Review Article  Open Access
J. F. Scott, "Prospects for Ferroelectrics: 2012–2022", International Scholarly Research Notices, vol. 2013, Article ID 187313, 24 pages, 2013. https://doi.org/10.1155/2013/187313
Prospects for Ferroelectrics: 2012–2022
Abstract
A review is given of more than a dozen subtopics within the general study of ferroelectrics, with emphasis upon controversies, unsolved problems, and prospects for the next decade, including pure science and industrial applications. The review emphasizes work over the past two years, from 2010 to 2012.
1. Introduction
Ferroelectrics have undergone a minor renaissance in the past twenty years with the development of highquality thin (<300 nm) oxide films, capable of performing switching at the 5 V standard logic level for silicon transistors [1, 2]. The general field of integrated ferroelectrics is not limited to memory devices entailing polarization reversal but includes such things as electrically controlled tunnel junctions, [3, 4] which are much more demanding in their thickness requirements (<7 nm), or electrocaloric cooling devices [5, 6], THz emitters [7, 8], resistive random access memories (RRAMS) [9, 10], photochromics [11], domain nanoelectronics [12, 13], flexible polymeric ferroelectrics [14, 15], and photovoltaics [16, 17]. At present there are perhaps 500 laboratories worldwide with R and D interests in ferroelectric films, and the present review is a rather personal viewpoint of what the most promising lines of investigation will be over the next decade.
2. Mott Field Effect Transistors (MOTTFETs) and FerroelectricGated FETs
In a typical computer memory the area of the chip is taken up primarily by the capacitors. Historically the capacitance was provided by a very thin siliconoxide layer grown by exposing the Si chip to oxygen during processing. However, silicon oxide (mostly quartz) has a rather small dielectric constant (ca. 6.0), and hence the capacitance is small even for very thin films. Even using a highdielectric material (most of which are ferroelectric oxides), the capacitors in a memory take up most of the chip area; in the jargon of the trade, the capacitors leave a large footprint [1]. A possible solution to this problem is to make the active memory element a programmable gate. For example, a ferroelectric gate (FEFET) can exhibit a very small footprint [18, 19]. Although such FEFETs have been actively researched for a decade or more, with noticeable progress in Tokyo, their defect is that the gate must be grounded during the READ operation, so that the gate charge is eventually dissipated. This problem can be circumvented by designing logic cells that are large (six transistors per bit—a socalled “6T” design) but have not been commercialized.
A promising new direction in this area is to use the FET gate in materials such as rare earth nickelates [20, 21]. These materials exhibit a phase transition from semiconducting to metallic as a function of temperature or applied electric field. Hence they can be used as a bistable memory element in the gate of an FET. Their problems are primarily related to optimizing growth; no one has reported a commercially viable CVD (chemical vapor deposition) process, for example; Figure 1.
(a)
(b)
Prospects for the next decade are very high, due to the breakthrough (Zubko et al.) in achieving a Mott transition with applied voltage and not just with temperature change.
3. Multiferroics and Magnetoelectrics
3.1. Introduction and Oxides
There are several hundred compounds that exhibit magnetic ordering and ferroelectricity (multiferroics) at the same time [22, 23]. Although most of these are oxides, there are many fluorides, oxyfluorides, chlorides, phosphates, and so forth. Rather rare, however, are those which exhibit magnetization and spontaneous polarization at room temperature or above. The most studied of these is bismuth ferrite (BiFeO_{3}), discovered by Smolensky’s group in 1959 [24–26]. Very recently two other materials have been observed to be multiferroic at or near room temperature—copper oxide [27] and a doubleperovskite oxide [28]. However, these have extremely small switched polarization (nC/cm^{2} rather than μC/cm^{2}) and hence offer a more limited range of potential applications.
A different family of multiferroic is exemplified by PbFe_{1/2}Ta_{1/2}O_{3} [29] and PbFe_{1/2}Nb_{1/2}O_{3} [30]. When mixed with PZT—PbZO_{3}—it produces a wide range of singlephase compounds with quaternary occupation at the Bsite. For 60–70% PZT these materials are multiferroic (ferromagnetic) up to ca. 100°C, due to Fe clustering, although the longrange magnetic ordering is antiferromagnetic and sets in at ca. 50 K [31, 32].
Magnetoelectricity is a linear combination of polarization and magnetization in the free energy of a crystal, with a coupling coefficient . Multiferroicity is neither necessary nor sufficient for magnetoelectricity: Cr_{2}O_{3} is neither ferromagnetic nor ferroelectric, but bilinear antiferroic coupling is allowed. For BaCoF_{4} linear coupling is forbidden in its crystal structure since and are parallel, and yet has no diagonal terms for this lattice symmetry.
The related compounds of PbFe_{2/3}W_{1/3}O_{3}PZT are also multiferroic at temperatures near ambient, but their magnetoelectric coupling is not bilinear; since both the cluster ferromagnetism and the spontaneous polarization are only short range, it is biquadratic through strain via magnetostriction and electrostriction [33, 34].
3.2. Ferromagnetic Ferroelectric Fluorides
Most work on ferroelectrics is on oxides, because these are easy to grow, and there is a long history of ceramic devices driving the science and funding. More recently experts on oxides from the high superconductivity community and/or magnetism have also gravitated to oxide ferroelectrics in the search for increased funding. However, ferroelectrics and multiferroics include numerous families of fluorides, chlorides, and phosphates.
Soon after their experimental proof [35, 36] of linear magnetoelectric coupling in Cr_{2}O_{3}, Astrov et al. made related measurements [37–41] in BaMnF_{4} and BaCoF_{4}. But these results differed qualitatively from those in chromia: the BaMF_{4} effect is a frequencydependent ac response, not a dc electrostatic response. In fact these data have never been explained, although the role of domain walls has been suggested. A detailed frequency dependent bulk response was calculated for this family of multiferroic by Tilley and Scott [42], but that did not include domain walls and does not correspond closely to the data of Astrov et al. [37–41]. The structure of these compounds consists of MF_{6} octahedra linked at corners (Figure 2) and forming zig zag chains [42, 43]. Note that the magnetic Mn (Ni or Co or Fe) ions do not move in the ferroelectric softmode eigenvector, rather the motion consists of Baion displacements coupled to nearly rigid rotation of MF_{6} octahedra. This makes it less than obvious why there should be strong coupling between polarization and magnetization . That understanding required a more detailed recent ab initio model [44, 45]. The basic mechanism is that of DzyaloshinskiiMoriya anisotropic exchange, but the models and experiments are both subtle. In 1975 Venturini and Morgenthaler at MIT showed [46] that BaMnF_{4} has weak ferromagnetism (3 mrad canting angle), and that the axis of sublattice magnetization is also tilted (9 degrees of the axis), but both of these results remained controversial, with both Kizhaev and Prozorova in Leningrad and Moscow, respectively [47–49] finding no ferromagnetism, presumably due to the spatial averaging of domains in their specimens. However, recently another Russian work [50] confirmed the data of Venturini, including the 9degree tilt.
It is especially puzzling that BaMnF_{4} and BaCoF_{4} exhibit similar magnetoelectric data [37–41], because as shown in Table 1 [51, 52] and the more detailed model of Fox et al. [53], the Mn compound manifests ferroelectricallyinduced (weak) ferromagnetism [54], whereas the Co isomorph cannot, since its spins and polarization are collinear, yielding magnetic point group 2′ rather than 2, as in BaMnF_{4}. Moreover, BaMnF_{4} is incommensurately modulated, whereas BaCoF_{4} is not.

Other magnetoelectric effects in BaMnF_{4} arising from coupling of polarization and magnetization are the dielectric anomalies illustrated in Figures 3 and 4. The anomaly shown in Figure 3 is the dielectric susceptibility along the polar axis. This change in dielectric constant () near K is small (%), negative, and proportional [55, 56] to the sublattice magnetization squared , in accord with the general theory of Gehring [57]. All of these characteristics are expected for intrinsic effects, whereas extrinsic MaxwellWagner space charge effects are usually much larger, often positive, and not proportional to any power of [58–60]. Although these interpretations have remained contentious [61–66], recent studies discriminate carefully between intrinsic and extrinsic effects [58, 67, 68]. Note that an earlier theory by Albuquerque and Tilley [69] incorrectly predicted that the change in near must be positive definite. This was due to neglect of higherorder terms in the free energy they used; these terms are necessarily positive definite and can be larger than the lowestorder negative term. A very similar model was independently published by Glass et al. [70] and by Negran [71] to fit data on BaNiF_{4}. However, a more comprehensive model was detailed by Fox et al., [53] which explains the magnitude, temperature dependence, and rather importantly, the signs of the dielectric constant changes at both in BaMF_{4} and also at (the higher temperature ca. 90 K at which the spins order inplane. The latter is a larger magnetoelectric effect on the nonpolar axis electric susceptibility; this occurs at approximately , where the magnetic spins order inplane in two dimensions, and is proportional to the magnetic energy. This is an early study of magnetoelectric effects well above the temperature of longrange () ordering, and recently we see something similar (discussed in the following sections) for PbFe_{1/2}Ta_{1/2}O_{3} compounds, where . 150 K, but magnetoelectric effects persist up to ca. 400 K due to shortrange spin ordering (clustering).
The dielectric data discussed above that are shown in Figure 4 are for the magnetic axis in BaMnF_{4}. Here the anomaly is larger, still negative, and goes well above . It is maximal near 90 K, which the temperature at which magnetic inplane ordering sets in Zorin et al. [39, 41]. It arises from the linearquadratic term in the free energy , which is nonzero well above in any antiferromagnet, since , but is very large (nearly equal to inplane) in any magnet that orders in two dimensions.
This is a particularly fine example of the linearquadratic magnetoelectric coupling first discovered by Hou and Bloembergen [72] because it permits very quantitative analysis of inplane. This quadratic magnetoelectric effect is also strong in BaMnF_{4} [73, 74].
Ferroelectricallyinduced ferromagnetism: in 1979 Scott showed [52] that it is plausible that the weak ferromagnetism in BaMnF_{4} measured by Venturini and Morgenthaler [46] arises from the ferroelectricity. The key term in the free energy developed explicitly by that group [51] is of form where is the polarization; is the sublattice magnetization; and is the weak ferromagnetic moment. is a DzyaloshinskiiMoriya anisotropic exchange term; it signifies physically that the ferroelectric displacement of the magnetic ion will modify the quantum mechanical exchange in particular directions. More recently PerezMato [75] and Benedek and Fennie [76] have independently shown that an interaction of this algebraic form is generic and is required for ferroelectricallyinduced ferromagnetism in all crystals, and not just the BaMF_{4} family. Fennie and Benedek have extended the treatment of such trilinear coupling to ferroelectrics in which all three parameters , , and are structural (nonmagnetic), so that polarization arises from coupling of form rather than . We can see from (1) why such a ferroelectric canting of spins is favored in BaMnF_{4}, since is along the axis; is along the axis; and is along . However, in BaCoF_{4}, and are both along the axis, and this spin flop makes the interaction term vanish. The space group requirements for ferroelectrically induced (weak, canted) ferromagnetism are given in Table 1, from Scott [52], based upon the original theory of Birss [51].
Using the definition of the magnetoelectric tensor , Fox and Scott write for the magnetization along the axis. But by the usual model of spins with spin for Mn^{+2} and approximately 2.0, with cm^{−3} [77] and C/cm^{2} [77], we can also express as where is the canting angle of the spins. Solving (2) and (3) together for , using the known values of offdiagonal magnetoelectric tensor components for other Mn^{+2} systems, Venturini and Morgenthaler estimated as mrad, in good agreement with the measured value of 3.0 mrad [46].
In addition to explaining the induced ferromagnetism, a magnetoelectric theory of BaMnF_{4} should be able to explain the dielectric anomalies. The assumed free energy of Fox et al. was where ; is the remnant polarization; and is the part of the polarization induced by applied magnetic field .
Note that this is a meanfield (Landau) theory; this is quite allowed for weak ferromagnets, because the order parameter (the canting) is small at all temperatures. Singleion anisotropy (originally favored by Rado in some materials) has been ignored. More importantly, no electrostriction or magnetostriction has been included; these are of paramount importance in the discussion of PbFe_{2/3}W_{1/3}O_{3} on sections of this review that follow.
Minimizing this free energy showed that the dielectric anomaly at the Neel temperature is of form This shows several important things. Firstly, the dielectric anomaly varies as magnetization squared; secondly, it can be positive or negative, depending upon the sign of ; thirdly, it is not very large (numerically of order 1% of the background dielectric constant). Therefore when we see publications about other materials in which the dielectric anomaly is 20–30% of the background value and is not proportional to the magnetization or its square, we can be skeptical [24, 26–31].
The theory of Fox et al. explains very well the small negative anomaly in the axis dielectric constant in BaMnF_{4} at and below K, but it cannot explain the larger dielectric anomaly along the axis near . 90 K. As discussed above, this anomaly arises (Figure 4) because of the HouBloembergen linearquadratic term and is due to the inplane ordering up to ca. . Twodimensional systems cannot be modeled via meanfield theories, simply because integrating overall three dimensions gives zero. In this particular case, the correct details are given elsewhere [53, 68, 69], but the main conclusion is that the dielectric anomaly in this case is proportional not to , but to the magnetic energy. In other systems [60–66] the observed dielectric anomaly is not proportional to either; hence it may arise from extrinsic MaxwellWagner space charge. The work in [61] is especially suspicious and has never been reproduced or discussed further by the original authors.
A general ab initio theory of ferroelectricity in this BaMF_{4} family has been published by Ederer and Spaldin [79].
There is an added complication for careful analysis of BaMnF_{4}, which is that it is structurally incommensurate below its antiferroelectric phase transition [80] near 254 K. Cox et al. reported [81] that the initial value of the wave vector for the soft mode is at and that the incommensurate 0.39 value remains independent of temperature down to 4 K. This is perhaps true only in their specimen, however, and probably due to incommensurate antiphase boundary pinning by defects (perhaps fluorine vacancies). In other samples several transitions are found via dielectric studies [82], by piezoelectric resonance [83], a double peak in specific heat [84], and most importantly, neutron scattering [85, 86], and it would appear that a Devil’s staircase of wave vectors of probable form exists, starting at and asymptotically reaching a lockin at , that is with a unit cell of ten MnF_{6} octahedra, compared with two in the paraelectric phase. Some modelling of this has been done [87].
3.3. Ferrimagnetic Ferroelectrics [88, 89]
The study of ferroelectric magnetic fluorides has recently been centered at two locations: Groningen [90] and Ljubljana [91–95]. The Ljubljana effort has emphasized the family whose structure is diagrammed in Figure 5. This is in fact an unusual ferromagnetic ferroelectric, with two Fe^{+3} ions and three Fe^{+2} ions per formula group (4Fe^{+3} and 6Fe^{+2} ions per primitive unit cell). It is possible to substitute separately for the Fe^{+2} ions, giving for example K_{3}Fe_{2}^{+3}Cu_{3}F_{15}, and for the Fe^{+3} ions, giving K_{3}Fe_{3}^{+2}Cr_{2}F_{15}. All of these are magnetoelectric, and the latter exhibits twophase transitions at low temperatures, possibly signifying the spin ordering of Fe (higher ) and Cr (lower ) ions. A more general discussion of the possibility of magnetoelectricity in the wider family of A_{3}Fe_{5}F_{15} has been given by Abrahams [96, 97]. Here the Aion can be Na, Li, K, and so forth. No lattice dynamical modelling of these structures has been published.
Models: Picozzi’s group has published [98] an ab initio model for with certain predictions of electronic character for its magnetoelectric transition. Unfortunately she had been unaware of the fact that the pertinent experimental results had been published several years before and did not agree with her postfacto predictions. It is sometimes difficult to get theoreticians to do literature searches at present. A similar example is the recent ab initio model for the family BaClF [99] where the authors were unaware of the Raman phonon experiments [100].
3.4. Magnetoelectric Fluoride Relaxors
General view: the idea of materials that are simultaneously ferroelectric relaxors and magnetic relaxors was initiated by Levstik et al. who developed the basic idea [88] and also showed a specific example [89] involving PbFe_{1/2}Nb_{1/2}O_{3} and PbMg_{1/2}W_{1/2}O_{3}.
A large amount of research has been carried out on three leadferritebased relaxors: PbFe_{2/3}W_{1/3}O_{3} [101–109]; PbFe_{1/2}Ta_{1/2}O_{3} [110]; and PbFe_{1/2}Nb_{1/2}O_{3} [111–116] and on their solid solutions with PZT (lead zirconate titanate). The Ta and Nb compunds have high Neel temperatures (ca. 150 K) and ferroelectric well above ambient (310 K and 380 K, resp.) and when combined with PZT are both ferroelectric and somewhat magnetic at room temperature, with evidence of coupling between the polarization and magnetization. The mechanisms are somewhat unclear yet, and spin clustering may be involved. The PZTmixed compounds are good singlephase materials, generally with the tetragonal BaTiO_{3} structure.
Many multiferroic relaxor materials exhibit glassy magnetic phases. In this regard it is important to recognize, as emphasized by Fischer and Hertz in their text, [117] that published spinglass theories generally do not apply to crystals such as ferroelectrics that lack inversion centers. In particular, they stress that such systems cannot be Ising like. Since some multiferroics exhibit properties resembling spin glasses [118], this means that existing theories are apt to be inapplicable [119]. Theorists should take note. This may be the cause of unusually low values for the critical exponent zv reported in the magnon cross sections of BiFeO_{3} [120]; however, we note that cluster models also give very low values ca. 12.
3.5. PbFe_{2/3}W_{1/3}O_{3} (“PFW”) and Its Solid Solutions with PZT
Lead iron tungstate has been known since the days of Smolensky are to be a multiferroic with a “diffuse” phase transition (now termed a “relaxor”). Very recently a theory has been developed that gives very specific predictions for magnetic field dependence of electrical properties in such materials [121]. Based upon the earlier work of Pirc and Blinc, in their newer paper Pirc et al. calculate that for systems like PFW that are both magnetic relaxors (nanoregions of oriented spins) and ferroelectric relaxors (polar nanoregions) the coupling of magnetization and polarization through strain , that is, via magnetostriction and electrostriction can be very large—much larger in fact than the direct biquadratic coupling . This kind of indirect straincoupled magnetoelectric effect is not subject to the mathematical limit on magnetoelectric susceptibilities imposed by the HornreichShtrikman constraint, that is, . We note parenthetically that the HornreichShtrikman constraint is not rigorous in any event, as shown recently by Dzyaloshinskii [122]; it is based upon linear response theory, which fails, for example, if there is a ferromagnetic phase transition at a temperature below the magnetoelectric transition (e.g., if Cr_{2}O_{3} were to become ferromagnetic at low temperatures).
The conclusion of this theory [121] is that materials near the instability limit between shortrange electric relaxor ordering and longrange ferroelectricity can be driven to the relaxor state by application of a magnetic field . This occurs as a continuous dynamic process in which the polarization relaxation time is increased with applied field . The explicit dependence of is given by where the critical field is estimated to be using averages of magnetostriction and electrostriction tensor components from related compounds (those for PFW/PZT are yet unmeasured; Figure 6). Readers will recognize the unusual algebraic dependence in (6) as that of a VogelFulcher equation (known to fit ordinary ferroelectric relaxors) in which the freezing temperature has been replaced with a critical magnetic field . As shown in Figures 6 and 7, this formula fits the observed data in PFW/PZT very well, and the critical field is evaluated as , rather close to the theoretical estimate. The drive of a longrange ferroelectric to become a relaxor in this model requires that the product of magnetostriction tensor and electrostriction tensor is to be negative; for a positive product, the applied magnetic field will conversely drive the relaxor to longrange ferroelectric ordering.
When the applied magnetic field becomes close to , the hysteresis loop becomes unmeasurable, and the material exhibits only a small extrinsic (spacecharge) loop of a very lossy linear dielectric [123]. If the time constant of the measuring apparatus were unlimited, this would occur at , but in reality it will occur at a slightly lower field, as the polarization relaxation time moves out of the frequency range of the detector. In the data shown in [123] , and the polarization relaxation time increases from ca. 200 ns at to 100 μs at . Longer relaxation times exceed the measuring window of the apparatus employed, but independent of the kit used, the hysteresis loop should vanish before .
Other Models: Inductance due to Charge Injection
Despite the excellent agreement between theory and experiment for these data, there are nagging worries because the experiments were not reproducible in Seoul (Noh, [124]) or Prague [125] and in our own lab were highly sensitive to substrates, electroding, and wire bonding. The electrode sensitivity suggests an extrinsic possibility, namely, that of inductance. A ferroelectric capacitor is normally assumed to function as a pure capacitance without inductance, but in these leaky semiconducting materials there is always some charge injection, and charge injection produces an inductance [126–128]. Such a “negative capacitance” (not in the very recent sense of the phrase) would explain why the dielectric data at high appear to drop to zero in the graph of [123]. Hence there is a possibility that the dependence of polarization arises from an LCR resonance. This is also supported somewhat by similar observations [129] by Martínez et al. in LSMO which is known to exhibit strong negative magnetoresistance at small magnetic fields, making charge injection in that material very dependent.
These PFW/PZT films also exhibit positive temperature coefficients of resistivity (PTCR) [130]. The data fit the model of Dawber and Scott [131]. PTCR is of commercial device importance because it eliminates the problem of thermalrunaway shorts.
3.6. Other Fluoride and Oxyfluoride Magnetoelectrics
In addition to the Pb(Fe,W)O_{3}, Pb(Fe,Ta)O_{3}, and Pb(Fe,Nb)O_{3} families [132], there are a number of other fluoride magnetoelectrics and some oxyfluoride crystals that are probably magnetoelectric. The latter are reviewed by Ravez [133]. Most of these are magnetic and ferroelectric below 100 K as follows:(a)Pb_{5}Cr_{3}F_{19} family [134, 135],(b)Sr_{3}(FeF_{6})_{2} family [136],(c)(NH_{4})_{2}FeF_{6} family [137, 138],(d)Oxyfluorides.
Of these Pb_{5}Cr_{3}F_{19} has received the most recent attention. It exhibits longrange magnetic ordering at K and ferromagnetic clustering at higher temperatures [139].
Prospects for development are high for basic physics (including copper oxide); modest to good for quaternary perovskite oxides. Switching of ferroelectric domains in PFT/PZT at 300 K by a weak magnetic field of Tesla is shown in Figure 8.
(a)
(b)
(c)
(d)
4. Nanodomains and Surface Phase Transitions
4.1. Nanodomains
Unlike domains in magnets, which can have complicated Bloch walls, Neel walls, and vortex structures, the domains in ferroelectrics were thought for many years to be very abrupt (one or two unit cells, compared with hundreds in magnets) and Ising like, with straight rectilinear boundaries. However, recently a plethora of nanostructures has been revealed in ferroelectrics, including complex vertex structures, of which some are vortices [140, 141] (having winding number 1 is not sufficient to make a vortex; div —an explosion—also has winding number +1 but lacks a ) and some are not. In the past domains were generally a nuisance, although their wall motion contributes a great deal to their effective dielectric constant [142, 143]. Now, however, we see that domain walls can be conducting [144] or even superconducting [145] in insulators, and the walls can be ferromagnetic even though the domains outside the walls are not [146, 147]. Note that Privratska and Janovec [148, 149] list all cases in which the domain walls can be ferromagnetic when the surrounding domains are not. A detailed microscopic theory of magnetic walls in nonmagnetic multiferroics has been developed by Daraktchiev et al. [150, 151].
One of the most profound differences between magnetic domain walls and ferroelectric domain walls has to do with inertia and momentum. Ferroelectric walls satisfy Newton’s equations of motion, which have mass and momentum. These are second order in time, and hence domain walls coast a long distance (up to ca. 50 microns) after large fields are turned off. In contrast, magnetic walls satisfy the LandauLifshitzGilbert equations, which are first order in time. Equations that are first order in time lead to motion that stops instantly when the driving field (or ) is terminated. This problem has been discussed in the literature, but not clearly resolved. It leads to apparent paradoxes, such as the experimentally long coasting of magnetic domain walls in racetrack memory devices. It also makes it complicated to write down equations of motion for domain walls in magnetoelectric multiferroics.
This failure to differentiate between magnetic domain walls and ferroelectric domain walls has occasionally led authors to ignore how far ferroelectric walls can coast after the external field is cut off. This produces, in my opinion, erromeous models of domain wall dynamics in high fields, [152, 153], where Molotskii et al. ignore the momentum of ferroelectric walls and assume that they stop the instant when the field is terminated.
The theory of such nonrectilinear domains was stimulated by the model calculation of Naumov et al. [154] and Fu et al. [155], but the idea of circular or toroidal domains is deeper and goes back to Ginzburg et al. [156, 157] or to Zeldovich before that, with a good recent review by Van Aken et al. [158].
Domain wall dynamics are as fascinating as their statics. Paruch has quantitatively analyzed creep [159], and some vertex dissociations and recombinations have been studied in detail by McQuaig [160], following the early SrolovitzScott model [161]. The latter is illustrated in Figure 9. Such adjacent pairs of threefold vertices have been reported by Jia et al. [141] and their collision to form a single fourfold vertex, and subsequent reseparation has been observed by McQuaid and Gregg. A skyrmion theory is given by Komineas [162].
In circular thinfilm 1micron diameter disks of PZT De Guerville et al. find domains form concentric circles whose aperiodic diameters resemble secondorder Bessel functions [163]. These are absent in square films of the same size, indicating an unexpectedly strong role for boundary conditions. For skyrmion theory of such ring domains, see Axenides et al. [164]. Figure 10 shows a graph in parameter space showing how the presence or absence of such concentric domains depends upon sample diameter; the horizontal axis is a material parameter. Figure 11 illustrates just how sensitive the existence of such domains is to boundary conditions. These domains in our simulation occur for disks, octagons, hexagons, and not for squares or triangles; pentagons are an intermediate situation. No analytic theories explain this critical dependence on the number of sides, but Baudry et al. [165] have derived such patterns from a nonlinear model, and his group [166] has further shown that a kind of surface tension in the film is involved; Figure 12 illustrates data.
Prospects for 2012–22: excellent for pure physics. Since devices in which the operation is entirely via domain wall motion exist in both magnets [167, 168] and ferroelectrics [169], the application prospects for industry are also outstanding.
Particularly interesting from the physics point of view are the fractal domains reported by Catalan et al. [170].
4.2. Surface Phases
Surface phases are lumped together in the present review because domains are usually studied on surfaces (via atomic force microscopy AFM and in particular in the polarization mode, PFM). Several important materials have had surface phases discovered in them, particularly in BiFeO_{3}.
In the initial study of BiFeO_{3}, Smolensky et al. reported [171] many temperatures at which anomalies were observed and suggested that this might be due in each case to a phase transition. Although other scientists generally expressed skepticism over the years, it appears now that her inferences were correct. BiFeO_{3} exhibits at least three bulk phases (R3c, Pbnm (insulating), Pbnm (metallic), and possibly Pm3m (cubic) very near to its melting point [172–176]. But it also exhibits several anomalies that appear to be surface phase transitions: 548 K [177], 458 K [178–180], 201 K, and 140.3 K [181–183]. A variety of techniques have been used to elucidate these transitions, including EPR, inplane interdigital electrode dielectric studies, neutron scattering [184], and both film and nanotube geometries (the latter to maximize surface/volume ratio).
Prospects: the surface studies show that the spin waves in BiFeO_{3} are propagating modes well above ambient temperatures, making them useful for THz devices. The use of BiFeO_{3} surfaces for picosecond THz emitters was developed in beautiful detail by Tonouchi’s group [185].
5. Artificially Grown Superlattices
Superlattices of alternating slices a few lattice constants thick have been made by several groups with two (or three) different kinds of ferroelectrics [186, 187], of a ferroelectric and paraelectric (e.g., SrTiO_{3}) [188, 189], or of a ferroelectric and a magnet [190, 191]. In many cases there is new physics learned from these geometries and combinations. For example, when BaTiO_{3 }with along [001] is interlaced with SrTiO_{3}, it is expected [192] that the strontium titanate develops a polarization along [001] also. However, accurate second harmonic generation (SHG) data show in SrTiO_{3} develops along [193, 194], as shown in Figure 13. This involves a high cost in energy due to Poisson’s equation for electrostatic charge at the interfaces, but Johnston et al. were able to show [195] that this is more than compensated by the savings in elastic energy. Some similar effects may be involved in O18 SrTiO_{3} at very low temperatures (<35 K) because the apparent symmetry [196, 197] is lower than that predicted from the TiO soft mode [198].
Rather more profound physical effects are observed in SrTiO_{3}/PbTiO_{3} superlattices, for which a good review is given by Dawber et al. [199].
Prospects: this is a very hot topic, particularly in oxide perovskites, because it is a precise way of analyzing interface oxide physics, which relates closely to the superconductivity in LaAlO_{3}/SrTiO_{3} interfaces [200]. In this regard the studies of oxygen vacancies and conduction in pure LaAlO_{3} [201] have new importance.
6. Photovoltaics
6.1. Basic Idea
The basic idea of photovoltaics is that in the presence of abovebandgapenergy light electronhole pairs are formed in a crystal, and the absence of an inversion center in the crystal lattice will electrically cause these eh pairs to diffuse away from the illuminated spot. This produces a photovoltage, and in a conducting material, a photocurrent. Generally the photovoltage peaks at the bandgap energy (wavelength), although Fridkin’s text [202] describes other possibilities.
This phenomenon has undergone a minor renaissance recently with the report by Seidel et al. [203] that voltages of order 500% of the bandgap Eg (13 eV in a 2.7 eV material, BiFeO_{3}) are observed in thinfilm specimens with many small domains. This immediately suggests that the observed process is one of series voltage connections among (ca. 5) domains, such that the total voltage generated is 5 Eg/e. Various theoretical models have been used recently to describe the photovoltaic effect in detail [204], of which a “shift model” is perhaps most popular [205]. Some authors have argued that the electrodedielectric interaction plays a dominant role [206], but this seems impossible based upon earlier optical measurements by the present author of photovoltaic effects in LiNbO_{3} with no electrodes [207, 208]. The photovoltaic effect is in general not along the polar axis of ferroelectric crystals, so that it is a morphic symmetrybreaking perturbation. Since the photovoltaic tensor is third rank, large (40 kV/cm) fields can be produced perpendicular to the polar axis and be modest laser illumination (e.g., 500 mW of Argonion light focussed to ca. 50 micron diameter spots). This shows up dramatically in the phasemarching conditions for smallangle Raman scattering, as shown in Figure 14 [207].
Impact: renewed interest in the theory (e.g., Rappe et al.). Significant funding for new improved devices (e.g., NASA).
7. Phase Transitions
Phase transitions will always be popular among physicists because they represent a pathological state of matter, and among chemists in part because of the complexity and dynamics of phase diagrams. Phase transitions in ferroelectrics have traditionally been modeled using simple meanfield theory, following Landau [209] and Devonshire [210]. Attempts to fit more sophisticated exponents to Heisenberg or Ising models have in general raised skepticism. The main problem in fitting any critical exponents is first to show that the temperature range fitted is not arbitrary, and second that alternative models such as the “defect exponent” model of Sigov et al. [211, 212] are not better choices. The defect model gives success for unusually large exponents, such as that for ultrasonic attenuation, in systems such as incommensurates (e.g., BaMnF_{4} [213, 214]) and relaxors such as PMNPT [215, 216] or SBN [217] where discommensurations or stoichiometric boundaries serve as extended defects. In particular Bobnar measures a very unusual exponent of for in several PMNPT samples, whereas the Sigov defect theory predicts exactly 5/2 in mean field [218, 219]. We note that SBN is now known to be a firstorder phase transition [220, 221], which makes the critical exponents claimed for it suspicious.
7.1. Stress/Temperature Diagrams
Early in the studies of the cubictetragonal and cubicrhombohedral phase transitions in and very nice phase diagrams were calculated and measured by Burke and Pressley in 1969 [222, 223], which showed in detail the critical stresses required to change phase on a uniaxial stresstemperature graph.
Many years later this form of presentation became popular with the calculations of Pertsev et al. [225] for situations in which the stress/strain in ferroelectric perovskite oxides was controlled by the lattice mismatch with the underlying substrate. Although not all of the latter phase diagrams were qualitatively correct, these graphs became known in some circles as “Pertsev diagrams.” In view of the 1969 work by Burke and Pressley on perovskite oxides, this seems to be an inappropriate misnomer. Even if one favors the “cult of personality,” a fairer label might be “BurkePressley diagrams.” The present author prefers “strain/temperature” or “stress/temperature” diagrams. In general it is not a good idea to name things after folks who rediscover them; not reading the literature should not be rewarded.
Phase diagrams are often pedagogically interesting in ferroelectrics. Figures 15 and 16 show [224, 227] in incommensurate sodium nitrite a triple point, a tricritical point, a critical end point, and something that extrapolates to a Lifshitz point where phase boundaries “kiss.” Trissarcosine calcium chloride (TSCC) has a number of newly discovered yet unexplained phase transitions under both temperature and pressure [226, 228, 229]. Rather remarkably, the one at 185 K detected via NMR [228] and probably isosymmetric neither is observable in any specific heat measurements, nor is the transition at 64 K [229]. Figure 17 illustrates the use of resonant ultrasonic spectroscopy (RUS) to reveal such subtle phase transitions; here the acoustic phonon response to ac driving frequencies changes slope or exhibits new resonances at the phase transition temperatures of 185 K and 64 K in TSCC. Surprisingly, very precise specific heat measurements (Figure 18) reveal nothing at these temperatures.
(a)
(b)
(a)
(b)
7.2. Quantum Critical Points
When superconductors or magnets have phase transitions exactly at , there exist peculiar phenomena. This situation is referred to as a Quantum Critical Point (QCP). Reviews discuss in some detail the interesting new physics at such points [230–232]. It is possible to prepare several ferroelectrics, such that . Examples are SrTiO_{3 }with 30% O18 [233], TSCC with 18% Br or iodine [234], or (a quantum ferroelastic) [235]. Studies of these three materials are underway in our group [236], and some work has been published [237] or submitted.
Prospects are scientifically interesting, especially for multiferroics. Applications are nil.
7.3. Phase Transitions without Domains
Landau and Lifshitz pointed out long ago that it is quite possible for a ferroelectric to reverse individual polarizations all at once without forming or moving any domain walls. Each local polarization would simply flip 180 degrees simultaneously. However, the LandauDevonshire free energy shows that in general this requires about 1000x as much field as is required for the usual domainwall controlled coercive field . So the problem experimentally is not to show that it happens, but to show why the domainwall process does not happen first; that is, any applied field has a finite rise time, and authors need to show unambiguously that the domain wall mechanism is somehow suppressed.
Such claims have been made occasionally over the years, such as by Ducharme Fridkin et al. [238, 239]. At present the best case has been argued by Zhang [240] and Scott [241]. A slightly weaker case has been made by the Argonne group [242].
Prospects: more experiments need to be done. Probably no industrial application for devices will exist.
8. Flexoelectricity
Flexoelectricity is the creation of a voltage via an inhomogeneous strain in a crystal (or vice versa). It was probably first analyzed by the present author in 1968 [243] in the Scheelite crystals represented by , , , , and so forth. As shown in Figure 1, these materials crystallize in a centric tetragonal structure with even and odd parity phonon modes that are, respectively, Raman and infrared active. However, the B_{u} symmetry vibrations are “silent,” forbidden in both infrared and Raman spectroscopy. The presence of an inhomogeneous shear strain of symmetry E_{u} makes the nominally forbidden B_{u} mode(s), such as that at 360 cm^{−1}, appear in the Raman spectra with apparent symmetry A_{g}, since the product contains the representation A_{g}.
When single crystals of these compounds are prepared for laser Raman studies they are mechanically polished to minimize reflections from the incident and transmitted laser beam. Unfortunately such polishing creates inhomogeneous strains. By considering which A_{u} and B_{u} modes occur in each Raman tensor component, we can infer the symmetry of the perturbation. An example is given below. The inferred perturbation transforms as and in the case studied corresponds to a surface shear strain of symmetry , with depth gradient along z, that is, . In presentday terminology this would be termed a flexoelectric perturbation. This analysis permitted the identification of the silent modes in the Scheelites and the explanation of their splittings according to the model diagrammed in Figure 1, which implies that theinternal vibrational modes of the WO_{4} ions are split into and symmetries by the tetragonal crystal field and further into gerade () and ungerade () symmetry pairs by Davidov interaction of the two WO_{4} ions per primitive unit cell [244]. The fact that these splittings in energy are proportional to the inverse sixth power of the  interionic distance implies that the interaction is dipoledipole. This use of Raman spectroscopy to study flexoelectricity should be exploited further.
In the 1960s this sort of flexoelectricity was generally considered a nuisance, not the basis for devices. In bulk it is a small effect and was carefully studied by the Penn State group [245, 246] and by Tagantsev [247]. More recently the first studies of oriented single crystals were reported [248], together with ab initio calculations [249]. There remain some unresolved controversies, with Resta maintaining that there are not separate bulk and surface flexoelectric effects [250], but Tagantsev argues that there are [251]. Some unpublished work by Zhou et al. [252] may resolve this question. In the interim, Lee et al. report [253] giant flexoelectric effects in very thin films, as shown in Figure 19, and Lu et al. [254] show flexoelectric switching as a memory device, Figure 20.
(a)
(b)
(c)
(a)
(b)
9. Relaxors and Birelaxors
9.1. Relaxors
Relaxor ferroelectrics are oxide compounds with large dielectric anomalies at phase transition temperatures but no longrange order or spontaneous polarization [255, 256]. It is important that the temperature at which the dielectric constant peaks varies strongly with probe frequency. They are of commercial importance as transducers and actuators because they exhibit large piezoelectric strain without fracture. The most important families are probably PMN (lead magnesium niobate), including PMN mixed with lead titanate (PMNPT) and SBN (strontium barium niobate).
These materials exhibit large local deviation from stoichiometry, such that PMN of nominal formula PbMg_{1/3}Nb_{2/3}O_{3} may have local Nb : Mg ratios of as little as 1 : 1 rather than 2 : 1. This implies that the systems are not in mechanical or thermal equilibrium, and hence that equilibrium statistical mechanics may not give a wholly accurate description of their dynamics. One should be particularly cautious in fitting subtleties such as critical (fluctuationdominated) exponents. Generally a good model for relaxors is the randombond, randomfield model of Pirc and Blinc [257, 258], which gives a quantitative description of most of their properties, including a critical end point [259].
However, a specific discrepancy in their modeling occurs in the area of critical exponents. Generally the application of critical phenomena requires that the phase transition in question is continuous (second order). In the contrary case of a phase transition with a small discontinuity (first order), no critical exponents technically exist, but erroneous fitting attempts will give small numerical values near 0.0–0.1 for the order parameter (polarization) exponent beta (1/2 in mean field) and equally erroneous values for isothermal susceptibility exponent gamma (1.0 in mean field). We emphasize that fitting critical exponents to a firstorder phase transition is usually physically nonsense [260–262].
The first suggestion that SBN had a firstorder phase transition was by J. Dec (EMF conference, Lake Bled, Slovenia, 2007), but this was strenuously rejected by his coauthor, W. Kleemann, in the discussion following Dec’s invited talk. However, this year it was shown conclusively that the transition in SBN is first order [220, 221].
Although true critical exponents are not applicable to firstorder phase transitions such as that in SBN, there is an approximate theory that fits very well because it is not asymptotically valid at . This is the defect exponential theory of Sigov et al. In general it gives large exponents such as 2.5 for the divergence with temperature of ultrasonic attenuation [260], and these have been measured very precisely experimentally by Fritz in BaMnF_{4} [215, 216] and by Bobnar and Kutnjak in PMNPT [218].
Our general conclusion regarding SBN is that the critical exponents published by Kleemann et al. are not physically meaningful because the transitions are first order (ironically as first suggested by Dec), and that more generally the defect theory of Sigov et al. is more applicable to relaxors due to their large local deviations from stoichiometry, which act as extended defects. However, the specific heat data of Kutnjak et al. [259] seem quite precise and suggest that real exponents characteristic of precursor fluctuations near Tc might give valid numbers, despite the discontinuous jump.
More work is required.
9.2. Birelaxors
Magnets with shortrange order have been called magnetic relaxors or sometimes micromagnets. When this shortrange magnetic ordering is combined with shortrange polarization ordering, the term birelaxor is used. Polarizations and magnetizations can couple boquadratically via electrostriction and magnetostriction, as shown schematically in Figure 21.
The theory of birelaxors has been given by Pirc et al. [33] with experiments from Kumar et al. [34]; good recent work was added from Ljubljana [263].
10. Composites
A general discussion of composites is beyond the scope of this review, but it would be remiss not to mention the exciting work of Viehland et al. on multilayer magnetoelectric composites, for example, of terfenold and PZT, which have reached the level of commercial devices for weak magnetic field sensors, competitive with some respects to SQUID superconducting devices [264, 265]. It is worthy to note that multiferroic composites were unintentionally made in extremely large numbers by the costsaving process if replacing Pt with Ni in multilayer capacitors, as illustrated in Figure 22 [266].
Prospects are basic physics—modest; applications—excellent.
11. Polymer and Flexible Ferroelectrics
Led by extensive studies of polyvinylidene and its fluoroethylene copolymers, flexible ferroelectrics, usually polymeric, have new basic physics in them yet and a host of applications, including switched capacitor RAMs, [267] and resistive RAMs (RRAMs) [268–270]. The field is led by Blom’s group in Groningen and Ducharme in Nebraska.
The only drawback is that it can be difficult to discriminate electret (mobile defect charge) effects from true ferroelectricity. This is an even greater problem with materials such as ZnO : Li. Wurtzite ZnO is pyroelectric but definitely cannot be ferroelectric; electrical hysteresis in ZnO : Li probably comes from electret transport of small Li ions and is not related to ferroelectricity, although there are numerous erroneous claims. The wurtzite structure ZnO is a good pyroelectric, but switching would require breaking ZnO bonds.
Prospects for PVDF basic physics—very good; devices—outstanding.
Ferroelectricity in ZnO : Li is unproven and very unlikely.
12. Electrocalorics
The electrocaloric effect was discovered by Kobeko and Kurtschatov [271]. This is the same man who led the development of the Soviet atomic bomb, although the German transliteration of his name in the electrocaloric paper as J. Kurtschatov renders that nonobvious.
It is the easiest to describe Carnotlike heat cycles for electrocalorics with and diagrams, where is temperature; is entropy, and is applied electric field. Figure 23 illustrates for () the case for a firstorder ferroelectric, where is the actual phase transition temperature, and is the higher temperature above which ferroelectricity cannot be induced by an applied field. Heating cycles of maximum interest cross the phase boundary as isotherms, at constant field or adiabatically at constant . Figure 24 illustrates the () graph, with numerical values appropriate for BaTiO_{3}.
It is well known that an electrocaloric effect (cooling under an electric field) exists. The author discusses this in an early encyclopedia article [227]. Usually the effect (measured as cooling degrees per volt K/N) is very small, ≪1 K/V in bulk. However, since the actual physics involves cooling per unit electric field, the effect is very large in thin films [272, 273] and can even be “giant” [274]. However, making the samples thin dramatically decreases the amount of heat removed (calories). That is, the temperature change remains large, but the cooling load becomes very small. Nevertheless, values of 660 J/kg have been reported at room temperature [275]. Fully integrated prototypes have been made by KarNarayan [276]. The leading material is the PVDF family of polymers (polyvinyldifluoride) [277, 278]. Fundamental ab initio theory of electrocalorics has also been published [279].
13. Biological Ferroelectrics
There has been a recent flurry of papers on biological ferroelectrics, with exaggerated claims about their relevance to human physiology. [280–282]. These follow many piezoelectric studies in soft tissue and not just bone and teeth [281]. The new works include measurements of dessicated tissue from a human aorta, but experts in this technique have expressed skepticism about the results. A different problem is the paper on nglycine Oak Ridge and Aveiro [282]. Here the data are good, but crystalline nglycine is not found in the human body (or any other living creatures). Therefore too much hyperbole has been invoked. Readers should keep in mind that crystalline ferroelectrics are not known to exist in humans, and no in vitro or even in situ work has been reported. Showing electrical artifacts in a piece of dead aorta is a debatable beginning, and certainly no relevance to human physiology or evolution is established.
Prospects are disappointing and sloghtly exaggerated claims in publications.
14. Resistive Random Access Memories (RRAMs)
There are two kinds of resistive memories. The first involves a dendritic short (“moving cathode”) and was first discovered by Plumlee at Sandia in 1967 [284]. See also Lou et al. [285, 286]. This process is highly reversible in some materials and has reached prototype development stage in a number of Asian and European corporations, with 10^{10} cycle performance shown in Korea. Very good reviews have been published of this work [287, 288]. It seems likely that some commercialization will occur within five years. The favorite material is rutile TiO_{2}.
A second kind of ferroelectric resistive RAM utilizes the Schottky barrier change at electrodeferroelectric interfaces. This was first analyzed by Blom et al. in 1994 [289]. His device switched only a small amount of charge in PZR, but in current switched was recently reported by Jiang et al., using semiconducting BiFeO_{3} [290]. Very recently Noheda has confirmed [291, 292] Jiang’s result and shown that the bandgap lowers from the 2.7 eV bandgap of unbiased BiFeO_{3} to ca. 0.2 eV with voltage bias, and hence the Schottky barrier height decreases dramatically with forward bias.
Prospects: For reversible microshortsm as in TiO_{2}—some commercialization within five years. For Schottkytype RRAM, excellent physics for five years; commercialization within ten.
15. Combinations with Graphene and with Carbon Nanotubes
It is of recent interest to fabricate functional ferroelectrics as end units onto both carbon nanotubes and graphene sheets [291–295]. The latter can serve as an FET gate, replacing the conventional (see “carbonferroelectric gates”) [296]. There is a longer history, reviewed elsewhere, of ferroelectric nanowires and nanotubes [297], with recent ab initio theory [298].
16. Second Sound
Since the early theoretical proposal by Gurevuch and Tagantsev [299] for second sound in SrTiO_{3} at low temperatures, there have been several experimental claims [300–302]. These are generally based upon the observed splitting of certain acoustic phonon branches in Brillouin spectra. Based upon the assumption that is tetragonal below 105 K [303], such splitting is forbidden. However, recent work by Blinc et al. [304] and by Scott et al. [305] shows that below ca. 60 K has Srion disorder along [111], which convoluted with the rotation about [001], renders triclinic. The observed Brillouin splitting is required for this triclinic symmetry. The paradox observed spectroscopically between Takesada et al. and Shigenari et al. is thereby resolved. In addition, the crystal symmetry of O18 SrTiO_{3}, which is now known to be lower than orthorhombic [306, 307] is also resolved.
Prospects: second sound in crystal is very hard to observe, requiring exquisite perfection and no isotopic variation (as in NaF). It is highly unlikely in oxide ferroelectrics.
17. Electrically Controlled Magnetic Tunnel Junctions
Beyond the scope of this review. See [308–312].
18. Summary
I have given a rather personal perspective on more than a dozen subtopics withing the general area of ferroelectrics, with predictions of shortterm progress and impact. In the area of memory applications they may still be competitive with phase change memories, magnetic RAMs, and FLASH. Ferroelectrically gated FETs (including MOTTFETs) look promising as do magnetic tunnel junctions that are electrically controlled.
I have emphasized the magnetoelectric properties of fluorides because they lack the covalent bonding of oxide perovskites that Cohen showed [313] to be important and contradict the oxidebased view of Spaldin [314] that there are few multiferroic/magnetoelectrics in nature. These offer new insights in physics, but alas, have no examples of magnetoelectric effects above ca. 123 K.
In general, the game has moved away sharply from the single crystal and bulk ceramics work of 19680. Future devices will undoubtedly be thin films, and operating voltages will be low (<5 V). Interfacial physics and chemistry will be emphasized. Emphasis will still be on oxides, and folks will be referring to “oxide electronics.” As we understood the role of grain boundaries over the past generation, the next decade will find analogous physics and chemistry in domain walls, albeit on a smaller length scale. Domain walls in ferroelectrics exhibit effects not seen in magnetic analogs. It should be fun.
References
 M. Dawber, K. M. Rabe, and J. F. Scott, “Physics of thinfilm ferroelectric oxides,” Reviews of Modern Physics, vol. 77, pp. 1083–1130, 2005. View at: Publisher Site  Google Scholar
 O. Auciello, J. F. Scott, and R. Ramesh, “The physics of ferroelectric memories,” Physics Today, vol. 51, no. 7, pp. 22–27, 1998. View at: Google Scholar
 V. Garcia, M. Bibes, L. Bocher et al., “Ferroelectric control of spin polatization,” Science, vol. 327, no. 5969, pp. 1106–1119, 2010. View at: Publisher Site  Google Scholar
 A. Chanthbouala, A. Crassous, V. Garcia et al., “Solidstate memories based on ferroelectric tunnel junctions,” Nature Nanotechnology, vol. 7, pp. 101–104, 2012. View at: Google Scholar
 A. S. Mischenko, Q. Zhang, J. F. Scott, R. W. Whatmore, and N. D. Mathur, “Giant electrocaloric effect in thinfilm PbZr_{0.95}Ti_{0.05}O_{3},” Science, vol. 311, no. 5765, pp. 1270–1271, 2006. View at: Publisher Site  Google Scholar
 A. S. Mischenko, Q. Zhang, R. W. Whatmore, J. F. Scott, and N. D. Mathur, “Giant electrocaloric effect in the thin film relaxor ferroelectric 0.9 Pb Mg_{1/3}Nb_{2/3}O_{3}0.1 PbTiO_{3} near room temperature,” Applied Physics Letters, vol. 89, no. 24, Article ID 242912, 2006. View at: Publisher Site  Google Scholar
 K. Takahashi, N. Kida, and M. Tonouchi, “Terahertz radiation by an ultrafast spontaneous polarization modulation of multiferroic BiFeO_{3} thin films,” Physical Review Letters, vol. 96, no. 11, Article ID 117402, pp. 1–4, 2006. View at: Publisher Site  Google Scholar
 J. F. Scott, H. J. Fan, S. Kawasaki et al., “Terahertz emission from tubular Pb(Zr, Ti)O_{3} nanostructures,” Nano Letters, vol. 8, no. 12, pp. 4404–4409, 2008. View at: Publisher Site  Google Scholar
 D. S. Jeong, R. Thomas, R. S. Katiyar et al., “Emerging memories: resistive switching mechanisms and current status,” Reports on Progress in Physics, vol. 75, no. 7, Article ID 076502, 2012. View at: Google Scholar
 R. Waser and M. Aono, “Nanoionicsbased resistive switching memories,” Nature Materials, vol. 6, no. 11, pp. 833–840, 2007. View at: Publisher Site  Google Scholar
 J. Seidel, W. Luo, S. J. Suresha et al., “Prominent electrochromism through vacancyorder melting in a complex oxide,” Nature Communications, vol. 3, article 799, 2012. View at: Google Scholar
 A. Gruverman, D. Wu, H. J. Fan, and J. F. Scott, “Vortex ferroelectric domains,” Journal of Physics Condensed Matter, vol. 20, no. 34, Article ID 342201, 2008. View at: Google Scholar
 G. Catalan, J. Seidel, J. F. Scott, and R. Ramesh, “Domain wall nanoelectronics,” Reviews of Modern Physics, vol. 84, pp. 119–156, 2012. View at: Publisher Site  Google Scholar
 A. V. Bune, V. M. Fridkin, S. Ducharme et al., “Twodimensional ferroelectric films,” Nature, vol. 391, no. 6670, pp. 874–877, 1998. View at: Publisher Site  Google Scholar
 T. Furukawa, “Ferroelectric properties of vinylidene fluoride copolymers,” Phase Transitions, vol. 18, pp. 143–211, 1989. View at: Google Scholar
 D. Daranciang, M. Highland, H. Wen et al., “Ultrafast photovoltaic response in ferroelectric nanolayers,” Physical Review Letters, vol. 108, no. 8, Article ID 087601, 8 pages, 2012. View at: Google Scholar
 R. M. Swanson, “Photovoltaics power up,” Science, vol. 324, no. 5929, pp. 891–892, 2009. View at: Publisher Site  Google Scholar
 J. F. Scott and C. A. Paz De Araujo, “Ferroelectric memories,” Science, vol. 246, no. 4936, pp. 1400–1405, 1989. View at: Google Scholar
 E. Tokumitsu, R. I. Nakamura, and H. Ishiwara, “Nonvolatile memory operations of metalferroelectricinsulatorsemiconductor (MFIS) FET's using PLZT/STO/Si(100) structures,” IEEE Electron Device Letters, vol. 18, no. 4, pp. 160–162, 1997. View at: Google Scholar
 R. Scherwitzl, P. Zubko, I. G. Lezama et al., “Electricfield control of the metalinsulator transition in ultrathin NdNiO_{3} films,” Advanced Materials, vol. 22, no. 48, pp. 5517–5520, 2010. View at: Publisher Site  Google Scholar
 C. Girardot, S. Pignard, F. Weiss, and J. Kreisel, “SmNiO_{3}/NdNiO_{3} thin film multilayers,” Applied Physics Letters, vol. 98, Article ID 241903, 2011. View at: Google Scholar
 M. Lines and A. M. Glass, Theory and Application of Ferroelectrics and Related Materials, Clarendon Press, Oxford, UK, 1979.
 M. Fiebig, “Revival of the magnetoelectric effect,” Journal of Physics D, vol. 38, no. 8, pp. R123–R152, 2005. View at: Publisher Site  Google Scholar
 G. A. Smolensky, V. A. Isupov, and A. I. Agranovskaya, “A new group of ferroelectrics (with layered structure),” Soviet Physics Solid State, vol. 1, no. 1, pp. 149–150, 1959. View at: Google Scholar
 G. A. Smolensky, V. A. Isupov, and A. I. Agranovskaya, “Ferroelectrics of the oxygenoctahedral type with layered structure,” Soviet Physics Solid State, vol. 3, no. 3, pp. 651–655, 1961. View at: Google Scholar
 G. A. Smolensky, V. A. Isupov, and A. I. Agranovskaya, “New Ferroelectrics of a complex composition: 4,” Soviet Physics Solid State, vol. 2, no. 11, pp. 2651–2654, 1961. View at: Google Scholar
 T. Kimura, Y. Sekio, H. Nakamura, T. Siegrist, and A. P. Ramirez, “Cupric oxide as an inducedmultiferroic with highTC,” Nature Materials, vol. 7, no. 4, pp. 291–294, 2008. View at: Publisher Site  Google Scholar
 T. Kimura, “A roomtemperature multiferroic,” Nature conference, Aachen, Germany, June 2012. View at: Google Scholar
 W. Peng, N. Lemee, M. Karkut et al., “Spinlattice coupling in multiferroic Pb (Fe_{1/2}Nb_{1/2})O_{3} thin films,” Applied Physics Letters, vol. 94, no. 1, Article ID 012509, 2009. View at: Publisher Site  Google Scholar
 R. Martinez, R. Palai, H. Huhtinen, J. Liu, J. F. Scott, and R. S. Katiyar, “Nanoscale ordering and multiferroic behavior in Pb (Fe_{1/2}Ta_{1/2})O_{3},” Physical Review B, vol. 82, no. 13, Article ID 134104, 2010. View at: Publisher Site  Google Scholar
 D. Sanchez, N. Ortega, A. Kumar, R. S. Katiyar, and J. F. Scott, “Symmetries and multiferroic properties of novel roomtemperature magnetoelectrics: lead iron tantalate—lead zirconate titanate (PFT/PZT),” AIP Advances, vol. 1, Article ID 042169, 2011. View at: Google Scholar
 D. N. Evans, J. N. Gregg, A. Kumar, D. Sanchez, R. S. Katiyar, and J. F. Scott, “Magnetoelectric switching at room temperature in a new multiferroic,” Nature Communications. In press. View at: Google Scholar
 R. Pirc, R. Blinc, and J. F. Scott, “Mesoscopic model of a system possessing both relaxor ferroelectric and relaxor ferromagnetic properties,” Physical Review B, vol. 79, no. 21, Article ID 214114, 2009. View at: Publisher Site  Google Scholar
 A. Kumar, G. L. Sharma, R. S. Katiyar, R. Pirc, R. Blinc, and J. F. Scott, “Magnetic control of large roomtemperature polarization,” Journal of Physics Condensed Matter, vol. 21, no. 38, Article ID 382204, 2009. View at: Publisher Site  Google Scholar
 D. N. Astrov, “The magnetoelectric effect in antiferromagnets,” Soviet Physics JETP, vol. 11, pp. 708–709, 1960. View at: Google Scholar
 D. N. Astrov, “Magnetoelectric effect in chromium oxide,” Soviet Physics JETP, vol. 13, pp. 729–733, 1961. View at: Google Scholar
 B. I. Alshin, D. N. Astrov, and A. V. Tischen, “Magnetoelectric effect in BaCoF_{4},” JETP Letters, vol. 12, pp. 142–145, 1970. View at: Google Scholar
 D. N. Astrov, B. I. Alshin, R. V. Zorin, and L. A. Drobyshe, “Spontaneous magnetoelectric effect,” Soviet Physics JETP, vol. 28, pp. 1123–1127, 1969. View at: Google Scholar
 R. V. Zorin, A. V. Tischen, and D. N. Astrov, “2dimensional magnetic ordering in BaMnF_{4},” Fizika Tverdovo Tela, vol. 14, pp. 3103–3107, 1972. View at: Google Scholar
 B. I. Alshin, D. N. Astrov, and R. V. Zorin, “Lowfrequency magnetoelectric resonances in BaMnF_{4},” Zhurnal Eksperimenti Teoretische Fizik, vol. 63, pp. 2198–2204, 1972. View at: Google Scholar
 R. V. Zorin, D. N. Astrov, and B. I. Alshin, “Lowfrequency magnetoelectric resonances in BaCoF_{4},” Zhurnal Eksperimenti Teoretische Fizik, vol. 62, pp. 1201–1120, 1972. View at: Google Scholar
 D. R. Tilley and J. F. Scott, “Frequency dependence of magnetoelectric phenomena in BaMnf_{4},” Physical Review B, vol. 25, no. 5, pp. 3251–3260, 1982. View at: Publisher Site  Google Scholar
 E. T. Keve, S. C. Abrahams, and J. L. Bernstein, “Crystal Structure of pyroelectric paramagnetic barium cobalt fluoride, BaCoF_{4},” Journal of Chemical Physics, vol. 53, pp. 3279–3283, 1970. View at: Google Scholar
 C. Ederer and N. A. Spaldin, “Recent progress in firstprinciples studies of magnetoelectric multiferroics,” Current Opinion in Solid State and Materials Science, vol. 9, no. 3, pp. 128–139, 2005. View at: Publisher Site  Google Scholar
 C. Ederer and N. A. Spaldin, “Electricfieldswitchable magnets: the case of BaNiF_{4},” Physical Review B, vol. 74, no. 2, Article ID 020401, 2006. View at: Publisher Site  Google Scholar
 E. L. Venturini and F. R. Morgenthaler, “AFMR versus orientation in weakly ferromagnetic BaMnF_{4},” AIP Conference Proceedings, vol. 24, pp. 168–169, 1975. View at: Publisher Site  Google Scholar
 S. A. Kizhaev, Ioffe Institute, private communication, 1981.
 S. A. Kizhaev and R. V. Pisarev, “Dielectric and magnetic properties of BaMnF_{4} at low temperatures,” Fizika Tverdogo Tela, vol. 26, pp. 1669–1674, 1984. View at: Google Scholar
 L. A. Prozorova, Kapitza Institute, private communication, 1981.
 A. K. Zvezdin and A. P. Pyatakov, “Symmetry and magnetoelectric interactions in BaMnF_{4},” Low Temperature Physics, vol. 36, no. 6, Article ID 006006LTP, pp. 532–537, 2010. View at: Publisher Site  Google Scholar
 R. R. Birss, “Magnetic symmetry and forbidden effects,” Americam Journal of Physics, vol. 32, no. 2, Article ID 142150, 1964. View at: Google Scholar
 J. F. Scott, “Phase transitions in BaMnF_{4},” Reports on Progress in Physics, vol. 42, no. 6, pp. 1055–1084, 1979. View at: Publisher Site  Google Scholar
 D. L. Fox, D. R. Tilley, J. F. Scott, and H. J. Guggenheim, “Magnetoelectric phenomena in BaMnF_{4} and BaMn_{0.99}Co_{0.01}F_{4},” Physical Review B, vol. 21, no. 7, pp. 2926–2936, 1980. View at: Publisher Site  Google Scholar
 D. L. Fox and J. F. Scott, “Ferroelectrically induced ferromagnetism,” Journal of Physics C, vol. 10, no. 11, pp. L329–L331, 1977. View at: Publisher Site  Google Scholar
 J. F. Scott, “Mechanisms of dielectric anomalies in BaMnF_{4},” Physical Review B, vol. 16, no. 5, pp. 2329–2331, 1977. View at: Publisher Site  Google Scholar
 G. A. Samara and J. F. Scott, “Dielectric anomalies in BaMnF_{4} at low temperatures,” Solid State Communications, vol. 21, no. 2, pp. 167–170, 1977. View at: Google Scholar
 O. Bonfim and G. Gehring, “Magnetoelectric effect in crystals,” Advances in Physics, vol. 29, pp. 731–769, 1980. View at: Publisher Site  Google Scholar
 G. Catalan, “Magnetocapacitance without magnetoelectric coupling,” Applied Physics Letters, vol. 88, Article ID 102902, 2006. View at: Google Scholar
 J. F. Scott, “Electrical characterization of magnetoelectrical materials,” Journal of Materials Research, vol. 22, no. 8, pp. 2053–2062, 2007. View at: Publisher Site  Google Scholar
 G. Catalan and J. F. Scott, “Magnetoelectrics: is CdCr_{2}S_{4} a multiferroic relaxor?” Nature, vol. 448, no. 7156, pp. E4–E5, 2007. View at: Publisher Site  Google Scholar
 D. Staresinić, P. Lunkenheimer, J. Hemberger, K. Biljaković, and A. Loidl, “Giant dielectric response in the onedimensional chargeordered semiconductor (NbSe_{4})_{3}I,” Physical Review Letters, vol. 96, no. 4, Article ID 046402, 2006. View at: Publisher Site  Google Scholar
 P. Lunkenheimer, R. Fichtl, J. Hemberger, V. Tsurkan, and A. Loidl, “Relaxation dynamics and colossal magnetocapacitive effect in CdCr_{2}S_{4},” Physical Review B, vol. 72, no. 6, Article ID 060103, 2005. View at: Publisher Site  Google Scholar
 J. Hemberger, P. Lunkenheimer, R. Fichtl, H. A. Krug Von Nidda, V. Tsurkan, and A. Loidl, “Relaxor ferroelectricity and colossal magnetocapacitive coupling in ferromagnetic CdCr_{2}S_{4},” Nature, vol. 434, no. 7031, pp. 364–367, 2005. View at: Publisher Site  Google Scholar
 S. Krohns, F. Schrettle, P. Lunkenheimer, V. Tsurkan, and A. Loidl, “Colossal magnetocapacitive effect in differently synthesized and doped CdCr_{2}S_{4},” Physica B, vol. 403, no. 2324, pp. 4224–4227, 2008. View at: Publisher Site  Google Scholar
 J. Hemberger, P. Lunkenheimer, R. Fichtl, H. A. K. Von Nidda, V. Tsurkan, and A. Loidl, “Magnetoelectrics: is CdCr_{2}S_{4} a multiferroic relaxor? (Reply),” Nature, vol. 448, no. 7156, pp. E5–E6, 2007. View at: Publisher Site  Google Scholar
 S. Weber, P. Lunkenheimer, R. Fichtl, J. Hemberger, V. Tsurkan, and A. Loidl, “Colossal magnetocapacitance and colossal magnetoresistance in HgCr_{2}S_{4},” Physical Review Letters, vol. 96, no. 15, Article ID 157202, 2006. View at: Publisher Site  Google Scholar
 H. Kliem and B. Martin, “Pseudoferroelectric properties by space charge polarization,” Journal of Physics Condensed Matter, vol. 20, no. 32, Article ID 321001, 2008. View at: Publisher Site  Google Scholar
 N. Ortega, A. Kumar, R. S. Katiyar, and J. F. Scott, “MaxwellWagner space charge effects on the Pb(Zr,Ti)O_{3}—CoFe_{2}O_{4} multilayers,” Applied Physics Letters, vol. 91, no. 10, Article ID 102902, 2007. View at: Publisher Site  Google Scholar
 E. L. Albuquerque and D. R. Tilley, “Mode mixing and dielectric function,” Solid State Communications, vol. 26, no. 11, pp. 817–821, 1978. View at: Google Scholar
 A. M. Glass, M. E. Lines, M. Eibschutz, F. S. L. Hsu, and H. J. Guggenheim, “Observation of anomalous pyroelectric behavior in BaNiF_{4} due to cooperative magnetic singularity,” Communications on Physics, vol. 2, no. 4, pp. 103–107, 1977. View at: Google Scholar
 T. J. Negran, “Measurement of the thermal diffusivity in BaMnF_{4} by means of its intrinsic pyroelectric response,” Ferroelectrics, vol. 34, pp. 285–289, 1981. View at: Google Scholar
 S. L. Hou and N. Bloembergen, “Paramagnetoelectric effects in NiSO_{4}·6H_{2}O,” Physical Review, vol. 138, pp. A1218–A1226, 1965. View at: Google Scholar
 P. Sciau, M. Clin, J. P. Rivera, and H. Schmid, “Magnetoelectric measurements on BaMnF_{4},” Ferroelectrics, vol. 105, pp. 201–206, 1990. View at: Publisher Site  Google Scholar
 A. K. Zvezdin, G. P. Vorob'ev, and A. M. Kadomsteva, “Quadratic magnetoelectric effect and the role of the magnetocaloric effect in the magnetoelectric properties of multiferroic BaMnF_{4},” Journal of Experimental and Theoretical Physics, vol. 109, pp. 221–226, 2009. View at: Publisher Site  Google Scholar
 J. M. PerezMato, Summer School on Multiferroics, Girona, Spain, 2008.
 N. A. Benedek and C. J. Fennie, “Hybrid improper ferroelectricity: a mechanism for controllable polarizationmagnetization coupling,” Physical Review Letters, vol. 106, no. 10, Article ID 107204, 2011. View at: Publisher Site  Google Scholar
 E. T. Keve, S. C. Abrahams, and J. L. Bernstein, “Crystal structure of pyroelectric paramagnetic barium manganese fluoride, BaMnF_{4},” The Journal of Chemical Physics, vol. 51, no. 11, Article ID 4928, 9 pages, 1969. View at: Google Scholar
 C. Ederer and C. J. Fennie, “Electricfield switchable magnetization via the DzyaloshinskiiMoriya interaction: FeTiO_{3} versus BiFeO_{3},” Journal of Physics Condensed Matter, vol. 20, no. 43, Article ID 434219, 2008. View at: Publisher Site  Google Scholar
 C. Ederer and N. A. Spaldin, “Origin of ferroelectricity in the multiferroic barium fluorides BaMF_{4}: a first principles study,” Physical Review B, vol. 74, Article ID 024102, 2006. View at: Google Scholar
 J. F. Scott, “Phase transitions in BaMnF_{4},” Reports on Progress in Physics, vol. 42, no. 6, Article ID 1055, 1979. View at: Publisher Site  Google Scholar
 D. E. Cox, S. M. Shapiro, R. J. Nelmes et al., “Xray and neutrondiffraction measurements on BaMnF_{4},” Physical Review B, vol. 28, no. 3, pp. 1640–1643, 1983. View at: Publisher Site  Google Scholar
 A. Levstik, R. Blinc, P. Kadaba, S. Cizikov, I. Levstik, and C. Filipic, “Multiple phase transitions in BaMnF_{4},” Ferroelectrics, vol. 4, pp. 703–707, 1976. View at: Google Scholar
 M. Hidaka, T. Nakayama, J. F. Scott, and J. S. Storey, “Piezoelectric resonance study of structural anomalies in BaMnF_{4},” Physica B+C, vol. 133, no. 1, pp. 1–9, 1985. View at: Google Scholar
 J. F. Scott, F. Habbal, and M. Hidaka, “Phase transitions in BaMnF_{4}: specific heat,” Physical Review B, vol. 25, no. 3, pp. 1805–1812, 1982. View at: Publisher Site  Google Scholar
 M. BarthesRegis, R. Almairac, P. StGregoire et al., “Temperature dependence of the wave vector of the incommensurate modulstion in two BaMnF_{4} crystals—neutron and Xray measurements,” Journal de Physique Lettres, vol. 44, no. 19, pp. 829–835, 1983. View at: Google Scholar
 P. St. Gregoire, M. Barthes, R. Almairac et al., “On the incommensurate phase in BaMnF_{4},” Ferroelectrics, vol. 53, pp. 307–310, 1984. View at: Publisher Site  Google Scholar
 B. B. Lavrencic and J. F. Scott, “Dynamical model for the polarincommensurate transition in BaMnF_{4},” Physical Review B, vol. 24, no. 5, pp. 2711–2717, 1981. View at: Publisher Site  Google Scholar
 A. Levstik, V. Bobnar, C. Filipič et al., “Magnetoelectric relaxor,” Applied Physics Letters, vol. 91, no. 1, Article ID 012905, 2007. View at: Publisher Site  Google Scholar
 A. Levstik, C. Filipič, V. Bobnar et al., “0.3Pb(Fe_{1/2}Nb_{1/2})O_{3}0.7Pb (Mg_{1/2}W_{1/2})O_{3}: a magnetic and electric relaxor,” Journal of Applied Physics, vol. 104, no. 5, Article ID 054113, 2008. View at: Publisher Site  Google Scholar
 G. Nénert and T. T. M. Palstra, “Prediction for new magnetoelectric fluorides,” Journal of Physics Condensed Matter, vol. 19, no. 40, Article ID 406213, 2007. View at: Publisher Site  Google Scholar
 R. Blinc, G. Tavčar, B. Zemva, and J. F. Scott, “Electron paramagnetic resonance and Mossbauer study of antiferromagnetic K_{3}Cu_{3}Fe_{2}F_{15},” Journal of Applied Physics, vol. 106, Article ID 023924, 2009. View at: Google Scholar
 R. Blinc, G. Tavčar, B. Žemva et al., “Weak ferromagnetism and ferroelectricity in K_{3}Fe_{5}F_{15},” Journal of Applied Physics, vol. 103, Article ID 074114, 2008. View at: Google Scholar
 R. Blinc, B. Zalar, P. Cevc et al., “^{39}K NMR and EPR study of multiferroic K_{3}Fe_{5}F_{15},” Journal of Physics Condensed Matter, vol. 21, no. 4, Article ID 045902, 2009. View at: Publisher Site  Google Scholar
 A. Levstik, C. Filipic, and V. Bobnar, “Polarons in magnetoelectric (K_{3}Fe_{3}Cr_{2}F_{15}),” Journal of Apploed Physics, vol. 106, Article ID 073720, 2009. View at: Google Scholar
 R. Blinc, B. Zalar, P. Cevc et al., “^{39}K NMR and EPR study of multiferroic K_{3}Fe_{5}F_{15},” Journal of Physics Condensed Matter, vol. 21, no. 4, Article ID 045902, 2009. View at: Publisher Site  Google Scholar
 S. C. Abrahams, “Systematic prediction of new inorganic ferroelectrics in point group 4,” Acta Crystallographica Section B, vol. 55, no. 4, pp. 494–506, 1999. View at: Google Scholar
 S. C. Abrahams, “Structurally based predictions of ferroelectricity in 7 inorganic materials with space group Pba2 and two experimental confirmations,” Acta Crystallographica B, vol. 45, pp. 228–232, 1989. View at: Google Scholar
 K. Yamauchi and S. Picozzi, “Interplay between charge order, ferroelectricity, and ferroelasticity: tungsten bronze structures as a playground for multiferroicity,” Physical Review Letters, vol. 105, no. 10, Article ID 107202, 2010. View at: Publisher Site  Google Scholar
 N. Yedukondalu, K. R. Babu, C. Bheemalingam, D. J. Singh, G. Vaitheeswaran, and V. Kanchana, “Electronic structure, optical properties, and bonding in alkalineearth halofluoride scintillators: BaClF, BaBrF, and BaIF,” Physical Review B, vol. 83, no. 16, Article ID 165117, 7 pages, 2011. View at: Publisher Site  Google Scholar
 J. F. Scott, “Raman spectra of BaClF, BaBrF, and SrClF,” The Journal of Chemical Physics, vol. 49, no. 6, pp. 2766–2769, 1968. View at: Google Scholar
 A. Kumar, R. S. Katiyar, R. N. Premnath, C. Rinaldi, and J. F. Scott, “Straininduced artificial multiferroicity in Pb(Zr_{0.53}Ti_{0.47})O_{3}/Pb(Fe_{0.66}W_{0.33})O_{3} layered nanostructure at ambient temperature,” Journal of Materials Science, vol. 44, no. 19, pp. 5113–5119, 2009. View at: Publisher Site  Google Scholar
 A. Kumar, N. M. Murari, and R. S. Katiyar, “Investigation of dielectric and electrical behavior in Pb(Fe_{0.66}W_{0.33})_{0.50}Ti_{0.50}O_{3} thin films by impedance spectroscopy,” Journal of Alloys and Compounds, vol. 469, no. 12, pp. 433–440, 2009. View at: Publisher Site  Google Scholar
 W. Peng, N. Lemee, J. L. Dellis et al., “Epitaxial growth and magnetoelectric relaxor behavior in multiferroic 0.8Pb (Fe_{1/2}Nb_{1/2})O_{3}0.2Pb (Mg_{1/2}W_{1/2})O_{3} thin films,” Applied Physics Letters, vol. 95, no. 13, Article ID 132507, 2009. View at: Publisher Site  Google Scholar
 J. F. Scott, R. Palai, A. Kumar et al., “New phase transitions in perovskite oxides: BiFeO_{3}, SrSnO_{3}, and Pb(Fe_{2/3}W_{1/3})_{1/2}Ti_{1/2}O_{3},” Journal of the American Ceramic Society, vol. 91, no. 6, pp. 1762–1768, 2008. View at: Publisher Site  Google Scholar
 A. Kumar, I. Rivera, R. S. Katiyar, and J. F. Scott, “Multiferroic Pb (Fe_{0.66}W_{0.33})_{0.80}Ti_{0.20}O_{3} thin films: a roomtemperature relaxor ferroelectric and weak ferromagnetic,” Applied Physics Letters, vol. 92, no. 13, Article ID 132913, 2008. View at: Publisher Site  Google Scholar
 R. N. P. Choudhary, D. K. Pradhan, C. M. Tirado, G. E. Bonilla, and R. S. Katiyar, “Effect of la substitution on structural and electrical properties of Ba(Fe_{2/3}W_{1/3})O_{3} nanoceramics,” Journal of Materials Science, vol. 42, no. 17, pp. 7423–7432, 2007. View at: Publisher Site  Google Scholar
 A. Kumar, N. M. Murari, R. S. Katiyar, and J. F. Scott, “Probing the ferroelectric phase transition through Raman spectroscopy in Pb (Fe_{2/3}W_{1/3})_{1/2}Ti_{1/2}O_{3} thin films,” Applied Physics Letters, vol. 90, no. 26, Article ID 262907, 2007. View at: Publisher Site  Google Scholar
 R. N. P. Choudhary, D. K. Pradhan, C. M. Tirado, G. E. Bonilla, and R. S. Katiyar, “Impedance characteristics of Pb(Fe_{2/3}W_{1/3})O_{3}BiFeO_{3} composites,” Physica Status Solidi, vol. 244, no. 6, pp. 2354–2366, 2007. View at: Publisher Site  Google Scholar
 A. Kumar, N. M. Murari, and R. S. Katiyar, “Diffused phase transition and relaxor behavior in Pb(Fe_{2/3}W_{1/3})O_{3} thin films,” Applied Physics Letters, vol. 90, no. 16, Article ID 162903, 2007. View at: Publisher Site  Google Scholar
 R. N. P. Choudhury, C. Rodríguez, P. Bhattacharya, R. S. Katiyar, and C. Rinaldi, “Lowfrequency dielectric dispersion and magnetic properties of La, Gd modified Pb(Fe_{1/2}Ta_{1/2})O_{3} multiferroics,” Journal of Magnetism and Magnetic Materials, vol. 313, no. 2, pp. 253–260, 2007. View at: Publisher Site  Google Scholar
 W. Peng, N. Lemée, J. Holc, M. Kosec, R. Blinc, and M. G. Karkut, “Epitaxial growth and structural characterization of Pb(Fe_{1/2}Nb_{1/2})O_{3} thin films,” Journal of Magnetism and Magnetic Materials, vol. 321, no. 11, pp. 1754–1757, 2009. View at: Publisher Site  Google Scholar
 W. Peng, N. Lemee, and M. Karkut, “Spinlattice coupling in multiferroic thin films,” Applied Physics Leters, vol. 94, Article ID 012509, 2009. View at: Google Scholar
 A. Kumar, R. S. Katiyar, C. Rinaldi, S. G. Lushnikov, and T. A. Shaplygina, “Glasslike state in PbFe_{1/2}Nb_{1/2}O_{3} single crystal,” Applied Physics Letters, vol. 93, no. 23, Article ID 232902, 2008. View at: Publisher Site  Google Scholar
 M. Correa, A. Kumar, and R. S. Katiyar, “Observation of magnetoelectric coupling in glassy epitaxial Pb(Fe_{1/2}Nb_{1/2})O_{3} thin films,” Applied Physics Leters, vol. 93, Article ID 192907, 2008. View at: Google Scholar
 D. Varshney, R. N. P. Choudhary, C. Rinaldi, and R. S. Katiyar, “Dielectric dispersion and magnetic properties of Bamodified Pb(Fe_{ 1/2}Nb_{1/2})O_{3},” Applied Physics A, vol. 89, no. 3, pp. 793–798, 2007. View at: Publisher Site  Google Scholar
 D. Varshney, R. N. P. Choudhary, and R. S. Katiyar, “Low frequency dielectric response of mechanosynthesized (Pb_{0.9}Ba_{0.1}) (Fe_{0.50}Nb_{0.50})O_{3} nanoceramics,” Applied Physics Letters, vol. 89, no. 17, Article ID 172901, 2006. View at: Publisher Site  Google Scholar
 K. H. Fischer and J. A. Hertz, Spin Glasses, Cambridge University Press, Cambridge, UK, 1991.
 M. K. Singh, W. Prellier, M. P. Singh, R. S. Katiyar, and J. F. Scott, “Spinglass transition in singlecrystal BiFeO_{3},” Physical Review B, vol. 77, no. 14, Article ID 144403, 2008. View at: Publisher Site  Google Scholar
 M. M. Parish and P. B. Littlewood, “Magnetocapacitance in nonmagnetic composite media,” Physical Review Letters, vol. 101, no. 16, Article ID 166602, 2008. View at: Publisher Site  Google Scholar
 M. K. Singh, R. S. Katiyar, W. Prellier, and J. F. Scott, “The AlmeidaThouless line in BiFeO_{3}: is bismuth ferrite a mean field spin glass?” Journal of Physics Condensed Matter, vol. 21, no. 4, Article ID 042202, 2009. View at: Publisher Site  Google Scholar
 I. E. Dzyaloshinskii, “Magnetoelectric to multiferroic phase transitions,” Europhysics Letters, vol. 96, no. 1, Article ID 17001, 2011. View at: Publisher Site  Google Scholar
 R. Pirc, R. Blinc, and J. F. Scott, “Mesoscopic model of a system possessing both relaxor ferroelectric and relaxor ferromagnetic properties,” Physical Review B, vol. 79, no. 21, Article ID 214114, 2009. View at: Publisher Site  Google Scholar
 A. Kumar, G. L. Sharma, R. S. Katiyar, and J. F. Scott, “Magnetic control of large roomtemperature polarization,” Journal of Physics Condensed Matter, vol. 21, Article ID 382204, 2009. View at: Google Scholar
 M. Kempa, S. Kamba, M. Savinov et al., “Bulk dielectric and magnetic properties of PFWPZT ceramics: absence of magnetically switchedoff polarization,” Journal of Physics Condensed Matter, vol. 22, no. 44, Article ID 4453002, 2010. View at: Publisher Site  Google Scholar
 D. Lee, Y. A. Park, S. M. Yang et al., “Suppressed magnetoelectric effect in epitaxially grown multiferroic Pb(Zr_{0.57}Tix_{0.57})O_{3}Pb(Fe_{2/3}W_{1/3})O_{3} solidsolution thin films,” Journal of Physics D, vol. 43, no. 45, Article ID 455403, 2010. View at: Publisher Site  Google Scholar
 K. S. A. Butcher, T. L. Tansley, and D. Alexiev, “An instrumental solution to the phenomenon of negative capacitances in semiconductors,” SolidState Electronics, vol. 39, no. 3, pp. 333–336, 1996. View at: Publisher Site  Google Scholar
 P. Zubko, University of Geneva, Private Communication.
 M. Ershov, H. C. Liu, L. Li, M. Buchanan, Z. R. Wasilewski, and A. K. Jonscher, “Negative capacitance effect in semiconductor devices,” IEEE Transactions on Electron Devices, vol. 45, no. 10, pp. 2196–2206, 1998. View at: Google Scholar
 R. Martínez, A. Kumar, R. Palai, J. F. Scott, and R. S. Katiyar, “Impedance spectroscopy analysis of Ba_{0.7}Sr_{0.3}TiO_{3}/La_{0.7}Sr_{0.3}MnO_{3} heterostructure,” Journal of Physics D, vol. 44, no. 10, Article ID 105302, 2011. View at: Publisher Site  Google Scholar
 A. Kumar, R. S. Katiyar, and J. F. Scott, “Positive temperature coefficient of resistivity and negative differential resistivity in lead iron tungstatelead zirconate titanate,” Applied Physics Letters, vol. 94, Article ID 212903, 2009. View at: Google Scholar
 M. Dawber and J. F. Scott, “Negative differential resistivity and positive temperature coefficient of resistivity effect in the diffusionlimited current of ferroelectric thinfilm capacitors,” Journal of Physics Condensed Matter, vol. 16, no. 49, pp. L515–L521, 2004. View at: Publisher Site  Google Scholar
 A. Levstik, C. Filipič, and J. Holc, “The magnetoelectric coefficients of Pb (Fe_{1/2}Nb_{1/2})O_{3} and 0.8Pb (Fe_{1/2}Nb_{1/2})O_{3} 0.2Pb (Mg_{1/2}W_{1/2}) O_{3},” Journal of Applied Physics, vol. 103, no. 6, Article ID 066106, 2008. View at: Publisher Site  Google Scholar
 J. Ravez, “The inorganic fluoride and oxyfluoride ferroelectrics,” Journal de Physique III, vol. 7, no. 6, pp. 1129–1144, 1997. View at: Google Scholar
 S. C. Abrahams, J. Albertsson, and C. Svensson, “Structure of Pb_{5}Cr_{3}F_{19} at 295K,” Acta Crystallographica B, vol. 46, pp. 497–502, 1990. View at: Google Scholar
 S. Sarraute, J. Ravez, R. Von Der Mühll, G. Bravic, R. S. Feigelson, and S. C. Abrahams, “Structure of ferroelectric Pb_{5}Al_{3}F_{19} at 160 K, polarization Reversal and Relationship to Ferroelectric Pb_{5}Cr_{3}F_{19} at 295 K,” Acta Crystallographica Section B, vol. 52, no. 1, pp. 72–77, 1996. View at: Google Scholar
 E. Kroumova, M. I. Aroyo, J. M. PerrezMato, and M. R. Hundt, “Ferroelectricparaelectric phase transitions with no groupsupergroup relation between the space groups of both phases?” Acta Crystallographica B, vol. 57, pp. 599–601, 2001. View at: Publisher Site  Google Scholar
 M. Lorient, R. VonderMuhll, J. Ravez, and A. Tressaud, “Etude de la transition de phase de (NH_{4}) _{3}FeF_{6} par mesures dielectriques et de thermocourant,” Solid State Communications, vol. 36, no. 5, pp. 383–385, 1980. View at: Publisher Site  Google Scholar
 M. Lorient, R. Von der Mühll, A. Tressaud, and J. Ravez, “Polarisation remanente dans les varietes de basse temperature de (NH_{4})_{3}AlF_{6} ET (NH_{4})_{3}FeF_{6},” Solid State Communications, vol. 40, no. 9, pp. 847–852, 1981. View at: Google Scholar
 R. . Blinc, P. Cevc, G. Tavcar, Z. Trontelj, V. V. Laguta, and J. F. Scott, “Magnetism in Pb_{5}Cr_{3}F_{19},” Physical Review B, vol. 85, Article ID 054419, 2012. View at: Google Scholar
 C. T. Nelson, P. Gao, J. R. Jokisaari et al., “Domain dynamics during ferroelectric switching,” Science, vol. 334, no. 6058, pp. 968–971, 2011. View at: Publisher Site  Google Scholar
 C. L. Jia, K. W. Urban, M. Alexe, D. Hesse, and I. Vrejoiu, “Direct observation of continuous electric dipole rotation in fluxclosure domains in ferroelectric Pb(Zr, Ti)O_{3},” Science, vol. 331, no. 6023, pp. 1420–1423, 2011. View at: Publisher Site  Google Scholar
 A. Fousková, “Increase in permittivity of ferroelectrics as a consequence of polarization reversal,” Journal of the Physical Society of Japan, vol. 20, no. 9, pp. 1625–1628, 1965. View at: Google Scholar
 A. Fouskova and V. Janousek, “Permittivity of rochelle salt during switching,” Czechoslovak Journal of Physics, vol. 12, no. 5, pp. 413–416, 1962. View at: Publisher Site  Google Scholar
 J. Seidel, L. W. Martin, Q. He et al., “Conduction at domain walls in oxide multiferroics,” Nature Materials, vol. 8, no. 3, pp. 229–234, 2009. View at: Publisher Site  Google Scholar
 A. Aird and E. K. H. Salje, “Sheet superconductivity in twin walls: experimental evidence of WO_{3x},” Journal of Physics Condensed Matter, vol. 10, no. 22, pp. L377–L380, 1998. View at: Publisher Site  Google Scholar
 J. Guyonnet, I. Gaponenko, S. Gariglio, and P. Paruch, “Conduction at domain walls in insulating Pb(Zr_{0.2}Ti_{0.8})O_{3} thin films,” Advanced Materials, vol. 23, no. 45, pp. 5377–5382, 2011. View at: Google Scholar
 S. Farokhipoor and B. Noheda, “Conduction through 71 degrees domain walls in BiFeO_{3} thin films,” Physical Review Letters, vol. 107, no. 12, Article ID 127601, 2011. View at: Google Scholar
 J. Privratska and V. Janovec, “Pyromagnetic domain walls connecting antiferromagnetic nonferroelastic magnetoelectric domains,” in Proceedings of the 3rd International Conference on Magnetoelectric Interaction Phenomena in Crystals (MEIPIC '96), Novgorod, Russia, September 1996. View at: Google Scholar
 J. Privratska and V. Janovec, “Pyromagnetic domain walls connecting antiferromagnetic nonferroelastic magnetoelectric domains,” Ferroelectrics, vol. 204, no. 1–4, pp. 321–331, 1997. View at: Publisher Site  Google Scholar
 M. Daraktchiev, G. Catalan, and J. F. Scott, “Landau theory of ferroelectric domain walls in magnetoelectrics,” Ferroelectrics, vol. 375, no. 1, pp. 122–131, 2008. View at: Publisher Site  Google Scholar
 M. Daraktchiev, G. Catalan, and J. F. Scott, “Landau theory of domain wall magnetoelectricity,” Physical Review B, vol. 81, no. 22, Article ID 224118, 2010. View at: Publisher Site  Google Scholar
 M. Molotskii, Y. Rosenwaks, and G. Rosenman, “Ferroelectric domain breakdown,” Annual Review of Materials Research, vol. 37, pp. 271–296, 2007. View at: Publisher Site  Google Scholar
 A. Agronin, M. Molotskii, Y. Rosenwaks et al., “Dynamics of ferroelectric domain growth in the field of atomic force microscope,” Journal of Applied Physics, vol. 99, no. 10, Article ID 104102, 2006. View at: Publisher Site  Google Scholar
 I. I. Naumov, L. Bellaiche, and H. Fu, “Unusual phase transitions in ferroelectric nanodisks and nanorods,” Nature, vol. 432, no. 7018, pp. 737–740, 2004. View at: Publisher Site  Google Scholar
 I. I. Naumov and H. X. Fu, “Vortextopolarization phase transformation path in lead zirconatetitanate nanoparticles,” Physical Review Letters, vol. 98, Article ID 077603, 2007. View at: Google Scholar
 V. L. Ginzburg, A. A. Gorbatsevich, and Y. V. Kopaev, “On the problem of super diamagnetism,” Solid State Communications, vol. 50, pp. 339–343, 1984. View at: Google Scholar
 A. A. Gorbatsevich and Y. V. Kopaev, “Toroidal order in ferroelectric crystals,” Ferroelectrics, vol. 161, pp. 321–330, 1994. View at: Google Scholar
 B. B. Van Aken, J. P. Rivera, H. Schmid, and M. Fiebig, “Observation of ferrotoroidic domains,” Nature, vol. 449, no. 7163, pp. 702–705, 2007. View at: Publisher Site  Google Scholar
 P. Paruch, T. Giamarchi, T. Tybell, and J. M. Triscone, “Nanoscale studies of domain wall motion in epitaxial ferroelectric thin films,” Journal of Applied Physics, vol. 100, no. 5, Article ID 051608, 2006. View at: Publisher Site  Google Scholar
 R. McQuaig, Atomic force microscopy of ferroelectric domains [Ph.D. thesis], Queens University Belfast, 2012.
 D. J. Srolovitz and J. F. Scott, “Clockmodel description of incommensurate ferroelectric films and of nematicliquidcrystal films,” Physical Review B, vol. 34, no. 3, pp. 1815–1819, 1986. View at: Publisher Site  Google Scholar
 S. Komineas, “Scattering of magnetic solitons in two dimensions,” Physica D, vol. 155, no. 34, pp. 223–234, 2001. View at: Publisher Site  Google Scholar
 F. De Guerville, M. E. Marssi, I. Lukyanchuk, and L. Lahoche, “Ferroelectric domains in thin films and superlattices: results of numerical modeling,” Ferroelectrics, vol. 359, no. 1, pp. 14–20, 2007. View at: Publisher Site  Google Scholar
 M. Axenides, S. Komineas, L. Perivolaropoulos, and M. Floratos, “Dynamics of nontopological solitons: Q balls,” Physical Review D, vol. 61, no. 8, Article ID 085006, pp. 1–11, 2000. View at: Google Scholar
 L. Baudry, I. A. Lukyanchuk, and A. Sene, “Inhomogeneous polarization switching in finitesize cubic ferroelectrics,” Ferroelectrics, vol. 427, pp. 34–40, 2012. View at: Publisher Site  Google Scholar
 L. Baudry, I. A. Lukyanchuk, and A. Sene, “Switching properties of nanoscale multiaxial ferroelectrics: geometry and interface effects,” Integrated Ferroelectrics, vol. 133, pp. 96–102, 2012. View at: Publisher Site  Google Scholar
 D. A. Allwood, G. Xiong, C. C. Faulkner, D. Atkinson, D. Petit, and R. P. Cowburn, “Magnetic domainwall logic,” Science, vol. 309, no. 5741, pp. 1688–1692, 2005. View at: Publisher Site  Google Scholar
 S. S. P. Parkin, M. Hayashi, and L. Thomas, “Magnetic domainwall racetrack memory,” Science, vol. 320, no. 5873, pp. 190–194, 2008. View at: Publisher Site  Google Scholar
 G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, “Domain wall nanoelectronics,” Reviews of Modern Physics, vol. 84, pp. 119–156, 2012. View at: Publisher Site  Google Scholar
 G. Catalan, H. Béa, S. Fusil et al., “Fractal dimension and size scaling of domains in thin films of multiferroic BiFeO_{3},” Physical Review Letters, vol. 100, no. 2, Article ID 027602, 2008. View at: Publisher Site  Google Scholar
 G. A. Smolensky, V. A. Isupov, and A. I. Agranovskaya, “Ferroelectrics of the oxygen octahedral type with layered structure,” Soviet Physics, vol. 3, no. 3, pp. 651–655, 1961. View at: Google Scholar
 R. Palai, R. S. Katiyar, H. Schmid et al., “β phase and γβ metalinsulator transition in multiferroic BiFeO_{3},” Physical Review B, vol. 77, no. 1, Article ID 014110, 2008. View at: Publisher Site  Google Scholar
 G. Catalan and J. F. Scott, “Physics and applications of bismuth ferrite,” Advanced Materials, vol. 21, no. 24, pp. 2463–2485, 2009. View at: Publisher Site  Google Scholar
 D. C. Arnold, K. S. Knight, F. D. Morrison, and P. Lightfoot, “Ferroelectricparaelectric transition in BiFeO_{3}: crystal structure of the orthorhombic β phase,” Physical Review Letters, vol. 102, no. 2, Article ID 027602, 2009. View at: Publisher Site  Google Scholar
 D. C. Arnold, K. S. Knight, G. Catalan et al., “The βtoγ transition in BiFeO_{3}: a powder neutron diffraction study,” Advanced Functional Materials, vol. 20, no. 13, pp. 2116–2123, 2010. View at: Publisher Site  Google Scholar
 X. Martí, P. Ferrer, J. HerreroAlbillos et al., “Skin layer of BiFeO_{3} single crystals,” Physical Review Letters, vol. 106, no. 23, Article ID 236101, 2011. View at: Publisher Site  Google Scholar
 M. Polomska, W. Kaczmarek, and Z. Pajak, “Electric and magnetic properties of (Bi_{1X}La_{X})FeO_{3} solid solutions,” Physica Status Solidi A, vol. 23, no. 2, pp. 567–574, 1974. View at: Google Scholar
 A. Kumar, J. F. Scott, R. Martinez, G. Srinivasan, and R. S. Katiyar, “Inplane dielectric and magnetoelectric studies of BiFeO_{3},” Physica Status Solidi, vol. 309, pp. 1207–1212, 2012. View at: Google Scholar
 A. Kumar, J. F. Scott, and R. S. Katiyar, “Magnon raman spectroscopy and inplane dielectric response in BiFeO_{3}: relation to the polomska transition,” Physical Review B, vol. 85, Article ID 224410, 2012. View at: Google Scholar
 M. K. Singh, R. S. Katiyar, and J. F. Scott, “New magnetic phase transitions in BiFeO_{3},” Journal of Physics Condensed Matter, vol. 20, no. 25, Article ID 252203, 2008. View at: Publisher Site  Google Scholar
 M. Cazayous, Y. Gallais, A. Sacuto, R. De Sousa, D. Lebeugle, and D. Colson, “Possible observation of cycloidal electromagnons in BiFeO_{3},” Physical Review Letters, vol. 101, no. 3, Article ID 037601, 2008. View at: Publisher Site  Google Scholar
 J. F. Scott, M. K. Singh, and R. S. Katiyar, “Critical phenomena at the 140 and 200 K magnetic phase transitions in BiFeO_{3},” Journal of Physics Condensed Matter, vol. 20, no. 32, Article ID 322203, 2008. View at: Publisher Site  Google Scholar
 R. Jarrier, X. Marti, J. HerreroAlbillos et al., “Surface phase transitions in BiFeO_{3} below room temperature,” Physical Review B, vol. 85, Article ID 184104, 2012. View at: Google Scholar
 J. HerreroAlbillos, G. Catalan, J. A. RodriguezVelamazan, M. Viret, D. Colson, and J. F. Scott, “Neutron diffraction study of the BiFeO_{3} spin cycloid at low temperature,” Journal of Physics Condensed Matter, vol. 22, no. 25, Article ID 256001, 2010. View at: Publisher Site  Google Scholar
 M. Tonouchi, “THz radiation by optically controlled depolarization in BiFeO_{3},” in Proceedings of the 35th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMWTHz '10), Rome, Italy, September 2010. View at: Publisher Site  Google Scholar
 L. Esaki and R. Tsu, “Superlattice and negative differential conductivity in semiconductors,” IBM Journal of Research and Development, vol. 14, no. 1, pp. 61–65, 1970. View at: Google Scholar
 K. M. Rabe, M. Dawber, C. Lichtensteiger, C. H. Ahn, and J. M. Triscone, “Modern physics of ferroelectrics: essential background,” Topics in Applied Physics, vol. 105, pp. 1–30, 2007. View at: Publisher Site  Google Scholar
 M. Dawber, C. Lichtensteiger, M. Cantoni et al., “Unusual behavior of the ferroelectric polarization in PbTiO_{3}/SrTiO3 superlattices,” Physical Review Letters, vol. 95, no. 17, Article ID 177601, 4 pages, 2005. View at: Publisher Site  Google Scholar
 J. Y. Jo, P. Chen, R. J. Sichel et al., “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Physical Review Letters, vol. 107, no. 5, Article ID 055501, 2011. View at: Publisher Site  Google Scholar
 R. Martínez, A. Kumar, R. Palai, R. S. Katiyar, and J. F. Scott, “Study of physical properties of integrated ferroelectric/ferromagnetic heterostructures,” Journal of Applied Physics, vol. 107, no. 11, Article ID 114107, 2010. View at: Publisher Site  Google Scholar
 P. Zubko, S. Gariglio, M. Gabay, P. Ghosez, and J. M. Triscone, “Interface physics in complex oxide heterostructures,” Annual Review of CondensedMatter Physics, vol. 2, pp. 141–165, 2011. View at: Publisher Site  Google Scholar
 S. M. Nakhmanson, K. M. Rabe, and D. Vanderbilt, “Predicting polarization enhancement in multicomponent ferroelectric superlattices,” Physical Review B, vol. 73, no. 6, Article ID 060101, 2006. View at: Publisher Site  Google Scholar
 A. Q. Jiang, J. F. Scott, H. B. Lu, and Z. Chen, “Phase transitions and polarizations in epitaxial BaTiO_{3}/SrTiO_{3} superlattices studied by secondharmonic generation,” Journal of Applied Physics, vol. 93, pp. 1180–1185, 2003. View at: Google Scholar
 S. Ríos, A. Ruediger, A. Q. Jiang, J. F. Scott, H. Lu, and Z. Chen, “Orthorhombic strontium titanate in BaTiO3SrTiO_{3} superlattices,” Journal of Physics Condensed Matter, vol. 15, no. 21, pp. L305–L309, 2003. View at: Publisher Site  Google Scholar
 K. Johnston, X. Y. Huang, J. B. Neaton, and K. M. Rabe, “Unusual behavior of the polarization in BaTiO_{3}/SrTiO_{3} superlattices,” Physical Review B, vol. 71, no. 10, Article ID 100103, 2005. View at: Google Scholar
 T. Shigenari, K. Abe, T. Takemoto et al., “Raman spectra of the ferroelectric phase of Sr Ti_{18}O_{3}: symmetry and domains below Tc and the origin of the phase transition,” Physical Review B, vol. 74, no. 17, Article ID 174121, 2006. View at: Publisher Site  Google Scholar
 J. F. Scott, J. Bryson, M. A. Carpenter, J. HerreroAlbillos, and M. Itoh, “Elastic and anelastic properties of ferroelectric SrTi^{18}O_{3} in the kHzMHz regime,” Physical Review Letters, vol. 106, no. 10, Article ID 105502, 2011. View at: Publisher Site  Google Scholar
 M. Takesada, M. Itoh, and T. Yagi, “Perfect softening of the ferroelectric mode in the isotopeexchanged strontium titanate of (SrTiO_{3})^{18}O studied by light scattering,” Physical Review Letters, vol. 96, no. 22, Article ID 227602, 2006. View at: Publisher Site  Google Scholar
 M. Dawber, N. Stucki, C. Lichtensteiger, S. Gariglio, and J. M. Triscone, “New phenomena at the interfaces of very thin ferroelectric oxides,” Journal of Physics Condensed Matter, vol. 20, no. 26, Article ID 264015, 2008. View at: Publisher Site  Google Scholar
 N. Reyren, S. Thiel, A. D. Caviglia et al., “Superconducting interfaces between insulating oxides,” Science, vol. 317, no. 5842, pp. 1196–1199, 2007. View at: Publisher Site  Google Scholar
 S. A. Hayward, F. D. Morrison, S. A. T. Redfern et al., “Transformation processes in LaAlO_{3}: neutron diffraction, dielectric, thermal, optical, and Raman studies,” Physical Review B, vol. 72, no. 5, Article ID 054110, 2005. View at: Publisher Site  Google Scholar
 V. M. Fridkin, Photoferroelectrics, Springer, Berlin, Germany, 1979.
 J. Seidel, P. Maksymovych, Y. Batra et al., “Domain wall conductivity in Ladoped BiFeO_{3},” Physical Review Letters, vol. 105, no. 19, Article ID 197603, 2010. View at: Publisher Site  Google Scholar
 D. Daranciang, M. Highland, H. Wen et al., “Ultrafast photovoltaic response in ferroelectric nanolayers,” Physical Review Letters, vol. 108, no. 8, Article ID 087601, 2012. View at: Google Scholar
 N. Laman, M. Bieler, and H. M. Van Driel, “Ultrafast shift and injection currents observed in wurtzite semiconductors via emitted terahertz radiation,” Journal of Applied Physics, vol. 98, no. 10, Article ID 103507, 8 pages, 2005. View at: Publisher Site  Google Scholar
 M. Alexe and D. Hesse, “Tipenhanced photovoltaic effects in bismuth ferrite,” Nature Communications, vol. 2, no. 1, article 256, 2011. View at: Publisher Site  Google Scholar
 A. Anikiev, L. G. Reznik, B. S. Umarov, and J. F. Scott, “Perturbed polariton spectra in optically damaged LiNbO_{3},” Ferroelectrics Letters, vol. 3, pp. 89–96, 1985. View at: Google Scholar
 L. G. Reznik, A. A. Anikiev, B. S. Umarov, and J. F. Scott, “Studies of optical damage in lithium niobate in the presence of thermal gradients,” Ferroelectrics, vol. 64, pp. 215–219, 1985. View at: Publisher Site  Google Scholar
 L. Landau, “The theory of phase transitions,” Nature, vol. 138, no. 3498, pp. 840–841, 1936. View at: Google Scholar
 A. F. Devonshire, “Theory of BaTiO_{3},” Philosophical Magazine, vol. 40, no. 309, pp. 1040–1063, 1949. View at: Google Scholar
 A. F. Ermolov, A. P. Levanyuk, and A. S. Sigov, “Anomaly of high frequency sound absorption near the point of structurakl phase transitions in crystals with defects,” Fizika Tverdogo Tela, vol. 21, no. 12, pp. 3628–3633, 1979. View at: Google Scholar
 A. P. Levanyuk and A. S. Sigov, “The influence of defects on the properties of ferroelectrics and related materials near the point of a 2nd kind of phase transition,” Izvestia Akademii Nauk SSSR, vol. 45, no. 9, pp. 1640–1645, 1981. View at: Google Scholar
 A. I. Morozov and A. S. Sigov, “Point defect near the displacive phase transition,” Fizika Tverdogo Tela, vol. 25, no. 5, pp. 1352–1356, 1983. View at: Google Scholar
 Y. M. Kishinets, A. P. Levanyuk, A. I. Morozov, and A. S. Sigov, “Absorption coefficient and sound velocity anomalies in the vicinity of phase transitions of the 2nd kind in crystals with dislocations,” Fizika Tverdogo Tela, vol. 29, no. 2, pp. 601–604, 1987. View at: Google Scholar
 I. J. Fritz, “Ultrasonic attenuation and mechanism for the 250°K antiferrodistortive transition in BaMnF_{4},” Physical Review Letters, vol. 35, no. 22, pp. 1511–1514, 1975. View at: Publisher Site  Google Scholar
 I. J. Fritz, “Ultrasonic velocity measurements near the 250°K phase transition in BaMnF_{4},” Physics Letters A, vol. 51, no. 4, pp. 219–220, 1975. View at: Google Scholar
 T. Chen, S.J. Sheih, and J. F. Scott, “Temporal dependence of thermal selffocussing in ferroelectric Ba_{2}NaNb_{5}O_{15} and Ce^{+3}:SrXBa_{1X}Nb_{2}O_{6},” Ferroelectrics, vol. 120, pp. 115–129, 1991. View at: Publisher Site  Google Scholar
 V. Bobnar and Z. Kutnjak, “HighTemperature dielectric response of (1x)PbMg_{1/3}Nb_{2/3}O_{3} (x)PbTiO_{3}: does burns temperature exist in ferroelectric relaxors?” Journal of Applied Physics, vol. 107, Article ID 084104, 2010. View at: Google Scholar
 J. F. Scott, “Comment on 'HighTemperature dielectric response of (1x)PbMg_{1/3}Nb_{2/3}O_{3} –(x)PbTiO_{3}: does burns temperature exist in ferroelectric relaxors?',” Journal of Applied Physics, vol. 108, no. 8, Article ID 086107, 2010. View at: Publisher Site  Google Scholar
 K. Samanta, A. K. Arora, T. R. Ravindran, S. Ganesamoorthy, K. Kitamura, and S. Takekawa, “Raman spectroscopic study of structural transition in Sr_{x}Ba_{1x}Nb_{2}O_{6},” Vibrational Spectroscopy, vol. 62, pp. 273–278, 2012. View at: Publisher Site  Google Scholar
 J. Dec, private communication.
 W. J. Burke, R. J. Pressley, and J. C. Slonczewski, “Raman scattering and phase transitions in stressed SrTiO_{3},” Solid State Communications, vol. 9, no. 2, pp. 121–124, 1971. View at: Google Scholar
 W. J. Burke and R. J. Pressley, “Stress induced ferroelectricity in SrTiO_{3},” Solid State Communications, vol. 9, no. 3, pp. 191–195, 1971. View at: Google Scholar
 S. L. Qiu, M. Dutta, H. Z. Cummins, J. P. Wicksted, and S. M. Shapiro, “Extension of the Lifshitzpoint concept to firstorder phase transitions: incommensurate NaNO_{2} in a transverse electric field,” Physical Review B, vol. 34, no. 11, pp. 7901–7910, 1986. View at: Publisher Site  Google Scholar
 N. A. Pertsev, A. G. Zembilgotov, and A. K. Tagantsev, “Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films,” Physical Review Letters, vol. 80, no. 9, pp. 1988–1991, 1998. View at: Google Scholar
 S. P. P. Jones, D. M. Evans, M. A. Carpenter et al., “Phase diagram and phase transitions in ferroelectric trissarcosine calcium chloride and its brominated isomorphs,” Physical Review B, vol. 83, no. 9, Article ID 094102, 2011. View at: Publisher Site  Google Scholar
 J. F. Scott, “Dielectrics,” Encyclopedia of Applied Physics, vol. 5, pp. 25–35, 1993. View at: Google Scholar
 K. Lee, M. Lee, K. S. Lee, and A. R. Lim, “^{1}H NMR study of the phase transitions of trissarcosine calcium chloride single crystals at low temperature,” Journal of Physics and Chemistry of Solids, vol. 66, no. 10, pp. 1739–1743, 2005. View at: Publisher Site  Google Scholar
 H. Haga, A. Onodera, H. Yamashita, and Y. Shiosaki, “New phase transition in ferroelectric trissarcosine calcium chloride at low temperature,” Journal of the Physical Society of Japan, vol. 62, pp. 1857–1859, 1993. View at: Publisher Site  Google Scholar
 R. B. Laughlin, G. G. Lonzarich, P. Monthoux, and D. Pines, “The quantum criticality conundrum,” Advances in Physics, vol. 50, no. 4, pp. 361–365, 2001. View at: Publisher Site  Google Scholar
 E. Fradkin and S. A. Kivelson, “Electron nematic phases proliferate,” Science, vol. 327, no. 5962, pp. 155–156, 2010. View at: Publisher Site  Google Scholar
 S. Rowley, R. Smith, and M. Dean, “Ferromagnetic and ferroelectric quantum phase transitions,” Physica Status Solidi B, vol. 247, pp. 469–475, 2010. View at: Publisher Site  Google Scholar
 J. F. Scott, R. Pirc, A. Levstik, C. Filipic, and R. Blinc, “Resolving the quantum criticality paradox in O18 isotopic SrTiO_{3},” Journal of Physics Condensed Matter, vol. 18, no. 16, pp. L205–L208, 2006. View at: Publisher Site  Google Scholar
 W. Windsch, H. Braeter, U. Gutteck, B. Malige, and B. Milsch, “The concentration dependence of the ferroelectric transition temperature of the solid solution of TSCC and TSCB,” Solid State Communications, vol. 42, no. 12, pp. 839–842, 1982. View at: Google Scholar
 H. Suzuki, S. Naher, T. Shimoguchi, M. Mizuno, A. Ryu, and H. Fujishita, “Xray diffraction measurement below 1 K,” Journal of Low Temperature Physics, vol. 128, no. 12, pp. 1–7, 2002. View at: Publisher Site  Google Scholar
 S. E. Rowley, L. J. Spalek, R. P. Smith et al., “Ferroelectric quantum criticality,” Nature. In press. View at: Google Scholar
 S. E. Rowley, R. Smith, M. L. Sutherland, P. Alireza, S. S. Saxena, and G. G. Lonzarich, “Quantum criticality and unconventional order in magnetic and dielectric material,” Journal of Physics: Conference Series, vol. 400, Article ID 032048, 2012. View at: Publisher Site  Google Scholar
 A. V. Bune, V. M. Fridkin, S. Ducharme et al., “Twodimensional ferroelectric films,” Nature, vol. 391, no. 6670, pp. 874–877, 1998. View at: Publisher Site  Google Scholar
 R. Gaynutdinov, S. Yudin, S. Ducharme, and V. Fridkin, “Homogeneous switching in ultrathin ferroelectric films,” Journal of Physics Condensed Matter, vol. 24, no. 1, Article ID 015902, 2012. View at: Google Scholar
 L. Zhang, “Field induced phase transition and dielectric energy density in PVDF terpolymers,” Europhysics Letters, vol. 91, Article ID 47001, 2010. View at: Publisher Site  Google Scholar
 J. F. Scott, “Switching of ferroelectrics without domains,” Advanced Materials, vol. 22, no. 46, pp. 5315–5317, 2010. View at: Google Scholar
 M. J. Highland, T. T. Fister, M. I. Richard et al., “Polarization switching without domain formation at the intrinsic coercive field in ultrathin ferroelectric PbTiO_{3},” Physical Review Letters, vol. 105, no. 16, Article ID 167601, 2010. View at: Publisher Site  Google Scholar
 J. F. Scott, “Lattice perturbations in CaWO_{4} and CaMoO_{4},” The Journal of Chemical Physics, vol. 48, no. 2, pp. 874–878, 1968. View at: Google Scholar
 J. F. Scott, “Dipoledipole interactions in tungstates,” The Journal of Chemical Physics, vol. 49, no. 1, pp. 98–100, 1968. View at: Google Scholar
 W. Ma and L. E. Cross, “Flexoelectricity of barium titanate,” Applied Physics Letters, vol. 88, Article ID 232902, 2006. View at: Google Scholar
 W. Ma and L. E. Cross, “Flexoelectric effect in ceramic lead zirconate titanate,” Applied Physics Letters, vol. 86, no. 7, Article ID 072905, 2005. View at: Google Scholar
 A. K. Tagantsev, “Piezoelectricity and flexoelectricity in crystalline dielectrics,” Physical Review B, vol. 34, no. 8, pp. 5883–5889, 1986. View at: Publisher Site  Google Scholar
 P. Zubko, G. Catalan, P. R. L. Welche, A. Buckley, and J. F. Scott, “Strain gradient induced polarization in SrTiO_{3},” Physical Review Letters, vol. 99, Article ID 167601, 2007. View at: Google Scholar
 J. Hong, G. Catalan, J. F. Scott, and E. Artacho, “The flexoelectricity of barium and strontium titanates from first principles,” Journal of Physics Condensed Matter, vol. 22, no. 11, Article ID 112201, 2010. View at: Publisher Site  Google Scholar
 R. Resta, “Towards a bulk theory of flexoelectricity,” Physical Review Letters, vol. 105, no. 12, Article ID 127601, 2010. View at: Publisher Site  Google Scholar
 J.W. Hong and D. Vanderbilt, “Firstprinciples theory of frozenion flexoelectricity,” Physical Review B, vol. 84, no. 18, Article ID 180101, 2011. View at: Google Scholar
 H. Zhou, J. Hong, Y. Zhang, F. Li, Y. Pei, and D. Fang, “External uniform electric field removing flexoelectric effect in epitaxial ferroelectric thin films,” Europhysics Letters, vol. 99, no. 4, Article ID 47003. View at: Publisher Site  Google Scholar
 D. Lee, A. Yoon, S. Y. Jang et al., “Giant flexoelectric effect in ferroelectric epitaxial thin films,” Physical Review Letters, vol. 107, no. 5, Article ID 057602, 2011. View at: Publisher Site  Google Scholar
 H. Lu, C. W. Bark, D. E. De los Ojos et al., “Mechanical writing of ferroelectric polarization,” Science, vol. 336, no. 6077, pp. 59–61, 2012. View at: Publisher Site  Google Scholar
 L. E. Cross, “Relaxor ferroelectrics,” Ferroelectrics, vol. 76, no. 34, pp. 241–267, 1987. View at: Publisher Site  Google Scholar
 M. D. Glinchuk, “Relaxor ferroelectrics: from cross superparaelectric model to random field theory,” British Ceramic Transactions, vol. 103, no. 2, pp. 76–82, 2004. View at: Google Scholar
 R. Pirc and R. Blinc, “Spherical randombondrandomfield model of relaxor ferroelectrics,” Physical Review B, vol. 60, no. 19, pp. 13470–13478, 1999. View at: Google Scholar
 R. Pirc and R. Blinc, “VogelFulcher freezing in relaxor ferroelectrics,” Physical Review B, vol. 76, no. 2, Article ID 020101, 2007. View at: Publisher Site  Google Scholar
 Z. Kutnjak, J. Petzelt, and R. Blinc, “The giant electromechanical response in ferroelectric relaxors as a critical phenomenon,” Nature, vol. 441, no. 7096, pp. 956–959, 2006. View at: Publisher Site  Google Scholar
 J. Dec, W. Kleemann, and V. V. Shvartsman, “From mesoscopic to global polar order in the uniaxial relaxor ferroelectric Sr_{0.8}Ba_{0.2}Nb_{2}O_{6},” Applied Physics Letters, vol. 100, no. 5, Article ID 052903, 2012. View at: Google Scholar
 J. F. Scott, “Absence of true critical exponents in relaxor ferroelectrics: the case for defect dynamics,” Journal of Physics Condensed Matter, vol. 18, no. 31, pp. 7123–7134, 2006. View at: Publisher Site  Google Scholar
 W. Kleemann, J. Dec, V. V. Shvartsman, Z. Kutnjak, and T. Braun, “Twodimensional ising model criticality in a threedimensional uniaxial relaxor ferroelectric with frozen polar nanoregions,” Physical Review Letters, vol. 97, no. 6, Article ID 065702, 2006. View at: Publisher Site  Google Scholar
 D. Pajic, Z. Jaglicic, M. Jagodic et al., “Low temperature magnetic behaviour of PZTPFW bulk multiferroic ceramics,” Journal of Physics Conference Series, vol. 303, Article ID 012065, 2011. View at: Google Scholar
 H. Zheng, J. Wang, S. E. Lofland et al., “Multiferroic BaTiO_{3}CoFe_{2}O_{4} nanostructures,” Science, vol. 303, no. 5658, pp. 661–663, 2004. View at: Publisher Site  Google Scholar
 C. W. Nan, M. I. Bichurin, S. Dong, D. Viehland, and G. Srinivasan, “Multiferroic magnetoelectric composites: historical perspective, status, and future directions,” Journal of Applied Physics, vol. 103, no. 3, Article ID 031101, 2008. View at: Publisher Site  Google Scholar
 C. Israel, N. D. Mathur, and J. F. Scott, “A onecent roomtemperature magnetoelectric sensor,” Nature Materials, vol. 7, no. 2, pp. 93–94, 2008. View at: Publisher Site  Google Scholar
 Z. Hu, M. Tian, B. Nysten, and A. M. Jonas, “Regular arrays of highly ordered ferroelectric polymer nanostructures for nonvolatile lowvoltage memories,” Nature Materials, vol. 8, no. 1, pp. 62–67, 2009. View at: Publisher Site  Google Scholar
 K. Asadi, H. J. Wondergem, R. S. Moghaddam et al., “Organic ferroelectric optoelectronic memories,” Materials Today, vol. 14, no. 12, pp. 592–599, 2011. View at: Google Scholar
 T. J. Reece, S. Ducharme, A. V. Sorokin, and M. Poulsen, “Nonvolatile memory element based on a ferroelectric polymer LangmuirBlodgett film,” Applied Physics Letters, vol. 82, no. 1, pp. 142–144, 2003. View at: Publisher Site  Google Scholar
 M.Y. Li, N. Stingelin, J. Jasper et al., “Processing and low voltage switching of organic ferroelectric phaseseparated bistable diodes,” Advanced Functional Materials, vol. 22, no. 12, pp. 2750–2757, 2012. View at: Google Scholar
 P. Kobeko and J. Kurtschatov, “Pielectric (sic) properties of Rochelle salt crystals,” Zeitschrift für Physik, vol. 66, no. 34, pp. 192–205, 1930. View at: Publisher Site  Google Scholar
 Y. Liu, X.P. Peng, X.J. Lou, and H. Zhou, “Intrinsic electrocaloric effect in ultrathin ferroelectric capacitors,” Applied Physics Letters, vol. 100, Article ID 192902, 2012. View at: Google Scholar
 C. Israel, S. KarNarayan, and N. D. Mathur, “Eliminating the temperature dependence of the response of magnetoelectric magneticField sensors,” IEEE Sensors Journal, vol. 10, no. 5, pp. 914–917, 2010. View at: Publisher Site  Google Scholar
 S. KarNarayan and N. D. Mathur, “Direct and indirect electrocaloric measurements using multilayer capacitors,” Journal of Physics D, vol. 43, no. 3, Article ID 032002, 2010. View at: Publisher Site  Google Scholar
 S. KarNarayan and N. D. Mathur, “Predicted cooling powers for multilayer capacitors based on various electrocaloric and electrode materials,” Applied Physics Letters, vol. 95, no. 24, Article ID 242903, 2009. View at: Publisher Site  Google Scholar
 C. Israel, S. KarNarayan, and N. D. Mathur, “Converse magnetoelectric coupling in multilayer capacitors,” Applied Physics Letters, vol. 93, no. 17, Article ID 173501, 2008. View at: Publisher Site  Google Scholar
 Q. M. Zhang, V. Bharti, and X. Zhao, “Giant electrostriction and relaxor ferroelectric behavior in electron irradiated poly(vinylidene fluoridetrifluoroethylene) copolymer,” Science, vol. 280, no. 5372, pp. 2101–2104, 1998. View at: Publisher Site  Google Scholar
 S. G. Lu, B. Rožič, Q. M. Zhang et al., “Organic and inorganic relaxor ferroelectrics with giant electrocaloric effect,” Applied Physics Letters, vol. 97, no. 16, Article ID 162904, 2010. View at: Publisher Site  Google Scholar
 S. Prosandeev, I. Ponomareva, and L. Bellaiche, “Electrocaloric effect in bulk and lowdimensional ferroelectrics from first principles,” Physical Review B, vol. 78, no. 5, Article ID 052103, 2008. View at: Publisher Site  Google Scholar
 Y. Liu, Y. Zhang, M.J. Chen, Q. N. Chen, and J. Li, “Biological ferroelectricity discovered in aorta walls by piezo force microscopy,” Physical Review Letters, vol. 108, Article ID 078103, 2012. View at: Google Scholar
 T. Li and K. Zeng, “Piezoelectric properties and surface potential of green abalone shell studied by scanning probe microscopy techniques,” Acta Materialia, vol. 59, no. 9, pp. 3667–3679, 2011. View at: Publisher Site  Google Scholar
 A. Heredia, V. Meunier, I. K. Bdikin et al., “Nanoscale ferroelectricity in crystalline γglycine,” Advanced Functional Materials, vol. 22, no. 14, pp. 2996–3003, 2012. View at: Publisher Site  Google Scholar
 J. F. Scott, “Electrocaloric materials,” Annual Review of Materials Research, vol. 41, pp. 229–240, 2011. View at: Publisher Site  Google Scholar
 R. Plumlee, Sandia Laboratories Report SCRR67730, 1967.
 X. Lou, X. Hu, M. Zhang, S. A. T. Redfern, E. A. Kafadaryan, and J. F. Scott, “Nanoshorts,” Reviews on Advanced Materials Science, vol. 10, no. 3, pp. 197–204, 2005. View at: Google Scholar
 X. Lou, X. Hu, M. Zhang, F. D. Morrison, S. A. T. Redfern, and J. F. Scott, “Phase separation in lead zirconate titanate and bismuth titanate during electrical shorting and fatigue,” Journal of Applied Physics, vol. 99, no. 4, Article ID 044101, 2006. View at: Publisher Site  Google Scholar
 R. Waser, R. Dittmann, C. Staikov, and K. Szot, “Redoxbased resistive switching memories nanoionic mechanisms, prospects, and challenges,” Advanced Materials, vol. 21, no. 2526, pp. 2632–2663, 2009. View at: Publisher Site  Google Scholar
 D. S. Jeong, R. Thomas, R. S. Katiyar et al., “Emerging memories: resistive switching mechanisms and current status,” Reports on Progress in Physics, vol. 75, Article ID 076502, 2012. View at: Google Scholar
 P. W. M. Blom, R. M. Wolf, J. F. M. Cillessen, and M. P. C. M. Krijn, “Ferroelectric Schottky diode,” Physical Review Letters, vol. 73, no. 15, pp. 2107–2110, 1994. View at: Publisher Site  Google Scholar
 A. Q. Jiang, C. Wang, K. J. Jin et al., “A resistive memory in semiconducting BiFeO_{3} thinfilm capacitors,” Advanced Materials, vol. 23, no. 10, pp. 1277–1281, 2011. View at: Publisher Site  Google Scholar
 B. Noheda, private communication.
 P. Paruch, A. B. Posadas, M. Dawber, C. H. Ahn, and P. L. McEuen, “Polarization switching using singlewalled carbon nanotubes grown on epitaxial ferroelectric thin films,” Applied Physics Letters, vol. 93, no. 13, Article ID 132901, 2008. View at: Publisher Site  Google Scholar
 S. Kawasaki, G. Catalan, H. J. Fan, and J. F. Scott, “Conformal oxide coating of carbon nanotubes,” Applied Physics Letters, vol. 92, Article ID 053109, 2008. View at: Google Scholar
 A. Kumar, S. G. Shivareddy, M. Correa et al., “Ferroelectriccarbon nanotube memory devices,” Nanotechnology, vol. 23, no. 16, Article ID 165702, 2012. View at: Google Scholar
 F. Mendoza, A. Kumar, R. Martinez et al., “Conformal coating of ferroelectric oxides on carbon nanotubes,” Europhysics Letters, vol. 97, no. 2, Article ID 27001, 2012. View at: Google Scholar
 Y. Zheng, X. N. Guang, C.T. Toh, C.Y. Tan, K. Yao, and B. Özyilmaz, “Graphene fieldeffect transistors with ferroelectric gating,” Physical Review Letters, vol. 105, Article ID 166602, 2010. View at: Google Scholar
 F. D. Morrison, Y. Luo, I. Szafraniak et al., “Ferroelectric nanotubes,” Reviews of Advances in Materials Science, vol. 4, pp. 114–122, 2003. View at: Google Scholar
 J. Hong, G. Catalan, D. N. Fang, E. Artacho, and J. F. Scott, “Topology of the polarization field in ferroelectric nanowires from first principles,” Physical Review B, vol. 81, no. 17, Article ID 172101, 2010. View at: Publisher Site  Google Scholar
 V. L. Gurevuch and A. K. Tagantsev, “Second sound in ferroelectrics,” Journal of Experimental and Theoretical Physics, vol. 67, no. 1, pp. 206–212, 1988. View at: Google Scholar
 B. Hehlen, L. Arzel, A. K. Tagantsev et al., “Brillouinscattering observation of the TATO coupling in SrTiO_{3},” Physical Review B, vol. 57, no. 22, pp. R13989–R13992, 1998. View at: Google Scholar
 A. Koreeda, R. Takano, and S. Saikan, “Second sound in SrTiO_{3},” Physical Review Letters, vol. 99, no. 26, Article ID 265502, 2007. View at: Publisher Site  Google Scholar
 E. Courtens, B. Hehlen, E. Farhi, and A. K. Tagantsev, “Optical mode crossings and the low temperature anomalies of SrTiO_{3},” Zeitschrift fur Physik BCondensed Matter, vol. 104, no. 4, pp. 641–642, 1997. View at: Google Scholar
 P. A. Fleury, J. F. Scott, and J. M. Worlock, “Soft phonon modes and the 110°K phase transition in SrTiO_{3},” Physical Review Letters, vol. 21, no. 1, pp. 16–19, 1968. View at: Publisher Site  Google Scholar
 R. Blinc, V. V. Laguta, B. Zalar, M. Itoh, and H. Krakauer, “^{17}O quadrupole coupling and the origin of ferroelectricity in isotopically enriched BaTiO_{3} and SrTiO_{3},” Journal of Physics Condensed Matter, vol. 20, no. 8, Article ID 085204, 2008. View at: Publisher Site  Google Scholar
 J. F. Scott, M. A. Carpenter, and E. K.H. Salje, “Domain wall damping and elastic softening in SrTiO_{3}, evidence for polar twin walls,” Physical Review Letters, vol. 109, no. 18, Article ID 187601, 2012. View at: Google Scholar
 M. Bartkowiak, private communication.
 M. Bartkowiak, G. J. Kearley, M. Yethiraj, and A. M. Mulders, “Symmetry of ferroelectricphase of (SrTiO_{3})^{18}O determined by ab initio calculations,” Physical Review B, vol. 83, no. 6, Article ID 064102, 2011. View at: Publisher Site  Google Scholar
 E. Y. Tsymbal, A. Gruverman, V. Garcia, M. Bibes, and A. Barthelemy, “Ferroelectric and multiferroic tunnel junctions,” MRS Bulletin, vol. 37, no. 2, pp. 138–143, 2012. View at: Google Scholar
 M. Bibes and A. Barthélémy, “Multiferroics: towards a magnetoelectric memory,” Nature Materials, vol. 7, no. 6, pp. 425–426, 2008. View at: Publisher Site  Google Scholar
 A. Chanthbouala, A. Crassous, V. Garcia et al., “Solidstate memories based on ferroelectric tunnel junctions,” Nature Nanotechnology, vol. 7, no. 2, pp. 101–104, 2012. View at: Google Scholar
 M. Gajek, M. Bibes, S. Fusil et al., “Tunnel junctions with multiferroic barriers,” Nature Materials, vol. 6, no. 4, pp. 296–302, 2007. View at: Publisher Site  Google Scholar
 L. E. Hueso, J. M. Pruneda, V. Ferrari et al., “Transformation of spin information into large electrical signals using carbon nanotubes,” Nature, vol. 445, no. 7126, pp. 410–413, 2007. View at: Publisher Site  Google Scholar
 R. E. Cohen, “Origin of ferroelectricity in perovskite oxides,” Nature, vol. 358, no. 6382, pp. 136–138, 1992. View at: Google Scholar
 N. A. Hill, “Why are there so few magnetic ferroelectrics?” Journal of Physical Chemistry B, vol. 104, no. 29, pp. 6694–6709, 2000. View at: Google Scholar
Copyright
Copyright © 2013 J. F. Scott. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.