisms that open semiconductor-like energy gaps in the MX materials. Inter-chain interactions are influenced by changes in the hydrogen bonding network and inter-chain forces ŽCoulomb. that couple the chains. These microscopic effects drive the mesoscopic textures and their structural, electronic, optical and magnetic consequences. The tuning of dimensionality by subtle crystallog ra p h ic c h a n g e s is m o st strik in g in wPtŽen. 2 I 2 xwPtŽen. 2 xI 2 ŽPtI., where en denotes ethylenediamine, due to instabilities arising from weak hydrogen bonding and Coulomb interactions in the solid state. The remarkable feature is that mere deuteration of the ancillary ligand is sufficient to tip the delicate balance between Coulomb Žthrough charge-density-wave ŽCDW.. and van der Waals Žthrough H-bonding. forces resulting in novel 2-d and 3-d ordering of the material. D-PtI is a unique material from the viewpoint of its extreme sensitivity to isotopic chemistry resulting in global crystal packing effects. In PtI with normal isotopic distribution, the structure is comprised of weak inter-chain H-bonding between incoherent chains Ž‘D’-type. lacking CDW phase registry which gives rise to the observation of disorder of the halide position about the centroid between adjacent Pt atoms w21,22x. This disorder is a common structural feature for virtually all MX solids. Upon perdeuteration of the ancillary ethylenediamine ligands in D-PtI, a peculiar structural polymorph is observed consisting of sheets of phase coherent Žhalide-ordered. chains Ž‘O’-type. interleaved with sheets of phase incoherent chains Ž‘D’-type. in the C 2rm space group ŽFig. 1. w23–26x. An unexpected strengthening of intra-chain H-bonding in the lattice over the non-deuterated parent complex drives this structural peculiarity. In the O-sheet, Coulomb forces result in ordering of the chains along the a-axis Žinter-sheet interactions.. This registry results in ex-
treme Coulombic frustration in the D-sheets arising from the unfavorable Coulombic interactions with the next nearest neighbor O-type sheet. This result suggests that the structure of PtI is not explicitly dominated by electronic interactions, but rather by subtle cell packing forces. The subtleties of packing and systematic strengthening of interactions are essential for understanding and predicting the phase transitions. Both types of D-PtI chains exhibit disorder for the en ancillary ligands w23–26x. The D chain is distinguished by the crystallographic observation of partial occupation of the I position along the 1-d axis arising from a lack of phase registry between chains within the D sheet; while the O chain crystallographically shows single site occupation due to complete phase-registry within the O sheet ŽFig. 1b.. In the unit cell the crystallographic axes define specific interactions in the cell packing forces. The a-axis defines the inter-sheet interactions, predominantly Coulomb forces, the b-axis defines intra-chain forces, the CDW strength and the c-axis defines intra-sheet interactions, predominantly H-bonding Ži.e., van der Waals forces.. There exists a distinct difference in the CDW strengths Ž r . for the two chains D Ž r s 0.862. and O Ž r s 0.874. at room temperature arising from the subtle differences in competing interchain forces Žhydrogen bonding networks. within a sheet and between dissimilar sheets 1 w23–26x. The CDW strengths of the two chains exhibit temperature dependence, showing shifts in their respective CDW strengths as the temperature is lowered corresponding to a compression of the cell lattice w24,26x. Temperature-dependent studies in D-PtI suggest two phase transitions, a first-order phase transition and a peculiar phase transition associated with a change in space group from C 2rm to C 2 w27x. The first-order phase transition at 150 K results in a 2-d ordering Ždirectionality. within the D-sheet, accom-
1
The hydrogen bonding in D-PtI is comprised of two distinct interactions, NH–O and CH–O. The H-bonding in the O sheet is ˚ . from the en on dominated by strong NH–O bonding Ž3.01Ž3. A the PtŽIV. centers to the perchlorate counterions linking chains Žinterchain. within the sheet. In contrast, on the D-sheet the ˚ .. CH–O intrachain NH–O bonding is more significant Ž3.02Ž3. A hydrogen bonding in the D sheet is significant in the D-PtI ˚ .. structure Ž3.15 A
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Fig. 1. Ža. Projection of the crystallographic packing for D-PtI along the ac-plane at 298 K. D and O represent the two chain types observed in the crystal. Žb. Schematic representation showing the packing geometry for the O- and D-type D-PtI chains.
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Fig. 2. Temperature-dependent Raman of D-PtI between 150 and 10 K at an excitation wavelength of 960 nm Ž2 mW.. The fit curves are least- squares fits to three guassians. The dashed line represents the new O-type chains.
panied by a distortion of the c-axis in a C 2rm cell w10,11x. Coupled to the first-order phase transition, a continuous phase transition associated with weakening of the CDW strength of the D-chain Ž r s 0.923. and a slight increase of the CDW strength for the O-chain Ž r s 0.866. is observed by X-ray diffraction and temperature-dependent vibrational spectroscopy w24,26x. X-ray data at 170 K give rise to a surprising result, the structural phase transition is associated with a change in the CH–O bonding in the D-sheet, resulting in a ligand ordering transition, in which one conformer of the en is favored. The ordering of the en’s on the D-chains occurs in the C 2rm cell, doubling the c-axis, and resulting in a gauche conformer for the en’s on the Pt centers w24,26x. This suggests the H-bonding in the D-sheet is potentially more significant than in the structurally ordered O-sheet, consistent with stronger Coulombic coupling in the O-sheet. An important feature observed in the Raman spectrum with regards to the D-sheet is that the n 1 Raman active mode for the D-chain at 104 cmy1 Ž150 K. is extremely broad Žfwhm s 55 cmy1 ., suggesting significant dynamic disorder for the CDW strength between chains within
the D sheet 2 ŽFig. 2.. This dynamic disorder is not observed for the O-sheet. This disorder suggests an instability or a ‘frustration’ in the CDW strength, arising from intersheet Coulomb forces. The second structural transition at 120 K associated with a lowering of cell symmetry ŽC 2rm to C 2 . is more complex, neither a first- nor second-order phase transition, as observed by changes in acoustic modes Že.g., in resonant ultrasound ŽRUS.. and the optical phonon modes Žresonant Raman spectroscopy. w24,25x. The loss of centricity correlates with 3-d domain structures in the material, resulting in the D-PtI structure not being a single phase until below 4 K. Due to the domain structure, neutron diffraction studies have proven to be insufficient in describing the 3-d ordering transition w27x. Temperature-dependent Raman studies provide insight into the 3-d domain ordering of the separate chain types in D-PtI. Two main features in the Raman data
2 The Raman data was fit to a series of Gaussians. Peak positions for the Gaussian were fixed and the Gaussian intensity and width minimized using a Marquadt–Levenburg routine.
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below 160 K ŽFig. 2. are evident: a sharpening of the band at 104 cmy1 ŽD-chain. and the growth of a new feature at 112 cmy1 corresponding to a loss of intensity for the 114 cmy1 band ŽO-chain.. We speculate that the observed sharpening of the 104 cmy1 band below 120 K arises from chain-to-chain phase-registry within the D-sheet due to loss of dynamic CDW disorder. Curve resolution of the 112 and 114 cmy1 bands indicate two competing mesoscale structures for the O-sheet below 120 K. Based upon the coupled changes for the intensity of the Raman bands observed at 112 and 114 cmy1 , we assign these bands as different structural types for the O-sheets. The increase in intensity for the 112 cmy1 band nearly corresponds with the sharpening of the n 1 band Ž104 cmy1 . for the D-sheets, suggesting that ordering of the D-sheet directly perturbs the structure of the O-sheet. The appearance of a weaker CDW strength for the new phase in the O-sheet is consistent with increased Coulombic inter-sheet interactions between the D- and O-sheets. This is interpreted as local intersheet reordering, lowering Coulombic repulsion terms with a coupled decrease in CDW strength for the chains. The proteo and deutero PtI materials exist at the boundary between different CDW phase types dictated by differences in the strength of competing Coulomb ŽMadelung. and van der Waals Žhydrogen bonding. energies for the two structures. We model hydrogen bonding here as the interaction between charge fluctuations Žwithin the CDW. on two neighboring chains, i.e. via van der Waals forces. At room temperature, the model parameters associated with the PtI structures predict van der Waals and Coulomb forces with the same order of magnitude w20,26x. Thus a small change in parameters can make one interaction dominate over the other and can result in a phase transition from one type of CDW ordering to another. This is experimentally observed not only for the two isotopic structures, but also within the deutero-structure. The Coulomb interaction ŽMadelung energy. term between the two CDW chains in a sheet is V Mad s Ý Vn l Q nŽ1. Q lŽ2. , n, l
where we take
Ž 1a .
Vn l s
563
e2
(c q Ž br4. Ž n y l . 2
2
2
.
Ž 1b .
Here a, b and c denote the unit cell lattice parameters of D-PtI, e is the electronic charge, Q nŽ1. is the total charge on the nth ion on chain one and Q lŽ2. is the total charge of the lth ion on chain two. The charges Q nŽ1. and Q lŽ2. are calculated using a tight-binding unrestricted mean-field approach in which charge and lattice structure vary from site to site to achieve self-consistent distributions w26x. The above Madelung energy is evaluated using first-order perturbation theory. The contribution from the van der Waals interaction on two neighboring chains in a sheet is calculated within second-order perturbation theory w28,29x. VvdW s D E s y Ý n
<² n < V <0:< 2 En y E 0
.
Ž 2a .
If we denote by eg , f lŽ1. the single particle energies and the corresponding wavefunctions for the first chain and by ´a , cnŽ2. the single particle energies and the corresponding wavefunctions for the second chain, then D Esy
1
Ý a) ´ F) b
D ´ab q D egd
g) ´ F) d
=
Ý Vnl cnŽ a .)cnŽ b .f lŽg .f lŽ d .)
,
Ž 2b .
n, l
where ´ F is the Fermi energy and D ´a b s ´a y ´b . We estimated this energy using small cluster and small dipole approximations. Within this model, using a reasonable set of model parameters for the PtI materials, we find that DV Mad s V Žin-phase. y V Žout-phase. s 5 = 10y3 eV and DVvdW s V Žinphase. y V Žout-phase. s y7.8 = 10y3 eV w26x. Thus, we expect in-phase CDW ordering at room temperature. If the magnitude of the van der Waals forces is stronger the materials are predicted to be at a boundary between the phases, and a structural frustration would lead to phase-disorder as observed in the proteo case. In the deutero material, the structure rearranges increasing the van der Waals forces, leading to ‘in-phase’ ordering of the CDW on the O-sheet. The D-sheet remains disordered, either due
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to frustration in the CDW amplitude, or due to weaker van der Waals forces resulting in a lack of phase order as observed in the proteo material. We emphasize that the present results are not based on ab-initio total energy calculations, which are unfeasible for such large unit cells. The Raman observations can be interpreted in terms of changes in the competition between interacting forces, dominated by Coulombic interactions in the D-sheet. Two simple models for the intrasheet ordering of the D-sheet for the 120 K phase transition can be proposed ŽFig. 3.. Both models require a doubling of the b-axis to fulfill the symmetry constraints for a C 2 space group. The first model ŽFig. 3a. is optimized for van der Waals interactions; while the second model, with alternating 2–4 Pt ions is optimized for Coulombic terms. Based on theoretical predictions the second case is predicted to be the most energetically favorable. Lifting of the frustration in the CDW for the D-sheet results in the observed behavior with temperature, i.e., increased CDW strength coupled to an increase in Coulomb interactions. If there is a 2-d ordering of CDW in the D-sheets at low temperatures, then such an order will create an extra Coulomb force on the sheets, resulting in sliding of sheets and a strengthening of interaction of rA over r B Žwhere rA and r B denote
Fig. 3. Projection of D sheet ordering in the bc-plane at 120 K phase transition for: Ža. a van der Waals favored structure and Žb. a Coulomb favored structure. The numbers 2 and 4 refer to the nominal charge at the Pt ion.
Fig. 4. Ža. Sliding interaction projected in ab-plane minimizing inter-sheet Coulomb interactions as predicted from theoretical models, where rA and r B denote distances between Pt ions. Žb. Molecular projection of D-sheet to O-sheet ordering in the abplane below 120 K. The numbers 2 and 4 refer to the nominal charge at the Pt ion.
distances between Pt ions. ŽFig. 4a., producing the sheet-to-sheet ordering predicted in Fig. 4b. It is energetically favorable for the CDW on the O-sheet to slide with respect to the D-sheets at low temperatures. The reason is that sliding reduces Coulomb repulsion between X–M II –X clusters and increases Coulomb attraction between a X–M IV –X cluster and the M II ion. The sliding transition can be expected to proceed by a mesoscopic domain growth, as observed in the Raman data, and exhibits an increase in the polar nature of the crystal, as observed in the SHG data w28,29x. Based on the combination of theoretical predictions of competing interactions, crystallographic symmetry constraints and experimental data, we propose that the structural phase transition at 120 K is governed by mesoscopic domain growth ŽFigs. 3 and 4.. Initially, an incommensurate to commensurate phase transition occurs, resulting in inter-D-sheet ordering in a Coulombically favored arrangement ŽFig. 3b.. The ordering phenomenon within the sheet
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sets up domains of different CDW strengths for both the D- and O-chains. As the structure compresses and Coulombic forces dominate the interactions, the structure begins 3-d ordering ŽFig. 4. with subsequent domain wall motion and inter-D-sheet registry in the cell. The actual order of the single phase is not known. The 3-d ordering occurs in a C 2 space group. It is not possible to order both chains in the C 2 cell without doubling the b-axis. This was not observed at the lowest temperature neutron diffraction spectrum Ž20 K. w27x. However, our results, as well as symmetry considerations, strongly suggest a doubling of the b-axis must occur. We are continuing investigations of the results by measuring the cell below 20 K by X-ray diffraction, and using pair distribution function analysis of temperature-dependent neutron studies and anomalous X-ray scattering studies to probe the local structural changes w30x. In conclusion, complex electronic materials increasingly teach us that we need to probe a combination of structural, electronic, optical and magnetic properties to understand and control dimensionality. The MX class of materials is very rich in terms of the breadth of physical properties that may be obtained by simply changing chemistry, including the hydrogen bonding as demonstrated above through deuteration w17–19x. Based on the change in the total ŽMadelung plus van der Waals. energy and the experimentally known variation of lattice distortion we were able to model the ‘in-phase’ to ‘phase-disordered’ crossover in the CDW on D-PtI chains within the sheets Ž2-d ordering.. We also studied the 3-d ordering of D-sheets at low temperature within the same model. At present we have neglected explicit configurational entropy contributions in the modeling. As more experimental data become available, the model will be refined to study quantitatively the various structural transitions observed in these weak CDW materials. The above interchain coupling and intra-sheet ordering is very reminiscent of ordering transitions known in TTF-TCNQ and related mixed-stack charge-transfer salts, but with two notable differences: Ž1. The CDW is commensurate in D-PtI while it is incommensurate in TTFTCNQ and Ž2. both types of sheets are of the same material ŽD-PtI. in the MX case while they are of different materials ŽTTF and TCNQ. in TTF-TCNQ w1–3,26x. At least two structural transitions are known
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in both materials. The contrast with chainrsheet ordering in D-PtI with TTF-TCNQ is particularly instructive from the perspective of competing energies. It is essential that the CDW strength is weak in PtI for the effect observed: otherwise the strong lattice commensurability energy will dominate and the CDW deformation would be pinned. MX materials offer the opportunity to probe the question of dimensionality in low-d materials by specific molecular level engineering of the interactions dictating dimensionality in materials, i.e. Coulomb forces, van der Waals forces and H-bonding interactions. We believe that a greater control over the CDW strength in pure and mixed-halide MX solids will contribute to our understanding of the underlying physics of these and other low-dimensional electronic materials. The success of this level of modeling in conjunction with synthesis and elaborate characterization of these materials is allowing us to make quantitative predictions for more complex geometries and materials, thus enabling us to explore systematically their potential for applications. We believe that these studies will likely have a profound effect on our ability to predict and control microstructure, self-assembly and functionality in complex electronic materials, in both one- and higher dimensions.
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