Defeating depolarizing fields with artificial flux closure in ultrathin ferroelectrics

Material surfaces encompass structural and chemical discontinuities that often lead to the loss of the property of interest in so-called dead layers. It is particularly problematic in nanoscale oxide electronics, where the integration of strongly correlated materials into devices is obstructed by the thickness threshold required for the emergence of their functionality. Here we report the stabilization of ultrathin out-of-plane ferroelectricity in oxide heterostructures through the design of an artificial flux-closure architecture. Inserting an in-plane-polarized ferroelectric epitaxial buffer provides the continuity of polarization at the interface; despite its insulating nature, we observe the emergence of polarization in our out-of-plane-polarized model of ferroelectric BaTiO3 from the very first unit cell. In BiFeO3, the flux-closure approach stabilizes a 251° domain wall. Its unusual chirality is probably associated with the ferroelectric analogue to the Dzyaloshinskii–Moriya interaction. We, thus, see that in an adaptively engineered geometry, the depolarizing-field-screening properties of an insulator can even surpass those of a metal and be a source of functionality. This could be a useful insight on the road towards the next generation of oxide electronics.

interaction 5 .We thus see that in an adaptively engineered geometry, the depolarizing-fieldscreening properties of an insulator can even surpass those of a metal and be a source of new functionalities 6 .This should be a useful insight on the road towards the next generation of ferroelectric-based oxide electronics 7 .
Uncompensated bound charges at the surfaces of ferroelectric films trigger a depolarizing field 8 .It is oriented opposite to the spontaneous polarization and highest when this polarization is normal to the surface-the preferred orientation for ferroelectric devices.Thus, the ferroelectric properties are attenuated with decreasing thickness and disappear completely below about 5 unit cells (u.c.) in most perovskites 2,9 .This holds true even when ferroelectrics are deposited on metallic electrodes, which all have a finite screening length and normally cannot fully compensate for the bound charges 1 .To maintain polarization in the ultrathin regime, attempts have been made to minimize the surface-charge accumulation or to enforce polar displacements from the ferroelectric|electrode interface via interface engineering.For instance, interface chemistry can be tailored to create a favorable charge-screening environment and hence a net polarization in the ultrathin regime 10 .Polar metals were also suggested to eliminate the critical thickness in ferroelectrics by inducing inversion symmetry-breaking from the bottom interface 11 , but their experimental implementation remains nevertheless elusive due to the scarcity of lattice-matching systems.
The interfacial polarization discontinuity can be avoided with the use of in-plane polarized ferroelectrics, which are less susceptible to the depolarizing field even at low thicknesses 12,13 .
The in-plane polarization anisotropy, however, is incompatible with the coveted state of the art, energy-efficient out-of-plane capacitor device geometry.Thus, the mutually exclusive benefits of out-of-plane and in-plane polarized ferroelectrics pose a serious obstacle to the ongoing quest for the next generation of oxide electronics.
Here we combine the "best of both worlds" by eliminating the interfacial polar discontinuity in an out-of-plane-polarized ferroelectric heterostructure by creating a flux-closure-like domain architecture.We accomplish this by interfacing two of the most debated out-of-plane polarized systems, BaTiO 3 (BTO) and BiFeO 3 (BFO), with an in-plane polarized, layered ferroelectric of the Aurivillius phase 14 Bi 5 FeTi 3 O 15 (BFTO).In typical perovskite heterostructures, the substrate lattice sets the uniform polarization anisotropy of the epitaxial heterostructure.In our case, the integration of the in-plane polarized BFTO with the out-of-plane polarized systems provides polarization continuity at the interface and enables the onset of an out-of-plane ferroelectric polarization from the very first u.c.The functional impact of the flux-closure-like ferroelectric interface is highlighted in two ways.First, we demonstrate local switching of the BTO polarization, despite the absence of conducting bottom electrode.And second, we stabilize polar Néel domain walls with a deterministic chirality in multiferroic BFO thin films.Thus, we introduce ferroelectric heterostructures with perpendicular in-plane and out-of-plane polar anisotropies for the design of electric polarization at the nanoscale, offering a superior alternative to metal-based ferroelectric device paradigms.
We begin our investigation by monitoring the emergence of polarization in a BTO film epi- taxially grown on an in-plane-polarized BFTO buffer layer using optical second harmonic generation (SHG).This process is sensitive to inversion symmetry breaking and therefore an ideal probe for ferroelectricity.When measured during the pulsed-laser-deposition growth process, as in-situ SHG (ISHG 9 , see Methods), one directly accesses the emergence of polarization in ultrathin films with unit-cell accuracy thanks to the simultaneous reflection high-energy electron diffraction (RHEED) monitoring.We select the Aurivillius compound BFTO as our model inplane-polarized ferroelectric buffer, because it can be grown with single-crystal quality on NdGaO 3 (NGO) (001) o 13, 15 ("o" denotes orthorhombic indices) and exhibits a robust in-plane polarization from the first half-unit cell 13 .Furthermore, it is structurally compatible with functional perovskite oxides (Fig. 1a), and its charged layered architecture favors an upwards-pointing polarization in the BTO layer grown on top 9,16 (Fig. 1b).
The absence of an ISHG signal and, hence, of a spontaneous polarization, during the early stage of the growth of (001)-oriented BTO directly on the insulating NGO substrate, in Figure 1c, confirms the dominant role of the depolarizing field in a non-charge-screened environment.
Only after passing the thickness of 15 u.c., we detect a signal corresponding to a net out-of-planeoriented polarization.The conventional approach to combat the depolarizing field and reduce the critical thickness involves the use of a lattice-matching conducting buffer such as La 0.7 Sr 0.3 MnO 3 (LSMO).Indeed, the associated conduction leads to a significant improvement of the chargescreening environment.The ISHG measurement in Figure 1c reveals a reduction of the thickness threshold for the onset of ferroelectricity down to 4 u.c., however, it does not completely eradicate it.We therefore replace the metal by 0.5 u.c. of ferroelectric in-plane-polarized BFTO.Note that the first half-unit-cell of BFTO (∼2 nm in height) already contains four perovskite layers, which give rise to the net in-plane polarization, and thus, exhibits the full functionality of the Aurivillius compound 13,17 .At first glance, this seems counterproductive because of the insulating nature of this polar buffer.However, Figure 1c shows that we obtain an ISHG signal with the very first BTO u.c.deposited on top of the BFTO; the film grows right in the ferroelectric phase, without any critical thickness threshold.The subsequent continuous ISHG increase with the ongoing BTO deposition is consistent with an out-of-plane-polarized ferroelectric single-domain state 9 , characteristic of BTO.Ex-situ X-ray diffraction (XRD) studies confirm the presence of (001)-oriented BTO with the expected epitaxial relationship, involving a 45°in-plane rotation of the BTO u.c.
on the orthorhombic u.c. of the BFTO buffer (Supplementary Fig. S1, S2).We thus see that an in-plane-polarized insulating buffer layer, can surpass metallic electrodes in stabilizing an out-ofplane-polarized ferroelectric state in the ultrathin regime (Fig. 1d).In order to shed light on this seemingly counterintuitive observation, we investigate the fer-roelectric domain configuration in our BTO|BFTO bilayer by PFM.The uniform vertical-PFM (VPFM) contrast in Figure 2a is consistent with an out-of-plane-polarized single domain configuration in the top BTO layer as inferred from both ISHG and XRD.The lateral-PFM (LPFM) scan in Figure 2b, however, reveals a 200-nm-wide stripe-domain pattern with alternating tail-to-tail (TT) and head-to-head (HH) charged domain walls (CDWs) characteristic of the buried, fully in-planepolarized BFTO film of 0.5 u.c. 13,17 Thus, despite their rigid epitaxial relationship, the BTO and BFTO in the bilayer adhere to their respective polar anisotropies.The domain configuration of the BTO|BFTO heterostructure thus resembles a partial flux closure as sketched in Figure 2c.In ferroic materials flux-closure domain formation efficiently reduces the field energy by forming closed loops of field lines within the material 18 .Specifically, in ferroelectrics, flux closure 3,4 effectively minimizes the polarization discontinuities and bound charge accumulation at the domain boundaries or interfaces.In our case it means that the depolarizing field acting on BTO is successfully defeated, allowing the out-of-plane polarization to establish from the very first u.c.
Remarkably, we observe that the polarization in BTO can be reversibly poled with a scanning probe tip (±5V) once the thickness of BFTO buffer increases above 2 u.c.This is rather unexpected since ferroelectric poling ordinarily requires the insertion of a conducting electrode.In order to investigate the role of buffer thickness in the BTO poling behaviour, we perform tomographic PFM 19 (see Methods) on a buffer layer of 5 u.c.(approx.25 nm).Figure 2e shows a three-dimensional reconstruction of the domain configuration throughout the thickness of the BFTO film, with views from both above and below.The in-plane PFM contrast clearly reveals that the stripe architecture of in-plane-polarized 180°domains nearest the substrate gradually transitions into fine columnar domains with increasing film thickness (see Supplementary Fig. S3.1, S3.2).We conclude that the increased population of percolating CDWs, and of the corresponding density of mobile charges in buffer layers exhibiting such columnar domains (as schematically introduced in Figure 2f), emulates the functionality of a counterelectrode and thereby uniquely enables polarization switching of the BTO.
So far we considered an inherently out-of-plane-polarized ferroelectric (BTO) stabilized as ultrathin film by an in-plane-polarized buffer layer (BFTO).Replacing BTO with a ferroelectric that has its own in-plane polarization components, could bring additional degrees of freedom to the ferroelectric domain and domain-wall engineering in our flux-closing system.To explore this, we grow (001)-oriented BFO, the only known robust room-temperature multiferroic magnetoelectric material, onto the BFTO buffer.Its eight possible polarization components along pseudocubic 111 pc directions 20 lead to a rich variety of possible ferroelectric domain and domain-wall configurations with out-of-plane and also the desired in-plane polarization components.
We monitor the ISHG signal during the BFO deposition onto a BFTO layer of a single u.c.
As in the case of BTO, the ISHG yield (Fig. 3a) shows an onset of ferroelectricity in the BFO film with the first u.c., thus demonstrating the material-independent potential of the flux-closure-like architecture in defeating depolarizing fields.Post-deposition STEM imaging in Figure 3b reveals the high crystalline quality of the BFO|BFTO|NGO heterostructure.An evaluation of the dipolar displacements (Fig. 3c) extracted from the atomically-resolved HAADF-STEM image in Figure 3b shows that there is a clear polarization continuity at the BFO|BFTO interface, highlighting The VPFM signal is largely uniform (Fig. 4c), aside from some linear and dot-like discontinuities, which will be discussed later.This is consistent with a uniform downwards polarization across the BFO film, dictated by the BFTO atomic-plane termination 16 .Therefore, out of the eight possible domain states, the pristine BFO in our heterostructure exhibits only two, namely those with a polarization pointing along [11 1] pc BFO or [ 111 ] pc BFO , henceforth denominated as P 1 and P 2 , respectively (Fig. 4d).This geometry results in the formation of in-plane 109°domain walls, in which, unlike in commonly observed 109°domain walls in BFO films, the out-of-plane polarization component remains downwards oriented from one domain to the other, as sketched in Figure 4d.A restriction to such in-plane 109°domain walls only has never been observed in BFO films and shows that the in-plane polarized buffer can act as a powerful tool in setting the domain configuration.
To our surprise, we observe that the polarization is reorienting with the same sense of rotation across each of the BFO charged domain wall sections separating the 109°domains of the BFO.All the TT walls exhibit a rotation through an upwards polarized state (bright VPFM signal), whereas it is a downwards polarized state for the HH walls (dark VPFM signal) (see Supplementary Fig.

S5.2).
The reported behaviour was verified on six samples.The most striking aspect of this observation is that in the P 1 -P 2 domain wall on the right hand side of Figure 4g the dipolar reorientation prefers a 251°"detour" over the expected 109°rotation.In order to highlight the unusual structure of this domain wall and to distinguish it from the well-known appearance of 109°walls in thin films, we propose to introduce the notion of a 251°wall in this case.Note that the association of the HH walls to the 109°rotation and the TT walls to the 251°rotation leads to a non-zero net chirality of ferroelectric domain walls in our heterostructure, that a BFO film deposited directly onto the LSMO does not exhibit (Supplementary Fig. S6).
The homochirality of the domain walls and the fact that a 251°wall is usually energetically more costly than a 109°wall show that the BFTO buffer exerts a pronounced symmetry breaking effect.Its manifestation is reminiscent of the domain wall homochirality observed in ferromagnetic heterostructures, where it is a consequence of the Dzyaloshinskii-Moriya interaction (DMI) 21,22 .
It can arise from symmetry breaking at the magnetic surfaces or interfaces and generates noncollinear spin structures.Here, in close analogy, an interface with an in-plane-polarized BFTO layer could break the symmetry and give rise to the noncollinear polar textures we observe at the BFO domain walls.Mirroring the free energy invariant describing the DMI in chiral magnets and antiferromagnets [23][24][25] , the corresponding DMI-like 5 invariant for the polarization can be expressed as: , where x corresponds to the in-plane polarization axis, and z points out of plane.As for chiral magnets, it sets a deterministic rotation sense of the order parameter at the domain walls, as we demonstrate using phase field simulations (see Supplementary Fig. S7).Such ferroelectric DMI-like interactions have so far mostly been discussed from a theoretical standpoint 5,26 and the emergence of 251°domain walls in our BFO films is likely one of the first experimental observations of it.All this suggests the use of an in-plane polarized buffer as a novel, unforeseen route for the stabilization of polar homochirality 6,27 .
Thus, our work, introduces epitaxial flux-closing heterostructures that stabilize an out-of-plane polarization in ultrathin BTO and BFO right from the very first u.c.The interfacial symmetry breaking, occurring between in-plane and out-of-plane-polarized layers, can give rise to a net polar chirality at the domain walls of the BFO film.In particular, it leads to 251°BFO domain walls in our heterostructures, which may be a signature of a DMI-like behavior in ferroelectrics.
These results demonstrate that polar insulators can be more effective than metals in screening the detrimental depolarizing field in the ultrathin regime and can be used to initiate entirely novel functional architectures.Both aspects could make the epitaxial combination of perpendicular polar anisotropies a powerful tool in oxide-electronics research.
ISHG monitoring Optical SHG was probed in reflection and in situ, in the pulsed laser deposition growth chamber 9 .The probe beam of 860 nm (ISHG of BFO films) and 1200 nm (ISHG of BTO films) was incident onto the sample with a pulse energy of 20 µJ and onto a spot size of 250 µm in diameter.The ISHG signal was detected using a monochromator and a photomultiplier system 9 .
PFM The scanning probe microscopy measurements were recorded using a NT-MDT NTEGRA scanning probe microscope and two external SR830 lock-in detectors (Stanford Research) for simultaneous acquisition of in-plane and out-of-plane piezoresponse.The data acquisition was performed using a 2.3V AC modulation at 70 kHz applied to the Pt-coated tip.The ferroelectric domain configurations of the pristine BFO sample was identified using vector PFM (see Supplementary Figure S5.1).Deflection and torsion modes were recorded when measuring with cantilever perpendicular to the uniaxial polarization axis of BFTO/BFO.
PFM tomography Tomographic AFM is based on sequential AFM imaging and probe-based nanomechanical milling 28 .Operating in conventional PFM mode 19 , specifically while biasing the conducting tip with an AC field oscillating at the torsional contact-resonance, thereby volumetrically maps the in-plane domain contrast.A PFM tomogram constructed from a sequence of 95 images, all in the same field of view but for gradually diminishing film thicknesses, is presented in  To quantitatively assess the domain periodicity and alignment as a function of depth, 2D Fast Fourier Transforms (FFT) were computed in the top ∼45% of the field of view (dashed region) for each tomogram slice.Representative FFT results (from within the highlighted column) are shown in Figure S3.2a, revealing the magnitude (color) and any directionality (Cartesian with respect to the center as indicated) of periodicities ranging over a full field of view ± 0.02/nm.A weak but identifiable peak is apparent at ∼300 nm and -13.6°for the initial unit cells of the thin film (dotted overlays).As the film thickness increases, however, these peaks become difficult to distinguish from the apparently less ordered columnar domains.To analyze any orientationally-independent periodicities, the 2D FFT data per depth is furthermore recast in SI Figure Figure S3.2b -again for the representative frames from (a), though in fact calculated at every depth.These multidimensional histograms represent the range of detected FFT magnitudes (y axis) for distinct wavelengths (x-axis, instead of frequencies and hence shown as a log scale).The color contrast thus indicates the percent of data points with any given pair of spatial periodicity and magnitude.The peak magnitude nearest ∼300 nm (solid circular overlay) is obvious for the deepest frames, but diminishingly dominates as film thickness increases because other longer and shorter wavelength periodicities develop.Comparing the contrast within the spatially identical dotted rectangular overlays is especially revealing, confirming the increased prevalence of domain periodicities on the order of 100 down to 30 nm as film thickness increases.
The resulting high density of conducting domain walls can correspondingly serve as a 'phantom' back electrode.

Fig. 1 |
Fig. 1 | Absence of critical thickness for ferroelectricity in BTO grown on 0.5 u.c.BFTO.a, A visualization of epitaxial relationship between BFTO and BTO unit cells in the plane of the films.b, Atomic plane stacking at the BTO|BFTO interface, showing the BTO polarization direction set by the net positive layer charge at the interface.c, ISHG signal tracking the BTO thin-film polarization during the identical deposition on: 1) insulating NGO (001) o substrate, 2) on LSMO electrode on STO (001) and 3) on 0.5 u.c.BFTO on NGO (001) o .d, Variation in critical thickness for ferroelectricity in BTO thin films depending on the buffer utilized.

Fig. 2 |
Fig. 2 | Ferroelectric domain configuration in BTO|BFTO heterostructure.a, VPFM and b, LPFM scans of BTO|BFTO bilayer reveal a monotonous out-of-plane polarization in BTO and a stripe pattern of in-plane-polarized domains in BFTO, respectively.c, Sketch of the resulting domain configuration the two layers form, comparable to partial flux-closure domains.d, VPFM scan confirming a successful local polarization reversal in BTO grown on 3.5 u.c. of BFTO without a metal electrode.e, Three-dimensional PFM-tomographic reconstructions of in-plane-polarized domains in a 5 u.c.-thick BFTO film, viewed obliquely from above and below, directly revealing distinct stripe and columnar domain regimes.f, Representation of the thickness-dependent domain architecture in BFTO.Higher thickness results in increased density of mobile charges at the interface, which enables the polarization switching.

Fig. 3 |
Fig. 3 | Polarization continuity at the BFO|BFTO interface.a, ISHG signal tracking the net outof-plane polarization in the BFO thin film during its deposition on 1 u.c. of BFTO (red symbols).Inset shows the signal collected during the deposition of the first two u.c.b, HAADF-STEM image of the coherently strained BFO|BFTO|NGO heterostructure.c, Out-of-plane (∆z) and in-plane (∆x) polar displacements of the B-site atomic columns from the center of their two nearest A-site neighbors measured from the atomically-resolved HAADF-STEM image in panel b, confirming the presence of the BFO polarization form the first u.c.

Fig. 4 |
Fig. 4 | Polar homochiral Néel domain walls in BFO grown on BFTO.a, LPFM scan performed prior to the BFO deposition shows that the BFTO film exhibits a unidirectional polarization pointing along [110] pc BFO .b, LPFM scan reveals only [11 1] and [ 111 ] as two in-plane polarization components of BFO when deposited on the BFTO.c, VPFM scan shows a downwards polarization across the film with scattered local out-of-plane-polarized features (see e,f).d, Schematic of inplane 109°HH and TT CDWs stabilized by the in-plane-polarized buffer.e,f, High-magnification LPFM (e) and VPFM (f) scans show that additional out-of-plane polarization components appear at the charged sections of domain walls, exhibiting the inhomogeneities seen in c. g, Polarization rotation profiles in the (110) pc plane across HH and TT domain walls, corresponding to downwards and upwards pointing polarization rotation, respectively.Deterministic polarization rotation at the walls implies a net chirality in the BFO film likely arising due to the unidirectional BFTO polarization underneath.

Figure 2e ,
Figure2e, which overall comprises more than 1 million 15.7×15.7×1nm 3 voxels of local piezoresponse signals.The color contrast depicts the product of the measured amplitude and the sign of the phase for in-plane torsion of the cantilever, i.e. the lateral piezoresponse.The AFM (Asylum Research Cypher VRS) is operated in contact mode using doped diamond probes (AppNano DD-ACTA).A setpoint of approximately 2.24 µN is sufficient to mill this specimen, while torsional PFM imaging is performed with a 1-V peak-to-peak AC bias at a frequency of approximately 2.8MHz.The amplitude and phase of the locally vibrated lever are simultaneously acquired via a

Fig. S3. 2 |
Fig. S3.2 | 2D FFT computed for each tomogram slice shown in Fig. S3.1.(a,b) Representative FFT results.(c) 2D FFT magnitude for every 1 nm deeper into the sample, specifically for two distinct periodicities: i) the peak initial domain pattern (∼300 nm and -13.6°); and ii) the overall peak radial periodicity.The ratio of these signals is also determined (right axis).

SI
Figure Figure S3.2c displays the 2D FFT magnitude for every 1 nm deeper into the sample (i.e. from every tomogram slice in SI Figure Figure S3.1), specifically for two distinct periodicities: i) the peak initial domain pattern (∼300 nm and -13.6°); and ii) the overall peak radial periodicity.The ratio of these signals is also determined (right axis), with a crossover at a depth of -10 nm indicative of the transition from aligned and regularly repeating stripe domains to finer columnar domains at a thickness of ∼15 nm (3-4 unit cells).

Fig. S5. 2 |
Fig. S5.2 | Confirmation of out-of-plane polarization originating at the charged sections of domain walls via rotation-dependent PFMThe VPFM signal appearing at the charged domain walls could have different origins: it could arise from the buckling due to additional in-plane polarization components at the walls (perpendicular to the uniaxial in-plane polarization axis) or due to the deflection force from the pure out-of-plane polarization.In order to distinguish which of the two is the source of the observed behaviour, we select a micron-sized area (marked in larger LPFM and VPFM scans) to resolve the domain wall signal.Then the sample is rotated by 180°a nd the same area is rescanned.The LPFM signal gets inverted, but the VPFM signal at the walls does not.This confirms that the signal has its origin as cantilever deflection and hence implies pure out-of-plane polarization localized at the walls.

Table 1 :
Landau parameters used for the simulation