pubs.acs.org/NanoLett
Low-Symmetry Phases in Ferroelectric Nanowires L. Louis,†,‡ P. Gemeiner,† I. Ponomareva,§ L. Bellaiche,‡ G. Geneste,† W. Ma,|,⊥ N. Setter,| and B. Dkhil*,† †
Laboratoire Structures, Proprie´te´s et Mode´lisation des Solides, CNRS-UMR8580, Ecole Centrale Paris, Grande voie des vignes, 92290 Chaˆtenay-Malabry, France, ‡ Physics Department, University of Arkansas, Fayetteville, Arkansas 72701, § Department of Physics, University of South Florida, Tampa, Florida, 33620, and | Ceramics Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland ABSTRACT Ferroelectric nanostructures have recently attracted much attention due to the quest of miniaturizing devices and discovering novel phenomena. In particular, studies conducted on two-dimensional and zero-dimensional ferroelectrics have revealed original properties and their dependences on mechanical and electrical boundary conditions. Meanwhile, researches aimed at discovering and understanding properties of one-dimensional ferroelectric nanostructures are scarce. The determination of the structural phase and of the direction of the polarization in one-dimensional ferroelectrics is of technological importance, since, e.g., a low-symmetry phase in which the polarization lies away from a highly symmetric direction typically generates phenomenal dielectric and electromechanical responses. Here, we investigate the phase transition sequence of nanowires made of KNbO3 and BaTiO3 perovskites, by combining X-ray diffraction, Raman spectroscopy, and first-principles-based calculations. We provide evidence of a previously unreported ferroelectric ground state of monoclinic symmetry and the tuning of the polarization’s direction by varying factors inherent to the nanoscale. KEYWORDS Ferroelectric nanowires, phase transition, depolarizing field, X-ray and Raman analysis, effective Hamiltonian
T
he discovery of new phenomena such as giant piezoelectricity1,2 or new pressure-induced ferro electricity3,4 and the continuous trend in miniaturization in devices have led to a flurry of recent investigations on ferroelectric materials.5-7 Actually, such latter compounds, especially in low-dimensional forms, constitute a rich playground for exploring new physical properties and novel device concepts. Among the low-dimensional nanostructures, ferroelectric nanowires may have the greatest potential for both future device applications and novel device architectures.8-11 As a matter of fact, potential applications of ferroelectric nanowires are truly impressive and broad, including data storage memories,11 energy harvesting devices,12 nanoelectromechanical systems13 or nanometerscale photonics.14 Besides, the recent advances in synthesizing one-dimensional nanomaterials (including perovskite oxides) by different chemical methods and organizing them in different arrays have led to an explosion of interest in both applied and fundamental researches in the past few years.15 However, in order to reliably integrate nanowires into electronic components in a controllable manner, a thorough understanding of their relevant physical properties is required. The crucial parameter for the performance of ferroelectric nanowire-based devices is the polarization. Inter-
estingly, this latter fundamental property is very sensitive, in both magnitude and direction, to several factors, including the temperature, mechanical constrains, applied electric field, and, especially in case of nanostructures, the finite size and associated depolarizing field. Indeed, it was demonstrated both theoretically9,10 and experimentally16 that the polarization disappears in ferroelectric nanowires when their diameters reach a critical value of around 1 nm, such disappearance being due to the depolarizing field originating from an incomplete compensation of the polarizationinduced surface charges. However, a better screening of the surface charges can be ensured by either using metallic electrodes or molecular adsorbates (which can even be more efficient than the metallic electrodes).16 Interestingly, several different dipolar configurations can exist, depending on the amount of screened charges. For instance, the polarization has been reported to be either axial (along the main, long axis of the wire) or transverse (i.e., perpendicular to the long axis) depending on the quality of such screening.8 Besides, the observed difficulties to completely pole the nanowire along the axial direction17,18 may be related to the existence of other configurations for which the polarization would have components parallel and perpendicular to the axial direction. However, such possible coexistence has never been undoubtedly reported by either experiment or theory, to the best of our knowledge. One possible reason behind this paucity of knowledge resides in the limitations, or even lack, of current experimental and theoretical tools able to investigate ferroelectric nanostructures. For instance, the com-
* To whom correspondence should be addressed,
[email protected]. ⊥
Present address: Department of Physics, Shantou University, Shantou, Guangdong, 515063, People’s Republic of China. Received for review: 10/16/2009 Published on Web: 03/15/2010 © 2010 American Chemical Society
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FIGURE 1. Experimental X-ray diffraction (XRD) results. At the top, the XRD data of a classical powder of KNbO3 bulk for different temperatures. (a), (b), (c), and (d) correspond to (200) Bragg peaks for 800 K (cubic state), 500 K (tetragonal state), 250 K (orthorhombic state), and 90 K (rhombohedral state), respectively. At the bottom, the XRD data obtained for KNbO3 nanowires (50 nm in diameters and 5 µm in length), showing the (200) Bragg peaks at different temperatures. (e), (f), (g), and (h) correspond to (200) Bragg peaks for 800 K (cubic-like state), 500 K (tetragonal-like state), 280 K (orthorhombic state), and 90 K (monoclinic state), respectively.
monly used experimental tool to measure polarization in ferroelectrics nanowires, that is, the piezo-force microscopy (PFM), can alter the polarization via mechanical forces and variations of the electrostatic forces under the dc voltages between the tip and the surface of the nanowire.19 Similarly, it is a nontrivial task to accurately simulate low-dimensional ferroelectrics, especially at finite temperature. Here, we investigate the phase transition sequence of KNbO3 and BaTiO3 ferroelectric nanowires as a function of temperature by using X-ray diffraction, Raman spectroscopy, and a first-principles-based technique. We provide evidence that these confined structures exhibit three different ferroelectric phases, each corresponding to a different direction of the polarization, including an unexpected monoclinic ground state that possesses both axial and transverse components of the polarization. Our work further shows that playing with the factors inherent to the nanoscale leads to a precise control of the polarization’s direction within the nanowire and therefore can yield an optimization of ferroelectric, dielectric, piezoelectric, or optical properties (since these latter quantities are known to be strongly dependent on the polarization’s orientation, and even to be enhanced in a monoclinic phase). These results therefore open new perspectives in the wide research field of nanowires and in using ferroelectric 1D structures in future devices. In the case of the classical BaTiO3 or KNbO3 ferroelectric systems, the phase sequence of the bulk material is as follows. At high temperature, these systems are both centrosymmetric and thus paraelectric. The lost of the center © 2010 American Chemical Society
of inversion of symmetry occurs at the Curie temperature, Tc, leading to the occurrence of a cubic Pm-3m-to-P4mm tetragonal phase transition and to the formation of a polarization along a 〈001〉 pseudocubic direction axis. These two bulks further undergo two other phase transitions when decreasing the temperature below Tc: first from the P4mm phase to a Amm2 orthorhombic phase where the polarization lies along a 〈110〉 direction, and finally from the Amm2 state to a R3m rhombohedral phase where the polarization is now along a 〈111〉 direction.20 It is legitimate to wonder if crystalline nanowires adopt a phase transition sequence that is qualitatively different from that of bulk materials, like twodimensional thin films6 or zero-dimensional nanoparticles21 do. However, no data concerning the full evolution of the structure as a function of temperature have ever been reported in ferroelectric nanowires, to the best of our knowledge. For instance, the remarkable work of ref 16 is rather “solely” devoted to the paraelectric-to-ferroelectric phase transition in BaTiO3 nanowires. It is demonstrated there, by using noncontact electrostatic force microscopy perpendicular to the main axis of the wire, that Tc is reduced as the nanowire diameter dnw decreases, following a 1/dnw scaling law. Actually, although local probes like electron and atomic force microscopy’s are elegant tools to study nanostructures, these methods pose significant challenges in practice for investigating phase transition sequences since it is difficult to achieve a good enough resolution and to work in a wide temperature range. On the other hand, X-ray diffraction and Raman spectroscopy are very sensitive and 1178
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FIGURE 2. Experimental Raman spectra results. Raman spectrum as a function of wavenumber (cm-1), obtained at different temperatures for (a) a classical bulk powder and (b) nanowires of KNbO3. Note that at 80 K in the nanowire sample, it is difficult to make any assignment as the group-subgroup relationships predict that going toward lower symmetry the degenerated phonon modes should split into A′ x A′′ modes whose wavenumber position cannot be determined a priori.
accurate techniques that can probe the structure at any temperature and without any external constraint. Here, both of these techniques are used to determine the phase transition sequence of a powder of KNbO3 nanowires synthesized hydrothermally.22 Note that these nanowires, which have a mean diameter of about 50 nm and a mean length of about 5 µm along the [001]-pseudocubic direction, are found to exhibit the perovskite crystal structure. Panels a-d of Figure 1 show the diffraction patterns as a function of temperature for selected (200) pseudocubic Bragg peaks for the KNbO3 bulk. These peaks clearly indicate that the KNbO3 bulk sample exhibits the three expected phase transitions: from the cubic to tetragonal phase (at around 700 K) by the splitting of the (200)C cubic Bragg peak into (002)T and (200)T tetragonal peaks (Figure 1a,b), then from the tetragonal to orthorhombic phase (at around 490 K) by the occurrence of the (022)O and (200)O orthorhombic © 2010 American Chemical Society
peaks (Figure 1c), and finally from the orthorhombic to rhombohedral phase (at around 250 K) by the recovering of a single (200)R rhombohedral Bragg peak (Figure 1d). All these phase transitions are found to be of first order, as evidenced by the coexistence of two adjacent phases within a well-defined temperature range. In parallel to the bulk system, panels e-h of Figure 1 display the corresponding temperature evolution for KNbO3 nanowires. The nanometric size of the wires is reflected in the Bragg reflection through a broadening of the peaks. By decreasing the temperature, the (200)C cubic Bragg peak splits into (002)T and (200)T at roughly the same Curie temperature (in the limit of our measurement, i.e., 20 K) than in the bulk (Figure 1e,f). The ratio intensity is also similar to that of the bulk, indicating a polydomain state. It is worth mentioning that the (002)T peak, which is representative of the c axis along which the polarization lies, has a broad width that corre1179
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sponds to a size of 29 nm (as obtained by the Scherrer formula). Such size is of the same order as the mean diameter of the nanowires, which thus strongly suggests that the polarization in the tetragonal-like phase is perpendicular to the main axis of the wire, in good agreement with previous polarization measurements.23 The tetragonal strain (c/a -1) at 500 K is weaker in the nanowire (1.22%) than in the bulk (1.70%) sample, which likely implies that the polarization in the nanowire is reduced by around 15% with respect to the one of the bulk at 500 K. A tetragonal-like to orthorhombic phase transition is also found to take place in the nanowires at a critical temperature that is close to that of the bulk. However, when further decreasing the temperature down to 80 K, i.e., far below the orthorhombic-torhombohedral transition point of the bulk, the single peak expected in the rhombohedral phase does not occur. Instead of that single peak, a pattern similar to the orthorhombic phase is found. Actually, such unexpected feature exhibits an additional intensity, as shown by an arrow in Figure 1h. This supplementary intensity appears around 250 K, which is the temperature corresponding to the orthorhombic-torhombohedral transition in the bulk. Therefore, it can either be explained by larger (bulklike) nanowires that transform into a rhombohedral phase or by another symmetry for our mean nanowires. To shed some light on this low temperature state, we display in Figure 2 Raman spectra obtained on bulk and nanowires of KNbO3. As one can see in Figure 2a, the rhombohedral phase of the bulk has a clear and specific spectrum with distinctive vibrational modes. Such a feature is never found in the nanowires. The final (i.e., at 80 K) Raman spectrum is rather close to an orthorhombiclike one in the nanowires. In order to better describe this “mysterious” structure, we also performed a Rietveld refinement on a full X-ray diffraction pattern recorded at 8 K (see Figure 3). The (200)-like peak of the nanowires is not single down to 8 K, confirming once again that the real ground state is clearly not rhombohedral. Different possible solutions were tried for the Rietveld refinement. This includes the pure Amm2 state, the mixed Amm2 + R3m phase, and lower symmetries such as monoclinic Pm and Cm space groups. The best refinement is obtained with the monoclinic Cm phase. For comparison, the result of the refinement for both Amm2 + R3m and Cm are shown in parts a and b of Figure 3, respectively. It is clear that the agreement factors (Rwp ) 6.79%, RB ) 4.91% against Rwp ) 7.29%, RB ) 5.42%) and the mismatch between the calculated and measured patterns unambiguously demonstrate that the low temperature ground state is monoclinic. This unexpected monoclinic phase is of great interest as it is related to high piezoelectric responses.24,25 Indeed, in such a phase, the polarization vector is no longer constrained to lie along a symmetry axis, as in the rhombohedral, orthorhombic, or tetragonal structures, but instead can rotate within a monoclinic plane. On the basis of the Rietveld refinement results, we extracted a polarization value of 0.2137 C/m2 and close © 2010 American Chemical Society
FIGURE 3. Obtained Rietveld refinement of the (200) Bragg diffraction peak of the KNbO3 nanowires at 8 K with two different symmetries: (a) an orthorhombic Amm2 state mixed with a rhombohedral R3m phase and (b) a monoclinic Cm phase. The polarization is localized within a (1-10)-type plane in between the [110] orthorhombic and the [111] rhombohedral directions, implying that the polarization moves away from the [111] bulk direction (and toward the [110] direction) when decreasing the diameter of the nanowire. Note that the decrease of ∼0.5% in the agreement factors is significant in the already weak values for the mix solution Amm2 + R3m.
to the [225]-direction which is around 25° away from the [111]-rhombohedral axis. Interestingly, this newly discovered phase in the nanowires can store a big amount of strain energy and therefore might explain the huge strain recently reported.26 1180
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FIGURE 4. Theoretical results for BaTiO3. Left: Cartesian components of the polarization Px, Py, and Pz (in C/m2) as a function of temperature in BaTiO3 with rectangular cross section of 7.2 × 7.2 Å2 (as mimicked by a 18 × 18 × 12 supercell) under (a) perfect SC, where β ) 1, and partial screening (b) with β ) 0.97, and (c) with β ) 0.96 conditions. The infinite direction of the wire is along the z axis. The x, y, and z axes are chosen along the pseudocubic [100], [010], and [001] directions, respectively. Right: Calculated XRD (200) Bragg peaks for BaTiO3 nanowires at 5 K under (d) perfect SC, for which β ) 1, and partial screening with (e) β ) 0.97, and with (f) β ) 0.96. The solid lines show such predicted XRD peaks while Figure 4e also displays the experimentally obtained peaks for KNbO3 nanowires at 10 K by means of dot symbols.
In order to gain a deeper understanding of such ground state and phase transition sequence, we decided to investigate stress-free nanowires from a first-principles-based effective Hamiltonian. The simulated nanowires are made of BaTiO3 rather than KNbO3 because an effective Hamiltonian is in our possession for the former material27,28 unlike for the latter one, while both compounds display the same phase transition sequence in the bulk. The studied system is a freestanding BaTiO3 nanowire having Ba-O terminated surfaces, with a cubic cross sections of 72 × 72 Å2 (in the (x,y) plane, with the x- and y-directions lying along the © 2010 American Chemical Society
pseudocubic [100] and [010] directions, respectively) and an infinite length along the z direction (with the z-axis being parallel to the pseudocubic [001] direction). Such a system is practically mimicked by a 18 × 18 × 12 supercell, that is finite along the x- and y-axes and that is periodic along the z-axis. The effective Hamiltonian is used to determine the local dipoles (and the corresponding atomic positions) in each of the five-atom cells. Let us first focus on how electrical boundary conditions can affect the structural properties of the nanowire. As a result, the screening parameter β (see section on Methods) 1181
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was varied from 1 to 0.96 representing the progression from ideal short-circuit (SC) electrical boundary conditions to a more realistic screening situation. The evolutions of the Cartesian components of the polarization (Px, Py, and Pz, along the x, y, and z axes, respectively) as a function of temperature for three chosen β values are shown in Figure 4. Under perfect SC conditions (see Figure 4a), the phase transition sequence starts with a paraelectric phase, where Px ) Py ) Pz ) 0, at high temperature. Such a paraelectric state transforms into a tetragonal-like phase at 380 K, where Px ) Pz ) 0 and Py > 0, indicating that the polarization in the tetragonal-like state is indeed perpendicular to the main axis, as consistent with our X-ray data, then a transition from the tetragonal-like state to an orthorhombic phase, for which Pz ) 0 and Px ) Py > 0, occurs at 150 K, and finally an orthorhombic-to-monoclinic transition, where Px ) Py > Pz > 0 is found to happen at 50 K. Interestingly, the rhombohedral-like phase, for which Px ) Py ) Pz is expected, is not reached in these calculations. Instead of such a state, a monoclinic Cm phase is obtained, which confirms our experimental findings. Note that the facts (i) that the polarization in the tetragonal-like phase is perpendicular to the main axis and (ii) that the polarization in the monoclinic phase (for β ) 1) has a z-component that is smaller than its x- and y-components both originate from a gain in energy related to short-range effects along finite directions. Furthermore, as β decreases with respect to its ideal SC-value of 1, the components of the polarization vector evolve from Pz < Px ) Py (β ) 1, Figure 4a), then Pz > Px ) Py (β ) 0.97, Figure 4b) and finally Pz . Px ) Py (β ) 0.96, Figure 4c) in the monoclinic Cm state. Such evolution characterizes a rotation of the polarization vector within the monoclinic phase, when the residual depolarizing field becomes bigger. Note also that panels a-c of Figure 4 indicate that the transition from the paraelectric-to-tetragonal-like state (for which the polarization is along the y-axis) is particularly sensitive to the screening parameter. Such a feature, as well as the fact that Pz becomes larger than Px ) Py in the monoclinic phase when β decreases, are consistent with the fact that the residual depolarizing field can only lie along nonperiodic directions (such as the x and y directions) and not along the main, infinite axis of the nanowires. On the basis of the simulated output data, we also computed X-ray peaks at low temperature (namely, 5 K) for our different β values (see panels d-f of Figure 4). Interestingly, the theoretical X-ray data of Figure 4e, which corresponds to β ) 0.97, remarkably agrees with the experimental ones, suggesting that a small, residual depolarizing field may exist in the grown samples. We also numerically found (not shown here) that the size of the cross section of the nanowires strongly influences the direction of the polarization in the low-temperature Cm phase. In other words, one can generate a specific direction for such polarization (and thus optimize physical properties) © 2010 American Chemical Society
by playing with the factors inherent to the nanoscale (e.g., boundary conditions and size). In summary, experimental techniques and a first-principles-derived scheme were used to determine the phase transition sequence, in general, and reveal the unexpected low-symmetric (monoclinic) ground state, in particular, of KNbO3 and BaTiO3 1D nanostructures. We further discovered that the direction of the polarization in this monoclinic ground state (as well as the Curie temperature) is dramatically altered by the magnitude of the residual depolarizing field and by the nanostructures’ size, implying that one can “easily” tune physical properties of these low-dimensional structures. Our observations and calculations thus demonstrate the versatility of the nanoworld and the existence of seemingly surprising effects of large technological promise there. Acknowledgment. This work is supported by NSF Grants DMR 0701558, DMR-0404335, and DMR-0080054 (C-SPIN), ONR Grants N00014-04-1-0413, N00014-08-1-0915 and N00014-07-1-0825, and DOE grant DE-SC0002220. Some computations were made possible thanks to the MRI NSF grant 0722625 and to a Challenge grant from HPCMO of the U.S. Department of Defense. This work is also supported by the COST 539 action. LL, LB and BD thank JH Schmitt for support by fellowships from Ecole Centrale Paris. Supporting Information Available. Descriptions of the X-ray technique and Rietveld refinement, Raman spectroscopy technique, and first-principle effective Hamiltonian. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1)
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