Colloidal synthesis

Early attempts at the synthesis of ferroelectric nanomaterials employed colloidal techniques involving decomposition of reactive organometallic precursors in the presence of long-chain surfactant molecules that passivate particle surfaces and prevent aggregation in solution. Early work by O'Brien et al. demonstrated the synthesis of monodisperse BaTiO₃ nanocrystals via hydrolytic decomposition of a bimetallic alkoxide precursor in the presence of oleic acid ligands (Fig. 2).^[Reference O'Brien, Brus and Murray^12] A subsequent study by Urban et al. demonstrated the synthesis of single-crystal nanowires of both BaTiO₃ and the incipient ferroelectric SrTiO₃ through hydrolysis and subsequent high-temperature growth using a simpler bimetallic alkoxide (Fig. 2).^[Reference Urban, Yun, Gu and Park^13] The synthesis of the binary semiconductor ferroelectric GeTe has recently been demonstrated through reaction of Ge(II) precursors with a trioctylphosphine–Te complex in the presence of trioctylphosphine and dodecanethiol stabilizers, and weak ferroelectric ordering has also been detected in nanorods of the ferroelectric semiconductor Sb₂S₃.^[Reference Polking, Zheng, Ramesh and Alivisatos^14, Reference Varghese, Barth, Keeney, Whatmore and Holmes^15] Despite these notable successes, the synthesis of monodisperse, soluble ferroelectric nanoparticles by standard organic-phase colloidal methods remains enormously challenging. These challenges may be due in part to the paucity of bimetallic alkoxide precursors for hydrolytic synthesis and the presence of a spontaneous polarization, which may drive aggregation in solution.

Figure 2.

Single-crystal BaTiO₃ nanomaterials synthesized via organic-phase colloidal chemistry. (a) Transmission electron microscope (TEM) images of monodisperse BaTiO₃ nanospheres capped with oleic acid ligands synthesized by hydrolysis of a bimetallic alkoxide precursor. Reproduced with permission from Ref. Reference O'Brien, Brus and Murray12, copyright 2001 American Chemical Society. (b) Single-crystal BaTiO₃ nanowires synthesized through hydrolysis of another bimetallic alkoxide, also in the presence of oleic acid stabilizers. Selected area electron diffraction patterns (top panel) and high-resolution TEM images (bottom panel) indicate that the wires are single crystals. Reproduced with permission from Ref. Reference Urban, Yun, Gu and Park13, copyright 2002 American Chemical Society.

Hydrothermal and solvothermal synthesis

Hydrothermal and solvothermal methods have yielded a greater range of ferroelectric materials than those produced by colloidal chemistry, although size dispersion and aggregation remain serious challenges. Nanostructures of BaTiO₃, PbTiO₃, and Pb(Zr_xTi_1−x)O₃ (PZT) have been prepared by hydro/solvothermal means, often through reaction of Ti isopropoxide with Ba metal or acetate salts.^[Reference Page, Proffen, Niederberger and Seshadri^16, Reference Moon, Kerchner, Krarup and Adair^17] Wong and co-workers also prepared both BaTiO₃ and SrTiO₃ using oxalate chemistry at high pressure (Fig. 3).^[Reference Mao, Banerjee and Wong^18] This general approach involving high-temperature, high-pressure reaction of metal salts has also been employed for synthesis of other perovskites, such as the colossal magnetoresistive material La_1−xBa_xMnO₃.^[Reference Urban, Ouyang, Jo, Wang and Park^19] In addition, Caruntu and co-workers have recently reported the growth of reasonably well-dispersed nanocrystals of the ferroelectric (and leading nonlinear optical material) LiNbO₃ via decomposition of a single-source precursor under high pressure.^[Reference Mohanty, Chaubey, Yourdkhani, Adireddy, Caruntu and Wiley^20] The hydrothermal approach has recently shown promise for the synthesis of the multiferroic perovskite BiFeO₃ through reaction of Bi and Fe salts in the presence of tartaric acid or ethylene glycol followed by calcination (Fig. 3).^[Reference Ghosh, Dasgupta, Sen and Maiti^21, Reference Park, Papaefthymiou, Viescas, Moodenbaugh and Wong^22] Templated growth procedures using either pre-existing arrays of nanowires, such as TiO₂ or ZnO, or lattice-matched substrates have also enjoyed modest success in the formation of quasi-one-dimensional nanostructures.^[Reference Zhou, Tang and Sodano^23–Reference Rørvik, Grande and Einarsrud^26] Although solvothermal techniques have broadened the range of available ferroelectric nanomaterials, these techniques generally yield products with poor size dispersion and serious agglomeration, rendering these materials of limited use for either applications requiring uniform particles or fundamental studies at the single-particle level.

Figure 3.

Perovskite nanostructures produced by hydrothermal synthesis methods. (a) Nanocrystals of the multiferroic material BiFeO₃ synthesized by a hydrothermal reaction in the presence of ethylene glycol. The four panels include a low-resolution TEM image, an electron diffraction pattern, a high-resolution TEM image, and an energy dispersive x-ray spectroscopy scan illustrating the stoichiometry (clockwise from top left). Reproduced with permission from Ref. Reference Park, Papaefthymiou, Viescas, Moodenbaugh and Wong22, copyright 2007 American Chemical Society. (b) Scanning electron microscope images of hydrothermally prepared nanostructures of both BaTiO₃ (top panel) and the incipient ferroelectric SrTiO₃ (lower panel). Reproduced with permission from Ref. Reference Mao, Banerjee and Wong18, copyright 2003 American Chemical Society.

Aqueous/organic multiphase synthesis

The development of a new synthetic method by Li and co-workers using both an aqueous and an organic phase at high pressures has enabled the high monodispersity and ligand passivation provided by colloidal techniques to be combined with the versatility of the hydrothermal approach.^[Reference Wang, Zhuang, Peng and Li^27] In this method, metal salts are dissolved in the aqueous phase, and organic capping ligands such as oleic acid are dissolved in the organic phase (Fig. 4). Decomposition of the metal carboxylates formed in-situ at high temperature and pressure results in oxide nanocrystals capped with carboxylate ligands that segregate in the organic phase. This method was leveraged by Do, Gao, and others to create highly monodisperse, organic-soluble nanocrystals of rare-earth oxide nanocrystals, particularly CeO₂.^[Reference Yang and Gao^28, Reference Nguyen and Do^29] Recently, two-phase techniques have been applied to the synthesis of ferroelectric oxides by Caruntu and co-workers, with impressive results (Fig. 4).^[Reference Adireddy, Lin, Cao, Zhou and Caruntu^30] Adireddy et al. reported the synthesis of highly monodisperse nanocrystals of BaTiO₃ with controlled sizes and shapes. In this work, the reaction of Ti butoxide with Ba nitrate in the presence of oleic acid at elevated pressure produces nanocrystals capped with oleic acid ligands that are well dispersed in organic solution. Broader application of this method may provide a promising path forward for the synthesis of other types of ferroelectric perovskites with controlled sizes, shapes, and surface structures that can be readily redispersed.

Figure 4.

An aqueous/organic two-phase method for producing ligand-passivated and monodisperse ferroelectric nanocrystals. (a) Schematic illustration of the synthesis process. Metal salts in the aqueous phase form metal carboxylates in-situ that subsequently decompose to nucleate nanocrystals. The growing nanocrystals are passivated by long-chain organic ligands dissolved in the organic phase, in which the particles remain. Reproduced with permission from Ref. Reference Wang, Zhuang, Peng and Li27, copyright 2005 Nature Publishing Group. (b) TEM image of monodisperse BaTiO₃ nanocubes prepared by this aqueous/organic two-phase synthesis procedure. Nanocubes capped with oleic acid ligands dissolved in an organic phase with sizes as small as ~5 nm can be obtained. Reproduced with permission from Ref. Reference Adireddy, Lin, Cao, Zhou and Caruntu30, copyright 2010 American Chemical Society.

Future directions in ferroelectric nanomaterial synthesis

Although considerable progress has been made in the synthesis of high-quality nanostructures of ferroelectrics, these materials continue to lag far behind the state of more common metal and semiconductor materials. Notably, promising solution-phase synthesis routes have thus far not been accompanied by significant progress in the vapor-phase growth of one-dimensional nanostructures. While nanowires of the semiconducting ferroelectrics GeTe and Sb₂S₃ have been synthesized by several groups using vapor-phase methods, few reports exist for traditional perovskite oxide materials.^[Reference Yu, Wu, Gu and Park^31, Reference Yang, Bachmann, Pippel, Berger, Woltersdorf, Gösele and Nielsch^32] Nanotubes and epitaxial nanowires of PbTiO₃ and PZT have been grown by templated MOCVD growth on ZnO nanowires^[Reference Fujisawa, Kuri, Nakashima, Shimizu, Kotaka and Honda^24] or vapor–solid growth on SrTiO₃ substrates,^[Reference Chen, Liu, Chen, Liu, Chen, Wu, Wang, He, Chu and Chueh^25] respectively, but reports of the growth of single-crystal perovskite nanowires of controlled, uniform diameter by vapor-phase methods are practically nonexistent. A great deal of open territory thus exists for the development of syntheses of high-quality nanowires by vapor-phase means.

The field of ferroelectrics would also benefit from an expansion of the library of available materials, particularly those exhibiting multiferroic properties. Given the difficulty of ambient-pressure colloidal synthesis for traditional oxides and the relatively poor size and shape control afforded by solvothermal techniques, the expansion of two-phase aqueous/organic synthetic methods to traditional ferroelectrics with larger polarization such as PbTiO₃ and multiferroics such as BiFeO₃ and YMnO₃ would appear an area ripe for intense exploration. The nanoscale synthesis of polar complex fluoride compounds also remains, to the best of our knowledge, almost entirely unexplored. Numerous ferroelectric (and even multiferroic) complex fluorides exist, such as BaMnF₄ and related materials.^[Reference Scott and Blinc^33] Monodisperse colloidal nanocrystals of other complex fluorides, including doped compounds with the same general formula ABF₄, have been grown successfully for photonic upconversion applications.^[Reference Ostrowski, Chan, Gargas, Katz, Han, Schuck, Milliron and Cohen^34]

The development of heterostructures, particularly of the core–shell variety, may provide another strategy to enhance polar phase stability and expand functionality. It would be particularly exciting to examine the strain-mediated magnetoelectric coupling in nanostructures composed of perovskite oxides and magnetic spinel ferrites, similar to BaTiO₃–CoFe₂O₄ nanocomposites examined in thin film structures.^[Reference Zheng, Wang, Lofland, Ma, Mohaddes-Ardabili, Zhao, Salamanca-Riba, Shinde, Ogale, Bai, Viehland, Jia, Schlom, Wuttig, Roytburd and Ramesh^35] It is conceivable that a well-established colloidal synthesis protocol for ferrites could be adapted for heterogeneous nucleation on perovskite nanocrystals grown through the two-phase route.^[Reference Sun, Zeng, Robinson, Raoux, Rice, Wang and Li^11] Strain engineering in nanoparticle heterostructures may also be exploited to stabilize novel material phases under ambient conditions. An intriguing step in this direction was recently reported by Chu and co-workers, who reported the growth of heterostructures composed of BiFeO₃ nanodots in the non-equilibrium tetragonal phase on LaAlO₃ nanoparticles formed by laser ablation.^[Reference Kuo, Chen, Ji, Liu, Chen and Chu^36]

An improved ability to tailor nanomaterial size and morphology may also enable the stabilization of non-equilibrium phases in single-component nanostructures under ambient conditions. Many common ferroelectrics, including BaTiO₃,^[Reference Kwei, Lawson, Billinge and Cheong^37] PZT,^[Reference Lines and Glass^8] and BiFeO₃^[Reference Zeches, Rossell, Zhang, Hatt, He, Yang, Kumar, Wang, Melville, Adamo, Sheng, Chu, Ihlefeld, Erni, Ederer, Gopalan, Chen, Schlom, Spaldin, Martin and Ramesh^38] exist near morphotropic phase boundaries separating phases with different crystallographic symmetry. The addition of a surface energy term to the free energy and internal strain arising from the free surface can lead to dramatic changes in the phase diagram of materials at reduced dimensions.^[Reference Tolbert and Alivisatos^39] Non-equilibrium phases have been stabilized in simple oxide materials such as ZrO₂ that exist close to a tetragonal-monoclinic phase boundary,^[Reference Sato, Abe and Ohara^40] and phases not otherwise observed in nature have been seen in other systems, most notably the epsilon phase in Co nanoparticles.^[Reference Sun and Murray^41] Indeed, a recent study by Louis et al. on BaTiO₃ and KNbO₃ nanowires reported a previously unobserved monoclinic ferroelectric phase not known to be present in bulk material.^[Reference Louis, Gemeiner, Ponomareva, Bellaiche, Geneste, Ma, Setter and Dkhil^42] It will be interesting to see whether size and morphological control can be leveraged in other ferroelectric nanostructures to stabilize novel material phases, such as the tetragonal phase of BiFeO₃ with one of the highest spontaneous polarization values yet reported.^[Reference Wang, Neaton, Zheng, Nagarajan, Ogale, Liu, Viehland, Vaithyanathan, Schlom, Waghmare, Spaldin, Rabe, Wuttig and Ramesh^43]

Ferroelectric stability at the nanoscale

Early studies of size effects in ferroelectrics on nanocrystalline ceramics frequently noted the apparent decline in the overall ferroelectric polarization as a function of particle size at size scales less than approximately 100 nm.^[Reference Uchino, Sadanaga and Hirose^44, Reference Frey and Payne^50–Reference Chattopadhyay, Ayyub, Palkar and Multani^54] This decline in polarization was generally attributed to the influence of the depolarization field at small dimensions, and it was widely believed that screening of the polarization-induced surface charges by metallic electrodes was necessary to stabilize the ferroelectric state. A seminal study by Spanier et al., however, demonstrated a stable ferroelectric polarization in single-crystal BaTiO₃ nanowires down to diameters of only a few nanometers.^[Reference Spanier, Kolpak, Urban, Grinberg, Ouyang, Yun, Rappe and Park^55] Calculations using density functional theory in this work showed that molecular adsorbates on the surface provided an even greater screening effect than that provided by metallic electrodes, and subsequent work on thin films highlighted the dramatic effects of atmospheric moisture and other adsorbates in manipulating the domain arrangements in two-dimensional systems.^[Reference Shin, Nascimento, Geneste, Rundgren, Plummer, Dkhil, Kalinin and Baddorf^56] Rigorous structural studies by the groups of Steigerwald,^[Reference Smith, Page, Siegrist, Redmond, Walter, Seshadri, Brus and Steigerwald^45] Petkov,^[Reference Tripathi, Petkov, Selbach, Bergum, Einarsrud, Grande and Ren^46, Reference Petkov, Gateshki, Niederberger and Ren^47] and others using atomic pair-distribution function analysis confirmed the presence of ferroelectric structural distortions in particles as small as 5 nm, and recent work has demonstrated a net polar distortion in single nanocrystals with sub-5 nm dimensions using direct atomic-scale imaging.^[Reference Polking, Urban, Milliron, Zheng, Chan, Caldwell, Raoux, Kisielowski, Ager, Ramesh and Alivisatos^57, Reference Polking, Han, Yourdkhani, Petkov, Kisielowski, Volkov, Zhu, Caruntu, Alivisatos and Ramesh^58] The realization that ferroelectricity can be preserved down to far smaller dimensions than previously imagined opened up new territory for both fundamental study and practical applications.

Evolution of domain structure with size

Although the evolution of domain structure with size in ferromagnetic materials had been well described theoretically by Kittel and verified experimentally, the scaling of domain structure in ferroelectrics has been subject to rigorous experimental investigation only more recently.^[Reference Kittel^6] The domain spacing, which was predicted to scale approximately as the square root of the sample dimensions, is a delicate balance among electrostatic energy, domain wall formation energy, and internal strain.^[Reference Kittel^6] Studies by Gregg and co-workers on individual free-standing pieces of BaTiO₃ cut from a bulk single crystal by a focused ion beam have yielded considerable insights into the evolution of domain patterns with both size and morphology (Fig. 5).^[Reference Schilling, Adams, Bowman, Gregg, Catalan and Scott^59–Reference Schilling, Bowman, Catalan, Scott and Gregg^61] Studies of the size-scaling of domain structures demonstrated the validity of the classical Kittel scaling relation over orders of magnitude in size, down to a size limit of approximately 100 nm.^[Reference Schilling, Adams, Bowman, Gregg, Catalan and Scott^59] A study of discrete nanodots fabricated using the same method illustrated the presence of quadrant-like domain structures, although no simple flux-closure structures could be observed.^[Reference Schilling, Byrne, Catalan, Webber, Genenko, Wu, Scott and Gregg^60] An additional study by this team demonstrated control of 90° domain arrangements by varying the morphology and size of single-crystal nanowires.^[Reference Schilling, Bowman, Catalan, Scott and Gregg^61] Additional work by Luk'yanchuk et al. attributed the presence of ferroelastic 90° domain walls, for which no electrostatic driving force exists, in such structures to the presence of internal strains arising from a surface “dead” layer created by ion milling.^[Reference Luk'yanchuk, Schilling, Gregg, Catalan and Scott^62] Internal strains may thus play a much larger role than previously thought in governing the size-scaling of ferroelectricity. This body of work has yielded powerful insights into the influence of size, morphology, and surface structure on domain arrangements at dimensions approaching the nanoscale. Owing to the use of focused ion beam milling, which creates a damaged surface layer several nanometers in thickness and is limited to structure dimensions of ~100 nm, these studies were unable to explore the possibility of a transition to a single-domain regime, and separating the effects of surface damage from intrinsic depolarization effects remains challenging. Recent work on GeTe nanocrystals demonstrated a transition to a single-domain regime at a size scale of approximately 30–50 nm.^[Reference Polking, Zheng, Ramesh and Alivisatos^14] Other recent studies on BaTiO₃ nanocubes also point to stable single-domain states in discrete nanocrystals at a size scale of <~50 nm.^[Reference Szwarcman, Prosandeev, Louis, Berger, Rosenberg, Lereah, Bellaiche and Markovich^63] Finer control over morphology and size will be necessary to fully elucidate the transition from the monodomain to the multidomain regime in nanomaterials with both size and morphology. The monodisperse BaTiO₃ nanocubes described in the previous section on synthesis would appear to provide in this respect a promising starting point for such a detailed analysis.

Figure 5.

Domains in freestanding ferroelectric nanostructures. (a) Domain patterns in fabricated ferroelectric nanodots show complex configurations that persist down to the smallest length scales studied (~100 nm). Reproduced with permission from Ref. Reference Schilling, Byrne, Catalan, Webber, Genenko, Wu, Scott and Gregg60, copyright 2007 American Chemical Society. (b) Scaling of domain periodicity with size in freestanding nanostructures. Domain spacing scales with the square root of side length for both nanodots and nanorods for all sizes observed experimentally, consistent with classical scaling laws. Reproduced with permission from Ref. Reference Schilling, Adams, Bowman, Gregg, Catalan and Scott59, copyright 2006 American Physical Society.

Ferroelectric coherence at the nanoscale

Implicit in much early work on low-dimensional ferroelectricity was the assumption that a decline in ferroelectric polarization at a global scale reflected a decline in ferroelectric distortions at a local scale. Spectroscopic experiments on BaTiO₃ thin films frequently showed the presence of tetragonal symmetry above the Curie temperature, and studies of BaTiO₃ nanocrystals with Raman spectroscopy, which is highly sensitive to local symmetry, in many cases showed tetragonal symmetry in particles otherwise believed to be in the cubic state.^[Reference Shiratori, Pithan, Dornseiffer and Waser^64] Recent studies combining a probe sensitive to global structure, such as Rietveld refinement of powder x-ray diffraction data, with a probe sensitive to local structure, such as atomic pair distribution function (PDF) analysis, have yielded powerful new insights into the fundamental changes that occur in ferroelectric ordering at the nanoscale.^[Reference Smith, Page, Siegrist, Redmond, Walter, Seshadri, Brus and Steigerwald^45–Reference Petkov, Gateshki, Niederberger and Ren^47] These studies demonstrated the presence of clear tetragonal distortions in BaTiO₃ down to particle sizes of only a few nanometers and illustrated clear structural changes relative to bulk material below a size scale of ~100 nm, as demonstrated in previous work. Importantly, however, although measurements with Rietveld refinement of powder diffraction data showed a decline in the overall tetragonal distortion with decreasing size, PDF measurements illustrated ion displacements on a local scale that were often larger than those for bulk material (Fig. 6). This disparity arises from a decline in the coherence of ferroelectric distortions across the particle volume. Recent work on monodisperse BaTiO₃ nanocrystals with different morphologies indicates a profound influence of particle shape on this structural coherence, implicating internal strains as an additional cause of disordering.^[Reference Polking, Han, Yourdkhani, Petkov, Kisielowski, Volkov, Zhu, Caruntu, Alivisatos and Ramesh^58] Cubic particles with more low-energy surface facets were found to have far greater coherence lengths for tetragonal distortions when compared with spherical particles, even those with larger volumes. Despite the decline in ferroelectric coherence, a net polarization in nanocrystals as small as 5 nm has been confirmed to be stable by both atomic-resolution imaging and electrical switching.^[Reference Polking, Han, Yourdkhani, Petkov, Kisielowski, Volkov, Zhu, Caruntu, Alivisatos and Ramesh^58] Atomic-resolution transmission electron microscope (TEM) images illustrated a significant net, coherent polarization in both GeTe and BaTiO₃ nanocrystals grown by solution-phase techniques (Fig. 7). More recent work with electron microscopy has also illustrated a tetragonal distortion in BaTiO₃ nanocubes that is larger than that for bulk material within the particle core but accompanied by a nearly undistorted “shell” region near the surfaces that reduces the overall distortion to more bulk-like values.^[Reference Szwarcman, Prosandeev, Louis, Berger, Rosenberg, Lereah, Bellaiche and Markovich^63] These structural studies reveal a picture of ferroelectric order that, although robust down to nanometer-scale dimensions, becomes markedly inhomogeneous in nature.

Figure 6.

Coherence of ferroelectric distortions at the nanoscale. (a) Unit cell parameters of BaTiO₃ nanoparticles as a function of size obtained from Rietveld refinement of powder x-ray diffraction patterns. Although the overall tetragonal distortion defined as the ratio of the c axis ([001]) lattice constant to the a axis ([100], [010]) lattice constant decreases for smaller BaTiO₃ nanoparticles (top panel), the local Ti cation displacements (Given here in fractional coordinates, where a value of 0.500 represents the Ti position for the undistorted, cubic phase) increase with decreasing size (bottom panel), suggesting larger but less spatially coherent local ferroelectric distortions. (b) Changes in the unit cell parameters of BaTiO₃ nanoparticles with sizes of 26, 45, and 70 nm and bulk material through the phase transition. The phase transition (near 130 °C) becomes noticeably more diffuse as particle size decreases. Both panels reproduced with permission from Ref. Reference Smith, Page, Siegrist, Redmond, Walter, Seshadri, Brus and Steigerwald45, copyright 2008 American Chemical Society.

Figure 7.

Atomic-scale mapping of ferroelectric polarization in individual nanocrystals. (a) Atomic-scale analysis of local polarization patterns in individual GeTe nanocrystals. Mapping of local atomic displacements obtained from atomic-resolution TEM images (top panel) reveals a coherent and linearly ordered polarization along the [111] axis (bottom panel). (b) Atomic-scale analysis of local polarization patterns in individual BaTiO₃ nanocrystals. Mapping of local atomic displacements also shows a coherent and linearly ordered polarization along the [001] axis (bottom panel). Reproduced with permission from Ref. Reference Polking, Han, Yourdkhani, Petkov, Kisielowski, Volkov, Zhu, Caruntu, Alivisatos and Ramesh58, copyright 2012 Nature Publishing Group.

Toroidal polarization states

As recent experimental work has changed the picture of nanoscale ferroelectrics as miniaturized bulk materials with diminished but coherent polarization, theoretical studies using ab initio techniques have uncovered still more intriguing behavior. At reduced dimensions, ferromagnetic materials frequently form flux-closure domain structures to reduce magnetostatic energy stored in fringing fields.^[Reference Kittel^6] Below the single-domain limit, energy may be minimized by formation of toroidal magnetization states characterized by continuous rotation of magnetic flux around a central core. Such toroidal magnetization states have been elegantly demonstrated experimentally by, for example, Snoeck et al. using off-axis electron holography.^[Reference Snoeck, Gatel, Lacroix, Blon, Lachaize, Carrey, Respaud and Chaudret^65] The anisotropy energy of the spontaneous polarization in ferroelectrics, however, is, in general, far greater than the anisotropy of the spontaneous magnetization in ferromagnets,^[Reference Lines and Glass^8] although this anisotropy may become vanishingly small in the vicinity of a morphotropic phase boundary.^[Reference Rossetti, Khachaturyan, Akcay and Ni^66] The spontaneous polarization is thus far more difficult to reorient along an arbitrary axis, leading many to believe that toroidal polarization states requiring continuous flux rotation would not exist in nature. A seminal ab initio study by Naumov et al. on PZT nanostructures, however, demonstrated stable vortex polarization states in nanodots and periodic arrangements of vortices in nanowires (Fig. 8).^[Reference Naumov, Bellaiche and Fu^48] An ultimate limit for the stability of the toroidally ordered polar state of 2.6 nm was also reported, further pushing the size limits of the polar phase. Subsequent work expanded these results to BaTiO₃^[Reference Fu and Bellaiche^49] and GeTe^[Reference Durgun, Ghosez, Shaltaf, Gonze and Raty^67] and demonstrated a smooth transition between vortex and conventional polarization states with increasing polarization screening.^[Reference Ponomareva, Naumov, Kornev, Fu and Bellaiche^68] In an effort to aid the search for toroidal ordering, Bellaiche and coworkers have also provided a list of properties that should be exhibited by such nanodots, including a c/a ratio (tetragonal distortion) of less than one for tetragonal ferroelectrics that could be observed by standard diffraction techniques.^[Reference Prosandeev and Bellaiche^69] The existence of continuous flux rotation and flux-closure-like domain structures has recently been directly demonstrated in ferroelectric thin films using atomic-resolution microscopy. Nelson et al. demonstrated the first example of a flux-closure-like structure with continuous flux rotation in a BiFeO₃ thin film grown on an insulating TbScO₃ substrate,^[Reference Nelson, Winchester, Zhang, Kim, Melville, Adamo, Folkman, Baek, Eom, Schlom, Chen and Pan^70] and Jia et al. followed up this study with a detailed analysis of continuous flux rotation in PZT thin films also grown on insulating TbScO₃ using a combination of atomic-resolution microscopy and rigorous image simulations (Fig. 8).^[Reference Jia, Urban, Alexe, Hesse and Vrejoiu^71] Despite these breakthroughs in thin-film systems, true single-domain vortex polarization states in discrete nanodots have yet to be observed conclusively. A notable effort by Rodriguez et al. demonstrated piezoresponse force microscope (PFM) data consistent with a flux closure-like domain arrangement in fabricated nanodots, but the size scale of these dots (~100 nm) is significantly above the single-domain regime.^[Reference Rodriguez, Gao, Liu, Lee, Naumov, Bratkovsky, Hesse and Alexe^72] Studies with electron holography similar to the work of Snoeck et al. on ferromagnetic nanocubes have shown evidence of a linear polarization state and external fringing fields, but no evidence of toroidal ordering has yet been uncovered.^[Reference Polking, Han, Yourdkhani, Petkov, Kisielowski, Volkov, Zhu, Caruntu, Alivisatos and Ramesh^58, Reference Szwarcman, Lubk, Linck, Vogel, Lereah, Lichte and Markovich^73] The lack of single-domain vortex states may be attributable to the aforementioned efficient screening of polarization-induced charges by surface adsorbates. It is notable that examples of continuous flux rotation in thin films occurred in films grown on insulating substrates rather than on a more typical metallic SrRuO₃ back electrode that provides effective screening. Stabilizing vortex states in freestanding nanocrystals may thus require an analogous arrangement consisting of a ferroelectric core surrounded by a highly insulating epitaxial shell.

Figure 8.

Novel polarization states in ferroelectric nanomaterials. (a) Schematic illustrations of polarization patterns in PZT nanodots of various shapes. Despite the large anisotropy energy of ferroelectrics, vortex-like polarization states with a stable toroid moment have been predicted theoretically in small, single-domain ferroelectric nanostructures. Reproduced with permission from Ref. Reference Prosandeev and Bellaiche69, copyright 2007 American Physical Society. (b) Direct observation of continuous flux rotation in a PZT thin film on an insulating TbScO₃ substrate by atomic-resolution TEM. Local polarization vectors are indicated by the small yellow arrows. Reproduced with permission from Ref. Reference Jia, Urban, Alexe, Hesse and Vrejoiu71, copyright 2011 American Association for the Advancement of Science.

Size-dependent polar phase transition

Like the question of the stability of the polar state at finite dimensions, the nature of the phase transition from the high-temperature prototype phase to the low-temperature polar-ordered phase has also been the subject of some contention. Studies of nanocrystalline ceramics and nanopowders of BaTiO₃ and PbTiO₃ have frequently shown a decrease in Curie temperature with particle size below a size scale of ~100 nm, but estimates for the degree of suppression of the ordering temperature vary considerably.^[Reference Frey and Payne^50–Reference Chattopadhyay, Ayyub, Palkar and Multani^54] Some reports have suggested a critical size for the disappearance of the polar phase transition as small as 10–30 nm,^[Reference Zhao, Buscaglia, Viviani, Buscaglia, Mitoseriu, Testino, Nygren, Johnsson and Nanni^52] while others cite values closer to 50 nm or even larger.^[Reference Schlag and Eicke^53] The study of the phase transition in individual BaTiO₃ wires by Spanier et al. cited earlier found a suppression of the Curie temperature to below ambient temperature at a diameter of 3 nm.^[Reference Spanier, Kolpak, Urban, Grinberg, Ouyang, Yun, Rappe and Park^55] Although wide scatter exists in measurements of the Curie point, a shift in the temperature of the paraelectric-ferroelectric phase transition with decreasing particle size has been consistently observed, often following a 1/d trend (where d is the particle diameter). The significantly lower critical size for the suppression of ferroelectricity in the Spanier study may be related to effective passivation of the wires with oleic acid ligands. A change to a more diffuse phase transition with decreasing size has also been consistently observed. Analysis of the polar phase transition with differential scanning calorimetry (DSC) and Raman spectroscopy in particular has often shown a pronounced broadening of the temperature range of the phase transition.^[Reference Smith, Page, Siegrist, Redmond, Walter, Seshadri, Brus and Steigerwald^45, Reference Shiratori, Pithan, Dornseiffer and Waser^64] Some portion of this effect may be related to inhomogeneity in particle size, but studies on relatively monodisperse particles have shown significant broadening of the transition as well.^[Reference Smith, Page, Siegrist, Redmond, Walter, Seshadri, Brus and Steigerwald^45] The increasing diffuseness of the phase transition with decreasing particle size is thus likely to be at least to some extent of intrinsic origin. The results of detailed structural studies with PDF and TEM mentioned earlier suggest increasing inhomogeneity of polarization as a likely cause of this broadening. Deconvoluting size inhomogeneity from intrinsic effects, however, will ultimately require single-particle studies. An interesting effort in this direction was recently presented by Szwarcman et al. on individual BaTiO₃ nanocubes.^[Reference Szwarcman, Vestler and Markovich^74] The localized surface plasmon resonance of gold nanoparticles grown on the nanocubes was used in this work as a local probe of the material phase. The group concluded that surface effects dominated the behavior of the smallest (~16 nm) nanocubes, but particle aggregation makes interpretation of the results somewhat problematic. The precise physical origins of the increasing diffuseness of the phase transition at finite size also remain at issue. Although depolarization effects have been traditionally implicated, a recent study of the size-dependent polar phase transition in highly conducting GeTe found a similar decrease in the polar phase transition temperature with decreasing size and a significant decrease in the magnitude of the polar distortion.^[Reference Polking, Urban, Milliron, Zheng, Chan, Caldwell, Raoux, Kisielowski, Ager, Ramesh and Alivisatos^57] The metallic conductivity of GeTe provides strong internal screening of depolarization fields; it is thus likely that internal strain effects at finite size also contribute to the suppression of the phase transition temperature and stability of the polar state.

Future possibilities for fundamental study

Although much progress has been made towards developing a clear picture of ferroelectricity at the nanoscale, many important questions remain. The parallel development of synthetic techniques for monodisperse ferroelectric nanocrystals with well-defined morphologies and new tools for nanoscale in situ characterization with TEM and scanning-probe microscopy provide, in our view, rich opportunities.

In situ studies of the ferroelectric phase transition and ferroelectric switching in individual particles represent a particularly exciting route for future exploration. The recent development of MEMS-based heating holders for the TEM allows for atomic-resolution imaging at elevated temperatures with minimal thermal drift and rapid stabilization.^[Reference Allard, Bigelow, Jose-Yacaman, Nackashi, Damiano and Mick^75] In situ heating of monodisperse BaTiO₃ nanocubes, such as those demonstrated by Caruntu and co-workers,^[Reference Adireddy, Lin, Cao, Zhou and Caruntu^30] could allow the ferroelectric phase transition to be characterized at the single-particle level for the first time. A combination of a global structural probe, such as electron diffraction, with a probe sensitive to local symmetry breaking, such as electron energy loss near edge structure, could allow the evolution of both local and global ferroelectric distortions through the phase transition to be analyzed free from ensemble averaging effects. Analysis with direct atomic-resolution imaging could yield even more exciting conclusions. The parallel development of new in situ electrical biasing sample holders could provide another exciting new direction. A simple parallel plate capacitor-like structure patterned using electron beam lithography on a silicon nitride heating chip could be used to apply an electric field across individual ferroelectric nanocubes to observe polarization switching in situ at atomic resolution. The use of discrete nanocubes provides an opportunity to study polarization switching at the simplest level, free from interference from substrates, other domains, and other complicating factors.

The combination of topographic information and nanoscale spectroscopy provided by recently developed instruments integrating AFM/PFM with tip-enhanced Raman spectroscopy may provide another powerful pathway to studies of polarization switching and phase transitions on a single-domain scale.^[Reference Berweger, Neacsu, Mao, Zhou, Wong and Raschke^76] The sensitivity of Raman spectroscopy to subtle changes in crystallographic symmetry may allow detection of local (and incoherent) structural perturbations accompanying ferroelectric phase transitions that would be highly challenging to resolve with TEM. In addition, the ability to readily combine this high sensitivity to local structure with polarization switching may furnish new insights into switching mechanisms at the single-domain scale and the origins of fatigue/retention effects.

The demonstration of polarization switching in thin BaTiO₃ nanowires^[Reference Spanier, Kolpak, Urban, Grinberg, Ouyang, Yun, Rappe and Park^55] and more recently in sub-10 nm BaTiO₃ nanodots^[Reference Polking, Han, Yourdkhani, Petkov, Kisielowski, Volkov, Zhu, Caruntu, Alivisatos and Ramesh^58] raises questions regarding the stability of the polarization as a function of time. The so-called superparamagnetic effect is well known in ferromagnetic nanocrystals at reduced size.^[Reference Murray, Kagan and Bawendi^9, Reference Sun and Murray^41] In the superparamagnetic regime, ambient thermal energy becomes comparable with the anisotropy energy of the magnetization, which scales with particle size, allowing for random, thermally induced collective reorientation of all spins within a single-domain particle. The existence of an analogous superparaelectric effect remains an open question. Analysis of individual sub-10 nm BaTiO₃ nanocubes with PFM could provide an avenue for exploring this question. The PFM phase signal provides direct information on the direction of the spontaneous polarization, with a 180° phase shift corresponding to a 180° flip in the direction of the spontaneous polarization. Random, rapid flips in the phase signal by 90° or 180° over time would provide a clear signature of superparaelectric behavior.

A final area ripe for future study centers around the search for toroidal polarization states in nanomaterials, which incorporates synthetic, theoretical, and characterization challenges. Given the effective screening of surface charges that produce the depolarization fields necessary to generate polarization vortices, it will likely be necessary to generate core–shell structures in which polarization charges are trapped at an epitaxial interface with an insulating shell layer, analogous to ferroelectric layers on insulating substrates in which flux rotation has been observed. Overgrowth of SrTiO₃ shells on BaTiO₃ (or preferably PbTiO₃) nanocubes may provide an appropriate system for observation of vortex states. Both BaTiO₃ and SrTiO₃ have been made using solution-phase synthetic techniques, so heterogeneous nucleation of SrTiO₃ on BaTiO₃ nanocubes may not be prohibitively difficult. The observation of novel polarization states in nanodots also presents challenges for theoretical modeling. Thorough understanding of polarization screening by capping ligands is lacking, as is work on the influence of internal strains on polarization coherence and character. A thorough theoretical treatment of screening provided by typical capping ligands and nanomechanical modeling to analyze the influence of morphology on internal strain fields and polarization would be quite beneficial in this area. A good step in this direction has recently been taken by Yasui and Kato, who analyzed in detail the effects of surface adsorbates and microstrain on ferroelectric ordering in small BaTiO₃ nanocubes,^[Reference Yasui and Kato^77] but further studies along these lines will be necessary to provide a complete picture of the size and shape-dependent interplay of depolarization effects, polarization, and internal strain. Characterization of appropriately engineered nanostructures with atomic-resolution TEM may then provide the first experimental evidence of true monodomain vortex states.

Ferroelectric nanomaterials for nonvolatile memories

For many years, the possibility of high-density, low-power nonvolatile memory devices has been a major driving force behind the study of ferroelectric nanomaterials. Although memory devices based on ferromagnetic bits have long been the mainstay of the industry, magnetic memories are rapidly approaching fundamental physical limits associated with superparamagnetic effects. Ferroelectrics, which exhibit a much larger anisotropy, can maintain a thermally stable polarization down to size scales of only a few nanometers.^[Reference Naumov, Bellaiche and Fu^48, Reference Spanier, Kolpak, Urban, Grinberg, Ouyang, Yun, Rappe and Park^55, Reference Polking, Han, Yourdkhani, Petkov, Kisielowski, Volkov, Zhu, Caruntu, Alivisatos and Ramesh^58] Recent experimental confirmation of ferroelectric phase stability at such dimensions in freestanding nanodots would in principle allow storage densities in the Tbit/in² range.^[Reference Spanier, Kolpak, Urban, Grinberg, Ouyang, Yun, Rappe and Park^55, Reference Polking, Han, Yourdkhani, Petkov, Kisielowski, Volkov, Zhu, Caruntu, Alivisatos and Ramesh^58] Realizing such devices, however, remains a daunting challenge.

The development of techniques for the templated growth of nanodots, particularly on doped SrTiO₃ substrates, has recently provided an interesting avenue to high-density memory devices. Deposition of ferroelectric nanoislands and nanorods using block copolymers^[Reference Lee, Han, Lotnyk, Schubert, Senz, Alexe, Hesse, Baik and Gösele^78, Reference Kim, Hong, Park, Zhe, Kim, Jang, Kim and No^80] and titania nanotube^[Reference Im, Jun, Lee, Lee, Yang, Jeong and Lee^81] templates has led to potential storage densities exceeding the Tbit/in² threshold, and formation of PbTiO₃ and BiFeO₃ nanodots with dimensions of the order of ~10 nm has been realized in a controlled fashion using dip pen lithography on SrTiO₃ substrates (Fig. 9).^[Reference Kim and Son^82, Reference Son, Shin, Ryu, Kim and Jang^83] BiFeO₃ also offers the possibility of multiferroic switching, potentially allowing for multistate devices. Robust ferroelectric switching has been observed in such nanoislands down to lateral dimensions of less than 10 nm.^[Reference Kim, Kim, Han, Jesse, Hyun, Lee, Kalinin and Kim^84] A new solution-phase approach employing block copolymer micelles filled with PbTiO₃ precursor has also yielded promising results for memory arrays. In this approach, a solution of discrete micelles can be spin-cast onto a substrate, and PbTiO₃ nanoislands with diameters of about 20 nm can be created via subsequent thermal annealing.^[Reference Kim, Han, Kim, Lee, Alexe, Baik and Kim^85] The development of well-dispersed nanocubes of BaTiO₃ raises the possibility of self-assembled memory devices as well. Monodisperse BaTiO₃ nanocubes have recently been organized into densely packed layers using an evaporative self-assembly approach,^[Reference Kato, Mimura, Dang, Imai, Wada, Osada, Haneda and Kuwabara^86] allowing for potentially unprecedented storage densities.

Figure 9.

Nanoscale ferroelectric nonvolatile memory arrays. (a,b) Atomic-force microscope image (a) and high-resolution TEM image (b) of discrete nanodots of PbTiO₃ fabricated using dip-pen lithography. Epitaxial dots smaller than 10 nm can be fabricated. Reproduced with permission from Ref. Reference Son, Shin, Ryu, Kim and Jang83, copyright 2009 American Chemical Society. (c,d) Arrays of PZT nanodots formed using a block copolymer template. The nanodots can be individually electrically addressed, potentially leading to information storage densities exceeding 1 Tbit/in². Reproduced with permission from Ref. Reference Lee, Han, Lotnyk, Schubert, Senz, Alexe, Hesse, Baik and Gösele78, copyright 2008 Nature Publishing Group.

The discovery of robust ferroelectric order down to ~5 nm size scales in GeTe, and the more recent discovery of ferroelectric switching in GeTe, raises new possibilities for memory devices. Recently demonstrated multiferroic switching in Mn-doped GeTe may allow for multistate memory devices,^[Reference Przybylińska, Springholz, Lechner, Hassan, Wegscheider, Jantsch and Bauer^87] and combining the ferroelectric and amorphous-to-crystalline phase-change properties of GeTe, as proposed by Durgun et al., may provide an avenue to tri-state memory devices.^[Reference Durgun, Ghosez, Shaltaf, Gonze and Raty^67]

Ferroelectric nanomaterials for energy conversion

In addition to a spontaneous polarization, ferroelectrics also possess large piezoelectric (relating strain and polarization) and pyroelectric (relating temperature changes and polarization) coefficients that have garnered attention in recent years for conversion of either mechanical or thermal energy, respectively, to electrical current. In addition, the discovery of photovoltaic effects in ferroelectrics,^[Reference Choi, Lee, Choi, Kiryukhin and Cheong^88] often accompanied by anomalously large above-band-gap voltages,^[Reference Yang, Seidel, Byrnes, Shafer, Yang, Rossell, Yu, Chu, Scott, Ager, Martin and Ramesh^4] has attracted interest for solar energy conversion as well, although ferroelectric nanomaterials have yet to be explored for this purpose.

Recently, a significant body of literature has emerged on piezoelectric nanogenerators in which mechanical motion can be converted into electrical current by arrays of piezoelectric nanowires (Fig. 10).^[Reference Wang and Song^89–Reference Qi, Jafferis, Lyons, Lee, Ahmad and McAlpine^92] A generic device consists of aligned piezoelectric (especially PZT) nanowires spanning an electrode array. In some cases, nanowire mats span interdigitated electrodes or are embedded in a polymer matrix to form a composite structure.^[Reference Chen, Xu, Yao and Shi^91] Aligned nanowire arrays may also be formed by growth and subsequent patterning on an inorganic substrate followed by transfer to polydimethylsiloxane.^[Reference Qi, Jafferis, Lyons, Lee, Ahmad and McAlpine^92] In many cases these arrays are sandwiched between flexible polymer layers to enable deformation of the entire device, leading to deformation of the nanowires and consequent piezoelectric charge generation. Although many nanowires are composed of the classic piezoelectric material PZT,^[Reference Chen, Xu, Yao and Shi^91] other nanogenerators have been demonstrated using more environmentally friendly ZnO,^[Reference Wang and Song^89, Reference Qin, Wang and Wang^90] KNbO₃,^[Reference Jung, Chen, Yun, Lee, Zhou, Jo, Chou and Wang^93] and NaNbO₃.^[Reference Jung, Lee, Hong, Ding, Chen, Chou and Wang^94] When a mechanical force is applied to a nanogenerator device, the deformation-induced piezovoltage results in a voltage spike across the electrodes and a corresponding transient current (Fig. 10). Release of the applied mechanical stress then results in a current pulse of opposite polarity. Cyclic application of mechanical force can then result in the generation of an alternating current that could potentially be used for powering devices. Such piezoelectric nanogenerators could provide an efficient means of converting random vibrations, including those produced by the human body, into useful electrical energy. Applications of such nanogenerators have already been envisaged in the form of running shoes that harvest the energy produced during the compression of the sole and in the form of in-vivo biosensors powered by mechanical motion inside the body.^[Reference Wang^3]

Figure 10.

Mechanical energy harvesting and biosensing using piezoelectric nanowires. (a) Schematic illustration of a typical nanowire energy harvesting device. Nanowires (shown in red) span arrays of electrodes and are often imbedded in a flexible matrix. Reproduced with permission from Ref. Reference Chen, Xu, Yao and Shi91, copyright 2010 American Chemical Society. (b) Operation of a piezoelectric nanogenerator. Application and removal of force from the structure results in current pulses arising from the generation of a piezovoltage by mechanical strain. Such structures can be employed to harvest mechanical energy, such as that produced by biological motion. Reproduced with permission from Ref. Reference Chen, Xu, Yao and Shi91, copyright 2010 American Chemical Society. (c) Detecting mechanical motion of individual cells using a piezoelectric PZT nanoribbon array. The nanoribbons measure mechanical deformations of cells in response to electrical signals applied via a glass pipette (PPT). (d) Measuring simulated respiration in cow lung tissue. An array of PZT nanowires embedded in PDMS is placed in contact with cow lung tissue (top photo), and mechanical motion during the simulated respiration is recorded via induced piezoelectric voltage spikes (bottom plot). Reproduced with permission from Ref. Reference Nguyen, Deshmukh, Nagarah, Kramer, Purohit, Berry and McAlpine5, copyright 2012 Nature Publishing Group.

The use of the pyroelectric effect, in which a change in temperature induces a change in polarization, for conversion of thermal energy has also been recently explored. Several groups have reported pyroelectric energy conversion devices based on aligned arrays of polar nanowires composed of ZnO and KNbO₃.^[Reference Yang, Guo, Pradel, Zhu, Zhou, Zhang, Hu, Lin and Wang^95, Reference Yang, Jung, Yun, Zhang, Pradel, Guo and Wang^96] Changes in the spontaneous polarization in these nanowires in response to a change in device temperature generate a voltage across planar electrodes between which the nanowire arrays are sandwiched. Temperature cycling can then produce an alternating current for powering nanoscale devices in a manner analogous to that for piezoelectric devices. Such nanogenerators could prove quite useful for small-scale waste heat recovery applications.

Nanoscale ferroelectrics for high-energy density nanocomposites

High-energy density nanocomposites have emerged as a major direction in nanoscale ferroelectrics research and may provide a promising avenue toward high-performance capacitors for energy storage applications. Achieving a maximum possible energy density in such a capacitor requires maximizing two important factors: the breakdown field of the structure and the dielectric constant.^[Reference Ducharme^79] Inorganic ferroelectrics such as BaTiO₃ and PZT have exceptionally large static dielectric constants, often measuring in the tens or even hundreds or thousands,^[Reference Lines and Glass^8] but generally have subpar breakdown fields. Polymers, on the other hand, in many cases have superior breakdown fields but relatively low dielectric constants. A common approach to high-energy density capacitors has thus been to disperse high-permittivity nanoparticles of ferroelectrics within a matrix of a polymer with an exceptionally large dielectric strength.^[Reference Tang, Lin, Andrews and Sodano^97–Reference Jung, Kang, Yang, Won and Kim^103] The ferroelectric polymer polyvinylidene difluoride (PVDF) is by far the most common choice due to its high breakdown strength (~500 MV/cm) and relatively large dielectric constant (~65) arising from its ferroelectric ordering.^[Reference Ducharme^79] Nanocomposites based on PVDF have been made most frequently with BaTiO₃ nanoparticles,^[Reference Almadhoun, Bhansali and Alshareef^99–Reference Jung, Kang, Yang, Won and Kim^103] although PZT-based composites have also been realized.^[Reference Tang, Lin, Andrews and Sodano^97] The use of nanorods of Ba_xSr_(1−x)TiO₃, the dielectric constant of which can be compositionally tuned to values of well over 1000, has also recently been demonstrated.^[Reference Tang and Sodano^98]

A key challenge in the development of high-energy density nanocomposites is the aggregation of ferroelectric nanoparticles due to the low surface energy of PVDF.^[Reference Ducharme^79] Nanocrystal aggregation results in electrical leakage pathways through the inorganic component and increases porosity in the polymer phase, both of which limit the attainable energy density. Much research has thus focused on improving the dispersal of the ferroelectric nanoparticles within the polymer matrix. Hydroxylation of BaTiO₃ using a hydrogen peroxide treatment has been employed,^[Reference Almadhoun, Bhansali and Alshareef^99] and ethylene diamine functionalization has been used successfully for both BaTiO₃ nanoparticles^[Reference Li, Claude, Norena-Franco, Il Seok and Wang^100] and high aspect ratio Ba_xSr_(1−x)TiO₃ nanorods.^[Reference Tang and Sodano^98] Functionalization with phosphonic acids^[Reference Kim, Doss, Tillotson, Hotchkiss, Pan, Marder, Li, Calame and Perry^101] has also recently been used in BaTiO₃-based composites. A second approach to improving the dispersal relies on shielding the inorganic nanocrystals with polymer layers polymerized directly on the surfaces of particles. This approach has been employed for BaTiO₃–PVDF composites using a polymer bilayer^[Reference Xie, Huang, Huang, Yang and Jiang^102] and for BaTiO₃–polystyrene composites using block copolymer shells.^[Reference Jung, Kang, Yang, Won and Kim^103] Although particle dispersal and lowered breakdown voltages remain problematic, ferroelectric nanoparticle/polymer composites are already starting to yield impressive results, with some devices already exceeding the performance of commercial polypropylene-based capacitors. A recent report of an energy density of 14.86 J/cm³ (versus 1.2 J/cm³ at 640 MV/cm for a standard polypropylene device) suggests these nanocomposites are poised to overtake conventional technologies.^[Reference Tang and Sodano^98]

Emerging and future applications of nanoscale ferroelectrics

As existing technologies based on nanoscale ferroelectrics have matured, exciting new applications continue to emerge. The application of ferroelectric nanowires to force sensing in biological systems is a particularly intriguing area for future study. A few approaches to nanoscale biological force sensing have been previously devised, including a luminescent stress sensor based on CdSe/S tetrapods,^[Reference Choi, Koski, Olson and Alivisatos^104] but the strong piezoelectric properties of nanoscale ferroelectrics, which allow small forces to be converted into easily measurable electrical signals, appear ideally suited to measuring stresses exerted by cells on their surroundings. In a recent experiment, McAlpine and coworkers employed arrays of PZT nanoribbons to measure the small deformations of neurons due to triggered action potentials and stresses exerted in cow lung tissue during a mimicked respiration process (Fig. 10).^[Reference Nguyen, Deshmukh, Nagarah, Kramer, Purohit, Berry and McAlpine^5] Such devices could allow sensitive detection of biological processes at the single-cell scale. In addition, the use of mechanical-to-electrical signal transduction makes ferroelectrics well-suited to large-scale parallel devices integrated with existing CMOS technology.

The integration of ferroelectrics into nanophotonic devices may provide another fruitful area for future research. The large birefringence that accompanies the spontaneous polarization has already been exploited in two-dimensional plasmonic devices to create electrically controllable optical switches,^[Reference Dicken, Sweatlock, Pacifici, Lezec, Bhattacharya and Atwater^105] and perovskites have served as the basis for metamaterial superlenses operating in the THz regime.^[Reference Kehr, Liu, Martin, Yu, Gajek, Yang, Yang, Wenzel, Jacob, von Ribbeck, Helm, Zhang, Eng and Ramesh^106] The transparency of most ferroelectrics throughout the visible spectrum (and often into the UV region) also renders them suitable for nanophotonic applications. Ferroelectric nanowires could be employed as tunable or reconfigurable nanophotonic waveguides, and the large nonlinear coefficients of ferroelectrics make them ideal candidates for second harmonic generation and other nonlinear optical processes. Efficient second harmonic generation has already been demonstrated in individual LiNbO₃ nanowires,^[Reference Dutto, Raillon, Schenk and Radenovic^107] and integration of LiNbO₃ nanowires with a plasmonic metal has been proposed theoretically to harness plasmonic field enhancement for high conversion efficiencies.^[Reference Lu, Li, Hu, Cheng, Zhu and Zhu^108] Second harmonic generation in BaTiO₃ nanocrystals has also been examined, and biofunctionalization of these materials could lead to new bioimaging applications.^[Reference Le Dantec, Mugnier, Djanta, Bonacina, Extermann, Badie, Joulaud, Gerrmann, Rytz, Wolf and Galez^109, Reference Kim, Steinbrück, Buscaglia, Buscaglia, Pertsch and Grange^110] Vortex polarization states, if they could be realized experimentally, may have intriguing optical properties as well. It would be interesting to see if the inherent “handedness” of a vortex polarization state could lead to chiral optical properties, including circular dichroism.