Electrostatic Coupling and Local Structural Distortions at Interfaces in

Letter pubs.acs.org/NanoLett

Electrostatic Coupling and Local Structural Distortions at Interfaces in Ferroelectric/Paraelectric Superlattices P. Zubko,*,† N. Jecklin,† A. Torres-Pardo,†,‡ P. Aguado-Puente,§ A. Gloter,‡ C. Lichtensteiger,† J. Junquera,§ O. Stéphan,‡ and J.-M. Triscone† †

DPMC, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva-4, Switzerland Laboratoire de Physique des Solides, Université Paris-Sud, CNRS-UMR 8502, Orsay 91405, France § Departamento de Ciencias de la Tierra y Física de la Materia Condensada, Universidad de Cantabria, Cantabria Campus Internacional, Avenida de los Castros s/n, 39005 Santander, Spain ‡

ABSTRACT: The performance of ferroelectric devices is intimately entwined with the structure and dynamics of ferroelectric domains. In ultrathin ferroelectrics, ordered nanodomains arise naturally in response to the presence of a depolarizing field and give rise to highly inhomogeneous polarization and structural profiles. Ferroelectric superlattices offer a unique way of engineering the desired nanodomain structure by modifying the strength of the electrostatic interactions between different ferroelectric layers. Through a combination of X-ray diffraction, transmission electron microscopy, and first-principles calculations, the electrostatic coupling between ferroelectric layers is studied, revealing the existence of interfacial layers of reduced tetragonality attributed to inhomogeneous strain and polarization profiles associated with the domain structure. KEYWORDS: Ferroelectric domains, oxide superlattices, electrostatic coupling, electron energy loss spectroscopy

U

that enhance the functional properties of these artificial materials.6 Domains in such layered ferroelectrics are expected to give rise to highly inhomogeneous polarization and structural profiles, which have so far been only predicted theoretically7,8 or inferred by indirect means.9−11 Here, we study the structure and interactions between ferroelectric layers in such polydomain superlattices using XRD, ultrahigh resolution electron energy loss spectroscopy (EELS), and first-principles calculations within density functional theory (DFT). Our findings reveal surprisingly weak electrostatic interlayer coupling and highly inhomogeneous near-interface structures within the PTO layers that point toward domain morphologies exhibiting significant departure from the classic Kittel model.12 When ferroelectric and paraelectric materials are combined in a superlattice structure, any discontinuity in the out-of-plane component of the polarization at the interfaces between the two materials will create large depolarizing fields in the structure and is energetically very costly. The system will therefore respond in one of a number of ways. For sufficiently thin paraelectric layers, the depolarizing field can be eliminated by adopting a uniform polarization throughout the thickness of the superlattice.13−15 The ferroelectric layers are thus electrostatically coupled and the price to

ltrathin ferroelectrics offer a number of possibilities for applications that include increased storage densities for conventional ferroelectric random access memories as well as novel devices such as ferroelectric tunnel junctions.1 This has motivated a tremendous amount of research aimed at understanding ferroelectricity at the nanoscale. The current consensus is that ferroelectricity can be preserved down to arbitrarily small thicknesses as long as depolarizing fields, which arise from the incomplete screening of the spontaneous polarization and act to suppress it, can be sufficiently reduced. These depolarizing fields can be kept at bay by careful design of the metal−ferroelectric interfaces,2,3 but even in the absence of electrodes or other sources of free charge, ultrathin ferroelectrics find ways of preserving their polar state. One possibility is to form regular stripe domain structures with alternating regions of opposite polarization that lead to macroscopic charge neutrality on the surfaces. Ordered ferroelectric domains, only a few nanometers in width, have been observed by X-ray diffraction (XRD) in films of lead titanate as thin as 3 unit cells.4 Studying the properties of such domains is, however, extremely challenging. The ultrathin films required to observe them are generally too conducting for application of macroscopic electric fields and even local scanning probe techniques are pushed to the limits of their resolution by the tiny domain sizes.5 Superlattices composed of ferroelectric and paraelectric layers offer a unique opportunity to investigate the response of such nanodomains to uniform applied fields and in addition to engineer domain structures © 2012 American Chemical Society

Received: January 28, 2012 Revised: April 8, 2012 Published: May 16, 2012 2846

dx.doi.org/10.1021/nl3003717 | Nano Lett. 2012, 12, 2846−2851

Nano Letters

Letter

Figure 1. (a) X-ray intensity along the specular rod of a (6|6)21 superlattice with SrRuO3 electrodes, showing superlattice peaks in red and substrate peaks in blue. (b) A sketch of the superlattice with domains, showing the different periodicities in the system. (c) Reciprocal space map for a (10|10) superlattice close to the (1̅1̅3) reflection of the STO substrate showing diffuse satellites around the superlattice Bragg peaks due to the periodic domain structure.

Figure 2. (a) Transition temperatures for (n|n)m superlattices with different PTO layer thicknesses compared with those of n unit cell thick PTO films from ref 19 (solid line), the coupled limit (dashed line), and bulk (free and strained) Pb0.5Sr0.5TiO3 alloy (placed arbitrarily at n = 0.2). (b) Measured average superlattice out-of-plane lattice parameters c ̅ (squares, right axis) and calculated cP̅ TO (same squares, left axis) compared with those of polydomain PTO thin films from ref 24 (circles, left axis). (c) Domain periodicities along the [100] direction as a function of PTO layer thickness. The blue line shows the scaling observed by Streiffer et al.19 for PTO thin films at T = Tc − 250 K.

paraelectric SrTiO3 (STO) repeated m times on top of singlecrystalline STO substrates. XRD and scanning transmission electron microscopy (STEM) measurements attest to the high quality of the heterostructures with sharp interfaces and welldefined periodicities leading to pronounced superlattice reflections and finite size oscillations in the X-ray diffractograms, and sharp contrast between the layers in the TEM images (see Figures 1 and 3). Coherence with the substrate was confirmed upon examination of the XRD reciprocal space maps and comparison of supelattice and substrate rocking curve widths. Details of sample preparation and typical structural characterization can be found in refs 6 and 21. Accompanying the superlattice peaks labeled 00l (Figure 1a) that appear at Qz = 2πl/(Nc), ̅ where N = (nP + nS), l = 0,1,2... and c ̅ is the average lattice parameter of the system, are diffuse satellite peaks at ΔQxy = ±2π/Λ (see Figure 1c). These peaks arise from the regular 180° ferroelectric stripe domains, sketched in Figure 1b with an in-plane periodicity of Λ ≈ 85 Å in this particular case. The periodic nanodomain structures are very similar to those observed in ultrathin films of PbTiO319,20 but rather different from the much larger and irregular domains found in BiFeO3/SrTiO322 and, most recently, BaTiO3/SrTiO3 superlattices.23 Nanoscale motion of domain walls under applied fields leads to large permittivity enhancements,6 as tiny displacements of domain walls are sufficient to cause large changes in the macroscopic polarization. The domain wall enhancement of the dielectric susceptibility persists over a broad temperature range, eventually freezing out at cryogenic temperatures.

pay for this arrangement is the energy required to polarize the paraelectric component (as well as reduce the polarization in the ferroelectric layers). As the paraelectric layer thickness is increased, however, it becomes progressively more costly to maintain a polarization in it. Thus, for thick paraelectric layers the system must either revert to a paraelectric state or form a polydomain structure with the polarization confined within the ferroelectric layers, which are thus electrostatically decoupled. For stripe domains composed of alternating dipoles pointing along the normal to the film plane (first proposed by Kittel for magnetic systems12 and sometimes referred to as Kittel domains), the costs of the polydomain configuration are: (i) the energy associated with the interfacial stray depolarizing fields that decay exponentially over length scales comparable to the domain width, and (ii) the energy of the domain walls. The equilibrium domain period that minimizes these energy costs scales with the square-root of the ferroelectric’s thickness (Kittel’s law), which in decoupled superlattices simply corresponds to the thickness of the individual ferroelectric layers. The degree of electrostatic coupling between the layers can thus be tuned by modifying the ferroelectric and paraelectric layer thicknesses with profound consequences for the functional properties of the superlattices. In KTaO3/KNbO3 superlattices, the evolution from strong to weak interlayer coupling has been inferred from measurements of the transition temperatures as a function of superlattice periodicity, but the associated changes in domain structures could not be directly probed.16−18 We have fabricated a series of (nP|nS)m superlattices with nP unit cells of ferroelectric PbTiO3 (PTO) and nS unit cells of 2847

dx.doi.org/10.1021/nl3003717 | Nano Lett. 2012, 12, 2846−2851

Nano Letters

Letter

Although the interactions between the ferroelectric layers appear to be relatively weak, analysis of the satellite peaks reveals surprisingly large out-of-plane coherence lengths, indicating a high degree of coherence for the domains over many layers. The mechanism for such domain alignment may involve a combination of the weak but finite electrostatic coupling and the inhomogeneous strain associated with the domain structure. The above measurements show that domain structures in PTO/STO superlattices can be controlled in an elegant way by exploiting Kittel’s law that relies only on simple electrostatics. To gain microscopic insight and direct access to the local distortions expected from the inhomogeneous polarization profiles of the polydomain samples, we resort to STEM studies employing EELS. Recent advances in TEM imaging (in particular spherical aberration corrections) have led to the possibility of imaging individual ionic displacements within a perovskite unit cell with high enough resolution to be able to determine the direction and even magnitude of the local polarization, albeit with some heavy modeling.27−29 We have adopted a different approach that relies on measuring the differences in crystal-field splitting of the Ti d-levels, revealed by analyzing the energy-loss near-edge structures (ELNES) recorded with unit-cell level spatial resolution. The crystal-field splitting of the Ti 3d eg and t2g orbitals is expected to decrease upon reduction in symmetry from the cubic perovskite structure, thus getting progressively smaller with increased polar distortion of the unit cell (see reference spectra in Figure 3b and refs 30−32). This splitting can therefore be used to probe semiquantitatively the ferroelectric distortion within individual layers of the superlattices. Details of the spectrum acquisition parameters and data analysis, as well as the results of ab initio coupled chargetransfer multiplet calculations that can be used to relate the spectral features to structural distortions can be found in ref 33. Figure 3c shows the layer-by-layer variation of the Ti L3 edge splittings across an (18|10)15 superlattice. Within the STO layers, the splitting is rather constant and slightly smaller than that of the substrate, indicating that the STO layers in the superlattice have a lower symmetry than those in the substrate, consistent with the larger lattice parameter cSTO measured in our paraelectric STO films. Deep within the PTO layers the splitting is also constant and much smaller due to the large tetragonality of PTO. On approaching the interface, however, the energy splitting exhibits a gradual change over a length scale of several unit cells. The chemical profile across the interface can be mapped by monitoring the energy loss near the O K edge. Very pronounced differences are observed depending on whether the oxygen is in a Pb or Sr environment.33 It can be seen that any possible roughness or interdiffusion is confined to within ±1 unit cell off the PTO/STO interface and cannot account for the much more gradual decrease of the energy splitting in the PTO layers. Interestingly, a gradual decrease in tetragonality within 4−5 unit cells off the interface, consistent with our observation, was also inferred from synchrotron XRD measurements on polydomain PTO thin films.34 A similar interface layer was also observed in ultrathin Pb(Zr,Ti)O3 capacitors using TEM.35 Given the known presence of domains in the superlattices, it is tempting to attribute this broad interfacial region of reduced tetragonality and polarization to the presence of inhomogeneous depolarizing fields due to the 180° domain structure. For classic Kittel domains, these interfacial stray fields should

In order to investigate the degree of electrostatic coupling between the PTO layers, we focus on a series of superlattices with nP = nS  n and a fixed total thickness of ∼100 nm. Using XRD, we have followed the evolution of the average lattice parameters c,̅ transition temperatures Tc, and domain periods Λ as a function of n. For n ≳ 3−4 unit cells the transition temperatures, shown in Figure 2a are in remarkably good agreement with the values observed for pure PTO films of the corresponding thickness by Streiffer et al.,19 indicating, surprisingly, that the PTO layers are not strongly interacting. For n ≲ 3−4 unit cells, the Tc’s depart from this behavior and approach the theoretical limit for strongly coupled layers. The similar values of Tc expected for Pb0.5Sr0.5TiO3 alloys, however, do not allow us to conclusively rule out possible influence of surface roughness and/or cation intermixing on the one unit cell level. Figure 2b shows the dependence of c ̅ on n. Extracting the lattice parameters of the individual layers is not trivial. However, if the paraelectric STO layers are only weakly polarized (as suggested by the Tc data) their lattice parameter cSTO may be approximated by that of nonpolar STO, allowing the average lattice parameter of the polydomain PTO layers cpoly P̅ TO(n) to be estimated using the relation poly c ̅(n) = xc PTO ̅ (n) + (1 − x)cSTO where x = nP/(nP + nS) = 0.5 is the PTO volume fraction in the superlattice and cSTO = 3.92 Å. The resulting cpoly P̅ TO(n) values are also shown in Figure 2b together with the lattice parameters for polydomain PTO thin films of equivalent thickness measured by Takahashi et al.24 Again, for n ≳ 3−4 unit cells there is excellent agreement between cpoly P̅ TO(n) of the PTO layers in the superlattices and PTO thin films. This shows the selfconsistency of the above analysis and reaffirms that these superlattices seem to behave as if little polarization (and hence additional tetragonality) is induced in the STO layers, consistent with relatively weak electrostatic coupling between the PTO layers. It should be noted that the value of cSTO = 3.92 Å, obtained independently from measurements on 100 nm thick STO films, is slightly larger than the bulk value of 3.905 Å, implying a small degree of nonstoichiometry (see ref 25 and references therein). Detailed electrical characterization, however, revealed that this has little influence on the dielectric properties with bulklike dielectric constants observed at room temperature. Since it is the dielectric constant and conductivity of the STO that are of primary importance for the electrostatic interactions and screening of the polarization, we believe that the augmented lattice parameter of STO plays no significant role here. The graph in Figure 2c shows the variation of domain periodicities along the [100] direction with layer thickness. Just as the Tc and c ̅ values, the domain sizes are in excellent agreement with those observed for thin PTO films.19 For n = 3 a small upturn is observed, whereas for n = 1 and 2 the domains are significanly larger (off scale) implying strong coupling and a uniform polarization throughout the superlattice thickness.15 Domain periodicities are observed along all in-plane directions, consistent with the results of ab initio calculations that reveal only very small energy differences (of order 1 mJ/m2) between the ⟨100⟩ and ⟨110⟩ domain wall orientations.26 An interesting feature of the experimental data is that the weak in-plane anisotropy in domain periodicities slightly favors ⟨100⟩ domain walls over ⟨110⟩ domain walls (not shown) for large n, whereas for small n the reverse is true.

2848

dx.doi.org/10.1021/nl3003717 | Nano Lett. 2012, 12, 2846−2851

Nano Letters

Letter

displacements of ions that lead to in-plane polarization components can develop near the interface with STO, closing the polarization flux.15,40,44−46 Another possibility is a Kittel-like structure but with a gradual polarization decay toward zero at the interface. This pumps the bound charges ρ = ▽·P from the interface to the near-interface layer, reducing the maximum depolarizing field (and also eliminating the need for domain branching).47 Polarization decay at surfaces of ultrathin films has also been observed by Jia et al.27 in PZT samples and by Eberg et al.48 in PTO samples where domains were not reported, and thus, in general, the presence of domains may not necessarily be a prerequisite for interface layer formation. The true domain structure in our case is likely to be a combination of polarization rotation and decay near the interfaces, as revealed by first principles calculations performed within the local density approximation to DFT using the SIESTA code.49 The simulated supercells consisted n unit cells of PTO and n unit cells of STO stacked along the [001] direction and replicated 12 times along [100], thus imposing a domain periodicity of 12 unit cells. Full details of the calculations can be found in ref 26. The relaxed structure displays highly inhomogeneous polarization and structural profiles with significant polarization variation both along the inplane and out-of plane directions within the PTO, as well as large in-plane atomic displacements near the domain walls, as shown in the inset of Figure 4. Figure 4 also shows the root-

Figure 3. (a) High-angle annular dark-field (HAADF) STEM image of an (18|10)15 superlattice. (b) Reference ELNES at the Ti L2 and L3 edges collected from a 12 nm PTO layer and a STO substrate. (c) 256 individual Ti L2,3 spectra with an energy resolution of 0.5 eV and energy dispersion of 0.05 eV/channel were recorded along the blue line in the HAADF image above and used to extract the spatial profile of the Ti t2g−eg splittings (blue points). The chemical profiles, shown as green and red lines, were obtained from 256 spectra collected at the O K edge (energy resolution = 0.6 eV, dispersion = 0.2 eV/channel) along the yellow line in the HAADF image. The two shaded gray curves show the HAADF intensities recorded simultaneously with the respective EELS measurements.

penetrate into both the PTO and the STO layers, decaying exponentially over length scales on the order of the domain size16,36(Λ/2 ≈ 55 Å for the (18|10)15 superlattice). Figure 3c, however, indicates that there is no significant variation in the structure of the paraelectric STO layers. Although, at present, we cannot conclusively rule out the classic Kittel model experimentally due to difficulties in resolving small magnitudes of polarization in STO, theoretical calculations point toward more complex domain morphologies, as discussed below. One possibility is the development of in-plane polarization components near the interfaces akin to the flux closure domains found in ferromagnets. Although perfect flux closure domains (▽·P = 0, E = 0) in highly anisotropic ferroelectrics such as PTO would lead to enormous disclination stresses at the ferroelastic domain boundaries37 and are thus only possible under very special circumstances,38 in ultrathin ferroelectrics significant polarization rotation can occur, confining the polarization flux within the ferroelectric layers and suppressing the stray interfacial fields associated with Kittel-like domains. Such polarization rotations have been predicted theoretically for thin Pb(Zr,Ti)O3 films39 and BaTiO3 capacitors40 and recently observed for the first time using aberration corrected TEM.41,42 The propensity for confining the polarization flux within the PTO, despite the availability of the nearby highly polarizable STO layers or even metallic SrRuO3 layers, is also in accord with the predicted polydomain ground state of SrRuO3/ PTO/SrRuO3 capacitors.43 Unlike for BaTiO3, rotations of the polarization vector are less costly in PTO and hence in-plane

Figure 4. The rms polarization and average lattice parameter for each (001) layer of a (6|6)∞ superlattice calculated from first principles. The inset shows the local dipole magnitudes and orientations.

mean-squared (rms) polarization and average tetragonalities for each (001) layer of a (6|6) superlattice. In agreement with the EELS data, a gradual decrease in polarization and tetragonality is observed near interfaces within the PTO layers; note that our EELS measurements are only sensitive to the distortions on the Ti sites. By contrast, the polarization and tetragonality are rather uniform throughout the STO layers. The rms polarization in STO was found to decrease with increasing layer thickness n, dropping from ∼26 μC/cm2 for a (3|3) superlattice to ∼17 μC/cm2 for a (6|6) structure. Although such values of polarization can be compatible with the experimental data in Figure 3, the difficulty in disentangling the effects of polarization and the augmented lattice parameter of our sputter-deposited STO films on the Ti L2,3 energy splittings does not, at present, allow us to make any firm conclusions about the magnitude of polarization within the STO layers. 2849

dx.doi.org/10.1021/nl3003717 | Nano Lett. 2012, 12, 2846−2851

Nano Letters

Letter

(5) Thompson, C.; Fong, D. D.; Wang, R. V.; Jiang, F.; Streiffer, S. K.; Latifi, K.; Eastman, J. A.; Fuoss, P. H.; Stephenson, G. B. Appl. Phys. Lett. 2008, 93, 182901. (6) Zubko, P.; Stucki, N.; Lichtensteiger, C.; Triscone, J.-M. Phys. Rev. Lett. 2010, 104, 187601. (7) Li, Y. L.; Hu, S. Y.; Tenne, D.; Soukiassian, A.; Schlom, D. G.; Chen, L. Q.; Xi, X. X.; Choi, K. J.; Eom, C. B.; Saxena, A.; Lookman, T.; Jia, Q. X. Appl. Phys. Lett. 2007, 91, 252904. (8) Lee, D.; Behera, R. K.; Wu, P.; Xu, H.; Li, Y. L.; Sinnott, S. B.; Phillpot, S. R.; Chen, L. Q.; Gopalan, V. Phys. Rev. B 2009, 80, 060102. (9) Jiang, A.; Scott, J.; Lu, H.; Chen, Z. J. Appl. Phys. 2003, 93, 1180− 1185. (10) Tenne, D. A.; et al. Science 2006, 313, 1614−1616. (11) Bruchhausen, A.; Fainstein, A.; Soukiassian, A.; Schlom, D. G.; Xi, X. X.; Bernhagen, M.; Reiche, P.; Uecker, R. Phys. Rev. Lett. 2008, 101, 197402. (12) Kittel, C. Phys. Rev. 1946, 70, 965−971. (13) Neaton, J. B.; Rabe, K. M. Appl. Phys. Lett. 2003, 82, 1586− 1588. (14) Dawber, M.; Lichtensteiger, C.; Cantoni, M.; Veithen, M.; Ghosez, P.; Johnston, K.; Rabe, K. M.; Triscone, J.-M. Phys. Rev. Lett. 2005, 95, 177601. (15) Aguado-Puente, P.; García-Fernández, P.; Junquera, J. Phys. Rev. Lett. 2011, 107, 217601. (16) Specht, E. D.; Christen, H.-M.; Norton, D. P.; Boatner, L. A. Phys. Rev. Lett. 1998, 80, 4317−4320. (17) Sepliarsky, M.; Phillpot, S. R.; Wolf, D.; Stachiotti, M. G.; Migoni, R. L. Phys. Rev. B 2001, 64, 060101. (18) Stephanovich, V. A.; Luk’yanchuk, I. A.; Karkut, M. G. Phys. Rev. Lett. 2005, 94, 047601. (19) Streiffer, S. K.; Eastman, J. A.; Fong, D. D.; Thompson, C.; Munkholm, A.; Ramana Murty, M. V.; Auciello, O.; Bai, G. R.; Stephenson, G. B. Phys. Rev. Lett. 2002, 89, 067601. (20) Takahashi, R.; Dahl, O. .; Eberg, E.; Grepstad, J. K.; Tybell, T. J. Appl. Phys. 2008, 104, 064109. (21) Dawber, M.; Stucki, N.; Lichtensteiger, C.; Gariglio, S.; Ghosez, P.; Triscone, J.-M. Adv. Mater. 2007, 19, 4153. (22) Ranjith, R.; Lüders, U.; Prellier, W.; Da Costa, A.; Dupont, I.; Desfeux, R. J. Magn. Magn. Mater. 2009, 321, 1710−1713. (23) Kathan-Galipeau, K.; Wu, P.; Li, Y.; Chen, L.-Q.; Soukiassian, A.; Xi, X.; Schlom, D. G.; A., B. D. ACS Nano 2011, 5, 640−646. (24) Takahashi, R.; Grepstad, J. K.; Tybell, T.; Matsumoto, Y. Appl. Phys. Lett. 2008, 92, 112901. (25) Brooks, C. M.; Kourkoutis, L. F.; Heeg, T.; Schubert, J.; Muller, D. A.; Schlom, D. G. Appl. Phys. Lett. 2009, 94, 162905. (26) Aguado-Puente, P.; Junquera, J. arXiv:1202.5481. (27) Jia, C. L.; Nagarajan, V.; He, J.-Q.; Houben, L.; Zhao, T.; Ramesh, R.; Urban, K.; Waser, R. Nat. Mater. 2007, 6, 64−69. (28) Jia, C. L.; Mi, S.-B.; Urban, K.; Vrejoiu, I.; Alexe, M.; Hesse, D. Nat. Mater. 2008, 7, 57−61. (29) Chang, H. J.; Kalinin, S. V.; Morozovska, A. N.; Huijben, M.; Chu, Y.-H.; Yu, P.; Ramesh, R.; Eliseev, E. A.; Svechnikov, G. S.; Pennycook, S. J.; Borisevich, A. Y. Adv. Mater. 2011, 23, 2474−2479. (30) de Groot, F. M. F.; Fuggle, J. C.; Thole, B. T.; Sawatzky, G. A. Phys. Rev. B 1990, 41, 928−937. (31) Sefat, A. S.; Amow, G.; Wu, M.-Y.; Botton, G. A.; Greedan, J. J. Solid State Chem. 2005, 178, 1008−1016. (32) Zhang, J.; Visinoiu, A.; Heyroth, F.; Syrowatka, F.; Alexe, M.; Hesse, D.; Leipner, H. S. Phys. Rev. B 2005, 71, 064108. (33) Torres-Pardo, A.; Gloter, A.; Zubko, P.; Jecklin, N.; Lichtensteiger, C.; Colliex, C.; Triscone, J.-M.; Stephan, O. Phys. Rev. B 2011, 84, 220102(R), arXiv:1112.4953. (34) Fong, D. D.; Cionca, C.; Yacoby, Y.; Stephenson, G. B.; Eastman, J. A.; Fuoss, P. H.; Streiffer, S. K.; Thompson, C.; Clarke, R.; Pindak, R.; Stern, E. A. Phys. Rev. B 2005, 71, 144112. (35) Nagarajan, V.; Junquera, J.; He, J. Q.; Jia, C. L.; Waser, R.; Lee, K.; Kim, Y. K.; Baik, S.; Zhao, T.; Ramesh, R.; Ghosez, P.; Rabe, K. M. J. Appl. Phys. 2006, 100, 051609.

Other possible origins of the observed interface layers also have been considered. Oxygen vacancy accumulation, used to explain similar surface layers in PZT films,50 seems unlikely to be responsible in this case since screening by oxygen vacancies would not explain the existence of the domains in the first place. Interfacial space charge layers that form due to differences in chemical potentials between the two materials can also lead to polarization suppression. However, given the symmetry of the system here, the electric fields at two neighboring interfaces must point in opposite directions and, thus, within any particular domain the polarization would be suppressed at one interface but enhanced at the other. It is therefore not obvious how space charge could explain the symmetric polarization decay at all interfaces. In summary, we have investigated the degree of electrostatic coupling in PTO/STO superlattices. The weak interactions between the ferroelectric layers result in domain structures that are primarily controlled by the thickness of the individual PTO layers, but which nevertheless remain coherent over many superlattice periods. EELS measurements revealed the presence of broad interfacial layers with reduced tetragonality and polarization extending over 5−6 unit cells into the PTO layers. First principles calculations suggest that the observed interface layers correspond to the inhomogeneous strain and polarization profiles associated with the ferroelectric nanodomains present in the superlattices.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

We thank Professor I. Luk’yanchuk for illuminating discussions made possible by the Leverhulme Trust and Marco Lopes for technical assistance. The authors are grateful for funding from the Swiss National Science Foundation through the NCCR MaNEP and division II, and the EU project OxIDes. P.A.P. and J.J. thankfully acknowledge financial support by the Spanish Ministry of Science and Innovation through the MICINN Grant FIS2009-12721-C04-02, by the Spanish Ministry of Education through the FPU fellowship AP2006-02958 (P.A.P.), and the computer resources, technical expertise, and assistance provided by the Red Española de Supercomputación. A.T.P., A.G. and O.S. acknowledge financial support from the EU Framework 6 program under a contract for an Integrated Infrastructure Initiative (reference 026019 ESTEEM). A.T.P. is also grateful for funding from the Spanish Ministry of Education and Science through the MEC postdoctoral fellowship EX2009-0156.

(1) Garcia, V.; Fusil, S.; Bouzehouane, K.; Enouz-Vedrenne, S.; Mathur, N. D.; Barthélémy; Bibes, M. Nature 2009, 460, 81. (2) Chang, L.-W.; Alexe, M.; Scott, J. F.; Gregg, J. M. Adv. Mater. 2009, 21, 4911−4914. (3) Stengel, M.; Vanderbilt, D.; Spaldin, N. A. Nat. Mater. 2009, 8, 392−397. (4) Fong, D. D.; Stephenson, G. B.; Streiffer, S. K.; Eastman, J. A.; Auciello, O.; Fuoss, P. H.; Thompson, C. Science 2004, 304, 1650− 1653. 2850

dx.doi.org/10.1021/nl3003717 | Nano Lett. 2012, 12, 2846−2851

Nano Letters

Letter

(36) Hinazumi, H.; Hosoya, M.; Mitsui, T. J. Phys. D: Appl. Phys. 1973, 6, L21. (37) Catalan, G.; Seidel, J.; Ramesh, R.; Scott, J. F. Rev. Mod. Phys. 2012, 84, 119−156. (38) McQuaid, R.; McGilly, L.; Sharma, P.; Gruverman, A.; Gregg, J. M. Nat. Commun. 2011, 2, 404. (39) Prosandeev, S.; Bellaiche, L. Phys. Rev. B 2007, 75, 172109. (40) Aguado-Puente, P.; Junquera, J. Phys. Rev. Lett. 2008, 100, 177601. (41) Jia, C.-L.; Urban, K. W.; Alexe, M.; Hesse, D.; Vrejoiu, I. Science 2011, 331, 1420−1423. (42) Nelson, C. T.; Winchester, B.; Zhang, Y.; Kim, S.-J.; Melville, A.; Adamo, C.; Folkman, C. M.; Baek, S.-H.; Eom, C.-B.; Schlom, D. G.; Chen, L.-Q.; Pan, X. Nano Lett. 2011, 11, 828−834. (43) Aguado-Puente, P.; Junquera, J. unpublished. (44) Lai, B.-K.; Ponomareva, I.; Naumov, I. I.; Kornev, I.; Fu, H.; Bellaiche, L.; Salamo, G. J. Phys. Rev. Lett. 2006, 96, 137602. (45) Lai, B.-K.; Ponomareva, I.; Kornev, I. A.; Bellaiche, L.; Salamo, G. J. Phys. Rev. B 2007, 75, 085412. (46) Hong, J.; Vanderbilt, D. Phys. Rev. B 2011, 84, 115107. (47) Luk’yanchuk, I. A.; Lahoche, L.; Sené, A. Phys. Rev. Lett. 2009, 102, 147601. (48) Eberg, E.; van Helvoort, A. T. J.; Takahashi, R.; Gass, M.; Mendis, B.; Bleloch, A.; Holmestad, R.; Tybell, T. J. Appl. Phys. 2011, 109, 034104. (49) Soler, J. M.; Artacho, E.; Gale, J. D.; García, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. J. Phys.: Condens. Matter 2002, 14, 2745. (50) Chisholm, M. F.; Luo, W.; Oxley, M. P.; Pantelides, S. T.; Lee, H. N. Phys. Rev. Lett. 2010, 105, 197602.

2851

dx.doi.org/10.1021/nl3003717 | Nano Lett. 2012, 12, 2846−2851