BiFeO₃ epitaxial thin films and devices: past, present and future

On (1 1 1)-oriented cubic substrates (for example SrTiO₃–STO), rhombohedral 'bulk-like' BFO is typically obtained (figure 3(d)) [43, 53–56], consistent with predictions of thermodynamic calculations [57]. Even for very small thicknesses (e.g. 20 nm) the film begins to relax and its lattice parameters approach their bulk values [43, 58]. Early reports of BFO films grown by liquid phase epitaxy (LPE) [42] or chemical solution deposition (CSD) [59] on (0 0 1)-oriented STO substrates evidenced a rhombohedral BFO symmetry, illustrating that the growth method, as well as substrate properties, can influence the structure of the film. Interestingly, for (1 1 1)-oriented growth on a substrate imposing tensile strain, thermodynamic calculations suggest that the structure is monoclinic M_B [57]; this has yet to be confirmed experimentally. A bulk-like rhombohedral phase has also been reported for thicker films of 500 nm on (0 0 1) (LaAlO3)_0.3(Sr₂AlTaO₆)_0.7 (LSAT) [60] and very thick films (2 µm) on (0 0 1) STO [41].

The vast majority of studies of BFO epitaxial thin films are conducted using STO (0 0 1) substrates, which impart a compressive strain to the film. Another common substrate choice is orthorhombic DyScO₃ (DSO), with the (1 1 0)_o crystallographic orientation forming a (0 0 1)_pc surface suitable for BFO growth. These substrates are chosen for their close lattice match to BFO, as well as to the commonly-used bottom electrode strontium ruthenate (SrRuO₃; SRO). On such substrates in a (0 0 1)_pc orientation, BFO typically grows with a monoclinic M_A structure, see figure 3(c) [47–49, 51, 61–63], and reciprocal space mapping [64] around (1 0 3), (0 1 3) and (1 1 3) families of reflections can be used to confirm this structure, as shown in figure 4(b) [41, 47, 48]. In this monoclinic phase, the unit cell is doubled in volume and rotated by 45° with respect to the pseudocubic cell (see figure 3(c)). The (0 1 1) substrate orientation yields a monoclinic M_B structure under compressive strain [51, 65], or an M_A structure in tensile strain³ [65]. More exotic orientations of STO—such as (1 0 3), or (2 0 3)—give rise to a triclinic structure; this structure acts as the transitional bridge between the M_A (STO 0 0 1) and M_B (STO 1 1 0) symmetries [52].

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There is evidence that ultrathin films (<10 nm) of BFO on STO (0 0 1) may be purely tetragonal [63, 66, 67]; this true tetragonal phase coincides with a suppression of octahedral tilting [68], imposed by the cubic substrate [67]. However, for typical thicknesses of 15 nm and above, monoclinic BFO is usually obtained. As the thickness is increased above about 30–90 nm [61, 66, 69–72] the BFO begins to relax via misfit dislocations and/or defects (such as oxygen vacancies) [73], and the out-of-plane lattice parameter approaches its bulk value. Experiments have routinely shown that BFO tolerates a wide range of strains: R-like BFO can be grown for strains −2.6% to +1.2% up to thicknesses of 60–70 nm without structural relaxation [60, 74, 75]. This characteristic may be related to the oxygen octahedra and their 'willingness' to rotate or tilt to accommodate strain [76, 77]. The rare-earth scandate substrates [78] such as DSO, TbScO₃ (TSO), GdScO₃ (GSO), SmScO₃ (SSO), NdScO₃ (NSO), and PrScO₃ (PSO) [79], can all be used to grow coherently-strained films with either M_A or M_B structure [50, 74–76, 80–82]. On substrates that impose a lower misfit strain—such as DSO—films up to 300 nm may be fully strained [71]. Furthermore, lower electrode properties can help to maintain strain coherency up to larger thicknesses; e.g. on SRO-coated STO substrates, Holcomb et al [83] were able to grow strained BFO films up to 200 nm thick.

The inhomogeneities of the strain-relaxation process can be probed by x-ray microdiffraction [84], and it has been shown that different regions of the film may show different relaxation rotation, as well as different ferroelectric variants [84, 85]. The step-bunching growth mode can induce tilt in the crystallographic planes of BFO when grown on vicinal STO substrates [86]. Substrate orientation also affects the strain relaxation process. A detailed study by Kan et al [58] showed that for BFO films on (1 1 1)-oriented STO substrates, the out-of-plane lattice parameter relaxed towards its bulk value for thicknesses above 50 nm, while for (0 0 1)-oriented films, the out-of-plane parameter exhibits a much slower relaxation, and even at thicknesses greater than 500 nm the bulk parameter is not yet reached.

In addition to a change in the atomic structure, the strain relaxation process influences the domain structure of the films, with certain domain variants being favoured as thickness increases [63]. Lower electrodes (e.g. SRO) also play an integral role in lattice relaxation [84, 87], and in ferroelastic domain structure [88]. For instance, step-flow SRO gives BFO that has two domain variants, while step-bunch SRO gives four-domain-variant BFO. We will describe the domain structures in more detail in section 3.1.

For large compressive strains (of more than about 4.5% in the (0 0 1) orientation), an epitaxially-stabilized polymorph of BFO can be formed. This polymorph is quite unique because it does not exist in the bulk (the reason for which is discussed in [89]), has a large tetragonality, with c/a ≈ 1.25–1.3, and vastly different physical properties. Early first-principles calculations alluded to a giant polarization of around 150 µC cm⁻² for BFO in a highly-distorted tetragonal P4 mm phase [90], and experimental work by Rincinschi et al suggested that this polarization is indeed accessible in thin films [36]. This first experimental report used, however, non-epitaxial films, and it was not until 2009 that reports appeared of epitaxial films of BFO grown on LaAlO₃ (LAO) substrates in the 'T-like' phase [37]. Initially thought to be a true tetragonal P4mm structure (figure 3(a)), this form of BFO was shown to be in fact monoclinic [37, 40, 41, 76, 91–94]. There is still some controversy regarding to which space group this structure should belong; for example, in [92] it is argued to be Cc, while some studies allude to the possible coexistence of Cm and Cc phases [37, 91], and others promote the space group Cm (figure 3(b)) [40, 76, 93, 94], where the monoclinic distortion is along the [1 0 0] direction.

The transition from R-like to T-like was initially thought to be isosymmetric [91, 95, 96], that is, in the same space group (namely Cc), but further experimental characterization [41, 76, 97] showed that the transition is in fact from M_A to M_C, in space groups Cc and Cm respectively. This was also consistent with other reported structural data [91]. The similarity of the free energies of the R-like and T-like structures at around 4–5% strain [41, 95, 98–100] (see figure 4(a)) gives rise to mixed phase films of BFO, with a distinctive surface morphology [38, 76, 101–103]. This stripe-like topography—comprised of R-like striped phases in the smooth T-like matrix [38]—observed in these mixed-phase films arises from the lattice mismatch between the R-like and T-like phases [101, 104], not unlike the ferroelastic domain walls that appear in many ferroelectrics, and in the R-like phase of BFO. The evolution of the c/a ratio in these domain walls is peculiar, since it is very gradual, over a 10–20-unit cell length [38].

In these mixed R-like/T-like specimens, a third polymorph of BFO, distinct from both the R-like and T-like phases, commonly appears [99, 101, 105, 106]. The crystal structure of this 'intermediate phase' is either monoclinic [101] or triclinic [105], with lattice parameters of about a = 3.81–3.82 Å and c = 4.15–4.18 Å, and often a tilt of the c axis of around 3° from the film normal [101]. It has been proposed that this third phase (sometimes called Tri-1 [105], M_I [99, 101], or S' [106]) exists to fulfil lattice matching conditions of two adjacent regions composed of different R and T phases. This intermediate state indeed appears to play a crucial role in the enhanced piezoelectric response of these mixed-phase films, which we discuss in section 3.4.

Strain relaxation in T-like films usually occurs in a pure T-like phase → mixed T–R phase → R-like phase progression [107]. Very thin films on LAO, for example, can be pure T-like phase, while thicker films tend to be almost pure R-like phase. This is a standard strain accommodation/relaxation process in these films, whereby at larger thicknesses the elastic stress is relieved by the formation of the more stable R-like BFO. The surface morphology is accordingly modified, with T-like regions progressively suppressed with increasing thickness [107].

A temperature-driven phase transition with evolution from monoclinic M_C → monoclinic M_A → true tetragonal was reported for 60 nm BFO films deposited on YAO [108], and later on LAO, with the transition temperature at about 100–150 °C [93, 99, 106, 109, 110]. In this transition, the unit cell goes from primitive M_C to a rotated and doubled M_A unit cell then to a primitive tetragonal cell—a point which has implications for the ferroelectric polarization. Interestingly, the first part of this transition (M_C → M_A) is also observed in R-like films [48] at around 750 °C.

Growth conditions play a strong role in the stabilization of T-like BFO [111], and more specifically, whether R-like, T-like, or a mixture of these phases appears. For instance, pure T-like films can be obtained on STO substrates with a nominal strain of only −1.4% [112–114], by controlling growth rate and/or substrate temperature, while on NdGaO₃ (NGO) substrates with strains of around 2.8%, R-like films have been grown [76, 82]. On LAO, by a careful fine-tuning of the growth conditions, almost phase-pure R-like BFO orT-like BFO can be grown [115]. This overlapping of the phase diagram highlights the fact that the many growth parameters, as well as epitaxial strain imposed by the substrate, all can be used as control parameters to tailor the structure of BFO films. As an even more dramatic example of this point, recently the T-like polymorph was stabilized in the (1 1 0) orientation by Liu et al [116]. Here the authors used LAO substrates with (1 1 0)-surfaces to form a monoclinic phase of BFO with a c/a of 1.2 and a polarization with sizeable components both in-plane and out-of-plane. This pioneering work on a non-conventional orientation of the T-like phase should lead towards epitaxial stabilization of the T-like phase with enhanced ferroelectric polarization in-plane—a feature that may be attractive for devices.

We now move to the other end of the strain/structure phase space. As shown in figure 4(a), phase-field simulations and first-principles calculations predicted that at tensile strains of 2% and beyond, an orthorhombic phase (figure 3(f)) of BFO may be stabilized [45, 117–120]. In this phase, the polarization would lie in the in-plane 〈1 1 0〉 directions while the antiferromagnetic vector appears (mostly) out-of-plane. This phase was epitaxially stabilized for rather thin films of 15 nm by Yang et al [45]. It was shown by a combination of piezoresponse force microscopy (PFM) and second harmonic generation that the ferroelectric polarization of this phase lies in the plane (along 〈1 1 0〉_pc), while x-ray absorption spectroscopy (XPS) showed that the antiferromagnetic vector lay 34° from the out-of-plane direction; a result consistent with that reported for other strongly tensile-strained films [75]. For films in the (−1 1 0) orientation, first-principles calculations suggest that an orthorhombic Pnma phase can be stabilized for compressive strain larger than about 1.6% [65, 121].

The various structures of BFO available to researchers afford a strong control of the ferroelectric properties, not least through the transition between the R-like and T-like phases, but the space in between as well. In the next section, we explore the ferroelectric and piezoelectric properties of BFO thin films. Before concluding this section, however, we would like to point out that there is a whole body of literature dealing with A and/or B site doping to dramatically modify BFO thin films' structure and physical properties—such as piezoelectricity, magnetism etc. Save for a few specific examples that we deem of particular illustrative and applicative importance, we do not discuss doping effects in this review. A more focused review of doping can be found in, for example, Yang et al [122].

Since BFO's parent phase is rhombohedral, in films deposited on (0 0 1) substrates, the polarization can point along one of eight directions (figure 5(a)), giving rise to eight possible domain variants [128]. Accordingly, there are three possible types of boundaries separating the domain regions: 71°, 109° and 180° domain walls (DWs) (figure 5(a)). The latter is a purely ferroelectric DW, while the former two are also ferroelastic DWs (since there is a difference in spontaneous strain between the separate domain regions [129]). The various domain types can be imaged using PFM, and through a combination of in-plane (IP) and out-of-plane (OP) responses at various cantilever/crystal axis angles [130, 131], the full 3D domain structure can be established [132], as presented in figure 5(b). The intricate domain structure of BFO has engaged many workers to try to reach insight into, and deterministic control of, polarization switching [132–134] and the factors that affect it; for instance, polarization fatigue can be linked to ferroelastic domain population [135], and the film's crystallographic orientation can markedly alter domain switching characteristics [136].

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Judicious choice of substrate type, orientation, and/or vicinality can be exploited to control the morphology and type of pristine ferroelectric and/or ferroelastic domains in epitaxial BFO films [137]. The lower electrode can also play an important role. For example, using vicinal STO substrates with miscuts along particular high-symmetry crystallographic directions, the eight polarization variants of BFO can be reduced to four, two, or just one polarization variant, see figure 5(c) [72, 138–140]. Alternatively, anisotropic strain induced by orthorhombic substrates such as TbScO₃ [80, 141] or DyScO₃ [88, 142] can be used to preference particular domain patterns. The specific domain morphology can range from a fractal, mosaic like arrangement, to straight stripe-shaped domains [143, 144]. Finally, doping BFO with La can reduce its T_C to below the growth temperature, providing another method to control domain morphology [145].

A rather curious attribute of BFO is that its ferroelectric domain walls can be conductive [8, 146–148]. Ferroelectric DW nanoelectronics has become an active area of research, striving to understand the physical origin of the walls' conductive properties, explore their other functionalities, and design and characterize domain wall-based devices. In addition, the domain walls may possess distinct magnetic properties. BFO domain walls will be covered in more detail in section 6.

Fully-saturated polarization hysteresis loops are routinely obtained on thin-film samples when the leakage is sufficiently low (see example in figure 6(a)). In (1 1 1)-oriented films, the total ferroelectric polarization can be measured in a capacitor geometry, and values close to 100 µC cm⁻² have been reported [43, 149]. For films in other orientations—such as (0 0 1) or (1 1 0)—the measured polarization is the projection of the (1 1 1) polarization vector along the measurement direction [53, 138, 150, 151], as illustrated in figure 6(b). Measured spontaneous polarization values for epitaxial BFO films are around 90–120 µC cm⁻² [43, 53, 61, 123, 152] along the [1 1 1]_pc direction. The T-like phase of BFO is suggested to have an even larger polarization of ∼150 µC cm⁻² [102], which would be a direct result of the larger cation shifts in this highly-distorted phase [153].

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The dependence of ferroelectric properties on strain in BFO is very different from that of tetragonal ferroelectrics such as BaTiO₃ [34]. In BFO, the two structural instabilities (cation displacement and antiferrodistortive rotations) coexist and compete [154]. As a result, strain-sensitive effects are more complex and cannot be extrapolated from the behaviour of other ferroelectric perovskites. As a notable example of the impact of these antagonistic degrees of freedom, the ferroelectric Curie transition temperature T_C in BFO was shown to be strongly reduced with increasing compressive strain [74, 155]. This is contrary to what occurs in e.g. BaTiO₃ [125]. First-principles calculations indicated that the cause of this phenomenon is the antiferrodistortive rotations, which have a stronger effect on T_C than the polar distortion induced by strain [74].

The influence of strain on the ferroelectric polarization is much less pronounced. The total polarization along (1 1 1)_pc does not show a strong strain dependence [156–159]; however, upon application of a biaxial strain in the (1 1 0) plane, the projection of the polarization onto the (0 0 1) direction changes considerably [61, 90, 156, 158]. This is the result of the rotation in the (1 1 0) plane of the polarization away from the 〈1 1 1〉 direction. Thermodynamic [57], first principles [90], and Landau-Devonshire [117, 159] calculations corroborate this trend of polarization change with strain, albeit with vastly different values of polarization and slope: the change of polarization varies between −4.7 µC/cm²/% strain [156] to −15.15 µC/cm²/% strain [158]. In figure 6(c) we gather many experimental and theoretical studies of the polarization with strain, where it can be seen that the general trend is an increase in the polarization along (0 0 1)_pc with increasing compressive strain, consistent with a rotation of the polarization vector, and that the T-like phase exhibits a much larger spontaneous polarization.

The rotation of the polarization vector with strain observed in BFO is part of a larger structural O → M_B → R → M_A → T progression in ferroelectrics as described by Vanderbilt and Cohen [160]. As the symmetry changes with epitaxial strain, the polarization direction is also inherently modified. A portion of this rotation path (M_A–triclinic–M_C) is observed in bulk relaxor crystals under electric field [161–163]. The polarization rotation in BFO is consistent with observations that show that orthorhombic BFO has its polarization in the plane [45], the M_B phase is rotated from [1 1 1] towards the [1 1 0] direction [50], the M_A phase has a polarization rotated towards [0 0 1] [156, 158], and the T-like M_C phase has its polarization slightly tilted away from the [0 0 1] direction in the (0 1 0) plane (see figure 6(d)). The strain-induced R → M_A → M_C → T transition (also seen in the 0.7Pb(Mg_1/3Nb_2/3)–0.3PbTiO₃ system under electric field [164]) in BFO is elegantly illustrated by Christen et al [41], where the authors used a combination of epitaxial and chemical strain (i.e. doping) to induce the various phases, as shown in figure 4(b).

The weak effect of strain on the polarization of BFO in its R-like phase can be attributed to its relatively small piezoelectric coefficient [10, 165], which amounts to around 40–60 pm V⁻¹ [132, 156, 166, 167] in unstrained films. We now discuss ways of improving the piezoelectric response, first by a composition-induced morphotropic phase boundary (MPB), and second by a strain-induced phase transition.

In ferroelectrics, the intimate link between crystal structure and the electromechanical response means that a compound that is compositionally-tuned between two different structures—that is, at a morphotropic phase boundary (MPB)—can exhibit a remarkably enhanced piezoelectric response [168, 169]. A classic example of this is Pb(Zr_xTi_1−x)O₃ (PZT): this solid solution displays exceptional piezoelectric coefficients, hence its use in actuators, acoustic sensors, etc [170]. With current environmental concerns regarding the toxicity of lead, researchers have been actively investigating other lead-free oxide compounds and solid solutions thereof, for use in these important applications.

While BFO was considered early as a possible alternative to lead-based piezoelectrics, its electromechanical coefficients are not large enough to compete with more conventional ferroelectrics. To explore the possibility of a MPB in the BFO system [171], Fujino et al prepared rare-earth substituted BFO films by a combinatorial method (i.e. compositional spread samples) [166]. It was observed that for samarium-substituted BFO, a peculiar phase transition occurs at around 14% Sm composition. The out-of-plane lattice constant exhibits a drastic change, the dielectric constant rises to ∼400, and the d₃₃ shows a dramatic increase up to over 100 pm V⁻¹ at the transition (figure 7(a)) [166]. Concomitantly, the ferroelectric hysteresis loops of Sm-doped BFO change progressively from a standard ferroelectric shape for Sm composition <13%, through to a double hysteresis at Sm composition 14% and above [166] (shown in figure 7(c)). Detailed high-resolution transmission electron microscopy (HRTEM) studies [172] and first-principles calculations [173] revealed the origin of this enhanced response to be the formation of a nanoscale mixture of BFO-Sm with a different structure: while Sm-doped BFO with low doping (<14%) is rhombohedral (polar), Bi_0.8Sm_0.2FeO₃ has an orthorhombic (non-polar) structure. Applying an electric field causes a structural transformation from the orthorhombic phase to the rhombohedral phase, i.e. causing domain boundary movement, giving rise to an enhanced electromechanical response [173].

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Additional studies using other rare earth substitutions (Dy, Gd, and La) showed universal behaviour, with a morphotropic phase boundary and a corresponding enhancement in the dielectric constant and piezoelectric coefficient [173]. The control parameter was shown to be the average A-site ionic radius, and after scaling the results for different A-site cations to their average, the curves for dielectric constant, d₃₃, and hysteresis curves (figure 7(c)), all collapse into one, confirming the universality of the behaviour. Importantly, it was shown that doping with La³⁺—a cation with the same nominal radius as Bi³⁺—did not cause the marked increase in the dielectric constant and electromechanical response [174, 175], indicating that the property enhancement is a direct consequence of the structural transitions induced by the chemical substitution of a smaller A-site cation. Deeper investigations with regard to temperature yielded the phase diagram shown in figure 7(b). Near room temperature, the transition between the rhombohedral and orthorhombic phases occurs through a phase boundary that exhibits antiferroelectric behaviour, while at higher temperatures this intermediate phase is suppressed [173].

In addition to the phase transition induced by the continuous Sm substitution, a rotation of the polarization vector is observed with increased Sm doping [176]. While the replacement of the Bi cations by Sm substitution causes a decrease in the absolute magnitude of polarization (since the ferroelectricity in BFO is primarily due to the lone pair electrons in Bi³⁺ [177, 178]), the out-of-plane component of P_R remains almost constant until 13% Sm composition, since the polarization vector rotates towards the [0 0 1]_pc direction. This conclusion was supported by additional data on Sm-substituted films on (1 1 0) and (1 1 1) oriented STO substrates, where it was observed that the measured polarization along the (0 0 1) direction was consistent with a rotation of the polarization direction [176]. Indeed, this rotation of the polarization vector probably plays an important role in the enhancement of the d₃₃ at the MPB in this compound, just as it does in the relaxor-based systems [168].

The piezoelectric response of BFO appears relatively sensitive to epitaxial strain [156]. This is particularly true of R-like BFO under compressive strain, for the proximity to the R-like/T-like transition at around 4–5% strain, causes a divergence of the piezoelectric coefficient d₃₃ [96]. However, as described in section 2.3, at these strain levels BFO films form in a mixed phase where both the R-like and T-like polymorphs appear. These mixed phases have been shown to have strongly enhanced piezoelectric response [38], with electric field-induced strains of the order of 2%. In fact, BFO at the boundary between these two phases can offer a piezoelectric response almost four times higher than the widely-used piezoelectric material PZT [179]. Since BFO is lead-free, these results created a stir in the community, for lead-free piezoelectrics are highly sought after [180].

The microscopic origin of the enhanced piezoelectric response has been elucidated to be a movement of the phase boundaries between the different phases [105, 181], with the third 'intermediate' polymorph playing an important role in the transformation, since it is the bridging phase between them [106]. The control of the relative ratios of R-like and T-like phases is important for potential device applications, as the R-like regions in the films tend to control the electromechanical response, and PFM-based techniques have proven very useful [182], through which regions of R-like and T-like BFO can be created at will.

The piezoelectric response also appears to be enhanced through a temperature-driven M_C → M_A phase transition that occurs at around 150 °C in mixed-phase films [99]. At this transition, the d₃₃ increases from about 60 pm V⁻¹ up to about 100 pm V⁻¹, which arises from the additional degrees of freedom in the lattice structure and the polarization and the fact that they can respond to an external electric field more strongly [99]. The expected polarization rotation from [x 0 z] at low temperature to [x x z] at high temperature was also observed.

The enhancement in piezoelectric response may not be limited to simply the R-like/T-like transition. There has been speculation [118] that the transition between the monoclinic M_B and orthorhombic phases that occurs at moderate tensile strain may uncover a bridging phase with a piezoelectric response even stronger than the R/T transition. Very recently a mixed rhombohedral/orthorhombic phase was explored [46] for films grown on GSO substrates; however, no enhancement of piezoelectricity was reported at the phase boundary.

It should be noted that while both the substitution-induced and strain-induced MPBs are highly interesting from a physical point of view, their use in devices is limited since the absolute strains induced in thin films are very small. The most likely envisageable application would be in nano-devices. In actuators, bulk crystals are used since their strains can be many orders of magnitude larger.

Most electronic devices based on BFO thin films exploit its very large polarization. They can operate in either a planar geometry (such as ferroelectric field-effect transistors—FeFETs) or a perpendicular geometry (ferroelectric diodes or ferroelectric tunnel junctions [238]). In the former case, the current flows in a conductive channel adjacent to the ferroelectric, while in the latter, the current flows across the ferroelectric (in different transport regimes [239, 240] including direct tunnelling, Fowler-Nordheim tunnelling, field emission, etc). Another family of devices utilize the transport properties of domain walls in BFO. This emerging field of ferroic domain wall nanoelectronics [241] is very young and many issues remain unresolved, as we will discuss.

To achieve the largest possible modulation of the channel resistance in FeFETs, the transport response of the channel material must be very sensitive to changes in the carrier density, and the ferroelectric must allow for a large carrier density modulation [242]. Nominally, the density of surface charge accumulated or depleted by the ferroelectric is equal to the polarization. If strongly correlated oxides are used as the channel, functional properties dependent on carrier density (such as magnetic order, as occurs in mixed valence manganites [243]) may also be controlled by switching the ferroelectric polarization direction. This type of device—combining correlated oxides and ferroelectrics—is central to Mottronics, a flavour of oxide electronics specifically aimed at the electrical control of strong correlations. The large polarization of BFO makes it an attractive gate oxide in FeFETs (P = 100 µC cm⁻² corresponds to n_s = 6.25 × 10¹⁴ electrons per cm²; for a typical perovskite oxide channel with an in-plane lattice constant of 3.8 Å this is 0.9 electrons per surface unit cell). Another advantage of BFO is that it can accommodate a broad range of lattice mismatches with underlying channel materials that can then be combined with R-like or T-like BFO.

CaMnO₃ is a Mott insulator in which a few per cent of Ce doping (being 4+, each Ce ion contributes two electrons) induces a transition to a metallic state [244, 245]. CaMnO₃ thus appears an attractive channel material for FeFETs. CaMnO₃ has a smaller lattice constant and is thus only compatible with T-like BFO. As visible in figure 12(a), the resistivity is indeed strongly modulated by the accumulation or depletion of charge in the channel [246]. The OFF/ON ratio reaches 10 at 200 K. Surprisingly, the OFF/ON ratio does not increase further if the channel thickness is decreased below ∼20 unit cells, likely due to dead layer effects. In these experiments, the maximum sheet carrier density modulation was Δn_s = 0.6 × 10¹⁴ cm⁻² (corresponding to ΔP = 11 µC cm⁻²). This is within the range of previously-reported values [247, 248] but more than one order of magnitude lower than the nominal value expected from the polarization of T-like BFO. FeFETs combining R-like BFO and LSMO channels have also been investigated [249, 250], where the maximum channel resistance changes by a factor of ∼3 at low temperature [250]. No information on the carrier density modulation was provided in these studies. Interestingly, the field effect from BFO also influences the magnetic properties of the manganites, as we will discuss later.

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In FeFETs combining R-like BFO and an ultrathin superconducting YBa₂Cu₃O_7−δ (YBCO) channel, a large change of the transport response of the channel was also measured. In cuprates, the superconducting critical temperature (T_supra) strongly depends on carrier concentration and in this YBCO/BFO FeFET a modulation of T_supra of 30 K (produced by a Δn_s = 1.8 × 10¹⁴ cm⁻², corresponding to about ΔP = 30 µC cm⁻²) was found (figure 12(b)). This is at least a factor of four larger than previous reports using other ferroelectrics (notably PZT) [251].

Charge transport modulated by polarization direction was also reported in perpendicular-geometry devices such as diodes and tunnel junctions. Figure 13(a) reproduces the results of Choi et al on Ag/BFO/Ag structures [30]. Current versus voltage—I(V)—characteristics measured across the device are strongly asymmetric, as occurs in p–n junction diodes. Interestingly, the sign of the asymmetry reverses as the polarization direction of BFO is switched. These particular results were on BFO crystals, but similar results have been reported in thin film heterostructures [252–255]. Practically, the device resistance is strongly dependent on the direction of the ferroelectric polarization, and resistive switching ratios in excess of 10² have been reported [253, 255]. The precise mechanisms responsible for the effect are still debated (bulk-driven, associated with charge accumulation/depletion and band bending [256]; or interface driven, with local defects such as oxygen [255] or bismuth [254] vacancies playing a major role [257]). These ferroelectric diodes also exhibit the bulk photovoltaic effect, which will be discussed further in section 6.3.

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In BFO-based capacitor structures, when the BFO thickness is reduced to just a few nanometres, quantum mechanical tunnelling of charge carriers becomes possible and, at very low thickness and bias voltage, dominates the transport response. Just as polarization charges can produce band bending at ferroelectric/metal interfaces, the intrinsic potential profile of a tunnel barrier is strongly modified if the barrier material is ferroelectric. Polarization charges are screened in the electrode over a finite thickness (ranging from one ångström in very good metals to a few nm and higher in poor metals and semiconductors) and this imperfect screening generates a (positive or negative) potential that adds to the intrinsic screening. With dissimilar electrodes, the resulting potential profile is strongly asymmetric; the sign of this asymmetry depends on the ferroelectric polarization direction, as does the average barrier height. Because tunnel transmission depends exponentially on the barrier height, polarization switching produces tunnel resistance switching [258, 259]. The first clear demonstration of a giant electroresistance effect (∼1000 at room temperature) produced by polarization switching in FTJs was provided by Garcia et al [260], and quickly confirmed by other groups [261, 262]. With BFO tunnel barriers, a few results have been reported. With 3 nm thick R-like BFO barriers, Hambe et al found a modest electroresistance of only 80% at low temperature [263]. In contrast, a very large effect (>10⁴) was measured at 300 K by Yamada et al (see figure 13(c)) [264], and resistance switching was clearly correlated to polarization switching. In addition, these BFO-FTJs behave as memristors [265, 266] in which the device resistance is not determined by voltage-controlled defect distributions (as in many memristive systems [267], including some based on thick BFO layers [268]), but by the ferroelectric domain configuration in the barrier [269]. Very recently, systematic tests revealed a good reproducibility for BFO-based ferroelectric memristors, with an endurance of 4 × 10⁶ cycles [270].

The discovery of finite conductivity at domain walls in BFO has triggered a flurry of activity in the scientific community working on BFO, multiferroics, and ferroelectrics in general. In the initial report by Seidel et al [8], only 109° and 180° DWs were found to be conductive, but not 71° DWs. This was consistent with theoretical calculations indicating that the band gap decreases in the vicinity of the boundary [8], arising from the step in electrostatic potential related to the change in polarization direction. A subsequent report however showed that conduction also occurs in 71° DWs [146]. This sparked controversy regarding the mechanism giving rise to conduction, i.e. intrinsic (band gap reduction, as argued in [8] and subsequently in [200, 271]) or extrinsic (oxygen vacancies being generated at or attracted to the wall, allowing conduction, as argued in [146], and in [272] on the basis of first-principles calculations indicating essentially no change of the electronic structure at the DW, for all three types). In a later paper, Seidel et al also showed that DW conductivity in La-doped BFO films can be controlled by oxygen vacancies [148], pointing at a dominant role of extrinsic factors in determining the electronic response of DW in BFO. We note that following these results, DW conductivity was also found in other ferroelectrics such as PZT [273], BaTiO₃ [274], LiNbO₃ [275], and rare earth manganites [276].

Since the field is in its infancy, very few device prototypes have been realized [277]. One is presented in figure 14, showing how transport between two electrodes separated by a BFO element can be modulated by writing and erasing DWs. Another interesting result is from Maksymovytch et al who found a memristive behaviour of conductive DWs in BFO characterized by scanning probe experiments [147].

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The concomitance of ferroelectricity and magnetic order at room temperature makes BFO an obvious candidate for applications in the field of spintronics. In particular, the magnetoelectric coupling between the two orders opens the way to the control of magnetic properties by an electric field, and thus to energy-efficient spintronic devices in which information is stored magnetically and written electrically. The prototypical example of such devices is a magnetic random access memory (MRAM) with an electrical writing procedure (MERAM) [6, 278, 279].

In BFO, the spins are rigidly coupled to the crystal lattice, and 71° or 109° switching of the ferroelectric polarization results in the rotation of the sublattice's magnetization, i.e. the antiferromagnetic (AFM) state can be modified by an applied voltage [195, 203, 280, 281]. Interestingly, in strained BFO epitaxial thin films, the absence of cycloidal modulation enables the linear magnetoelectric coupling term.

When combined with standard ferromagnets (FM) with high Curie temperature, the AFM property of BFO has been used to induce exchange bias [282, 283]. This exchange bias is characterized by either an enhanced coercive field when stripe-like domain morphology is observed [199], or with an additional shift of the hysteresis loop of the ferromagnet when mosaic-like domains are present in the BFO [199, 284]. In the latter case, the shift arises from the coupling between pinned uncompensated spins and the ferromagnet [284]. It varies as the inverse of the coupled AFM–FE domain size [284] (or equivalently the total length of domain walls divided by the sample surface [199]) as expected from Malozemoff's model of exchange bias extended to multiferroics [285]. More precisely, it has been shown that the exchange bias is related to the total length of 109° domain walls [199]. From this correlation, the main mechanism responsible for exchange bias in BFO/FM systems appears to be related to the exchange coupling between uncompensated spins in the FE–AFM domain walls of BFO and the ferromagnet magnetization. More recently, direct coupling between the net magnetic moment in the BFO domains and the FM was proposed as an explanation for the increased coercive field of CoFe on BFO [286].

The magnetoelectric coupling in BFO allows control of this exchange bias by an electric field, enabling, at room temperature, manipulation of the FM layer by purely electrical means. This has been shown in planar geometry through the manipulation of the magnetic state of Co₉₀Fe₁₀ dots on top of a BFO layer using PFM, synchrotron-based techniques [287], and magnetotransport measurements [286]. In the latter study, rotating the FE polarization of BFO by 71° by applying a large voltage resulted in a reversible 180° change of the net magnetization direction of the CoFe dot as evidenced by the shift of the angular dependence of the anisotropic magnetoresistance of the CoFe layer (see figure 15(c)) [286].

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From a device point of view, it is crucial to work in the vertical geometry which allows operation at moderate voltages, being thus compatible with standard integrated electronics. Zhang et al [288] and Allibe et al [289, 290] investigated the prospect of electrically controlling the magnetic state of a spin valve exchange-biased with BFO. The latter paper evidenced a strong reduction of the exchange bias of a Co₇₂Fe₈B₂₀/Cu/Co spin valve upon application of a moderate voltage, which manifests itself as a progressive shift of the giant magnetoresistance (GMR) signal (see figure 15(f)) [290].

In FeFET devices, the accumulation and depletion of charge from the BFO can modify the magnetic properties of an adjacent manganite channel [249, 250]. When cooled in the presence of a magnetic field, the BFO/LSMO system exhibits an exchange bias, and a magnetic moment is induced in the BFO [291]. As inferred from magnetoresistance curves collected for both polarization states both the magnetic coercive field and the exchange field are sensitive to the direction of polarization in BFO (that is, to the accumulation or depletion of carriers in the manganite channel). The former may reflect changes in the magnetocrystalline anistropy. For the latter, various mechanisms have been proposed, mainly relying on the influence of voltage on the magnetic moment in the LSMO [250, 292]. This electric-field control of exchange bias appears to be reversible but is limited to temperatures below about 30 K.

We have already mentioned that ultrathin BFO films can be used as tunnel barrier, and their ferroelectric character can produce giant tunnel electroresistance. When two ferromagnetic electrodes are used, tunnel magnetoresistance (TMR) can also be observed, as reported by Béa et al [283, 293] in LSMO/BFO/Co junctions. Interestingly the TMR is positive, in contrast with the situation in junctions combining LSMO and Co with other perovskite oxide barriers such as STO [294], TiO₂ [295], LaAlO₃ [296] or BaTiO₃ [297, 298]. This deserves further investigation to clarify the role of the spin-polarized density of states at the BFO/Co interface and possible spin-filtering effects by the BFO barrier. A TMR of about 60% was also reported by Hambe et al in LSMO/BFO/LSMO junctions [263], this value being weakly dependent on the ferroelectric polarization direction.

The large birefringence of BFO has clear potential in optical applications. Since the ferroelectric polarization direction defines the optic axis, rotating the polarization (either by 71° or 109° switching) is a simple way to induce a large change (∼0.2) in the refractive index. A plasmonic resonator/switch making use of this effect was proposed [299]; in this work the authors modelled the performance of a modulator based on an Au-wire grating on top of a 500 nm thick BFO film. The results suggested a strong modulation—around 30 dB—of the reflected beam amplitude depending on the polarization of the BFO layer. However, no working device prototype was reported.

In addition to the birefringence, as discussed in section 5, BFO has a sizeable electro-optic effect. This naturally could lend itself to application in thin-film optical modulators [300]. There are many technological problems to be overcome, not least of all how to reliably manufacture thick single-domain films, and how to guide a laser beam in a length of modulator long enough to yield a significant modulation of the beam, without large losses. Integration on substrates with a low dielectric constant can offer modulation over a wide range of frequency and bandwidth [209]. The T-like phase of BFO probably shows more promise for devices. Since it has a larger ferroelectric distortion, one can probably expect that its birefringence will be even higher than that of the R-like phase.

The bulk photovoltaic effect has been utilized in a prototype memory [301]. Here the BFO was the active storage medium in what was essentially a Fe-RAM, and upon illumination with a uniform light field, the BPV effect induced a voltage across the memory cell that was dependent on the ferroelectric polarization. Reading out the data was straightforward, as simply a voltage had to be read, avoiding the laborious re-writing step in Fe-RAM devices. Shown in figure 16, the proposed 16 cell device produced good retention properties, with no degradation after four months, and minimal ferroelectric switching fatigue.

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The bulk phase of BFO has been shown to exhibit photostriction [302, 303], arising from the combined influence of the bulk photovoltaic effect and inverse piezoelectricity. The effect appears to have a dependence on applied magnetic field as well, evidencing a spin-lattice coupling term. While this result has yet to be observed in thin films, the fact that BFO possesses such a wide array of properties opens the way to multifunctional devices making use of optical, magnetic, electric and elastic degrees of freedom in BFO thin films [304].