Nanoscale domain engineering in SrRuO₃ thin films

Ferroelectric polarization can be used to affect the properties of other materials. This is well known in ferroelectric field-effect transistors, for example, where the polarization surface charge of the ferroelectric film is used to reversibly dope the adjacent layer, as demonstrated in epitaxial oxide thin film heterostructures.¹ 

In this work, a PbTiO₃ layer is sandwiched between two SrRuO₃ layers. In bulk, SrRuO₃ is a ferromagnetic metallic transition-metal oxide and is often used as an electrode in the ferroelectric oxides community.² It is also an itinerant ferromagnet with a Curie temperature T_C = 160 K.³ In thin films of this material, the formation of complex spin textures can be induced by the ferroelectric polarization in an adjacent ferroelectric layer. These include the ferroelectric proximity effect near the BaTiO₃/SrRuO₃ interface giving rise to an emergent Dzyaloshinskii–Moriya interaction, thereby creating robust magnetic skyrmions.⁴ Most recently, in SrRuO₃/PbTiO₃ heterostructures, a ferroelectrically induced magnetic spin crystal was observed.⁵ 

SrRuO₃ is not only affected by the polarization in adjacent layers but also by the epitaxial strain imposed by the substrate.^6,7 When grown on SrTiO₃, epitaxial SrRuO₃ layers are organized into structural domains, according to six possible orientations of the orthorhombic unit cell with respect to the cubic substrate. The orientation of the orthorhombic unit cell and resulting domain strucutre are affected by the steps and terraces at the surface of the SrTiO₃ substrate.⁸ The growth of SrRuO₃ onto the vicinal planes of miscut SrTiO₃ substrates leads to the privileged development of a majority single domain orientation in which small domains with different orientations are embedded.⁹ In addition, control of the SrRuO₃ can be achieved not only through the choice of substrate¹⁰ but also by modifying the growth temperature.¹¹ Further structural domain engineering has been conducted through control of substrate miscut direction, demonstrating a one-to-one correspondence between structural domains and magnetic domains.¹² 

A structural coupling can also be achieved by strain propagation between the different layers themselves. As was shown in PbTiO₃/SrTiO₃/PbTiO₃ heterostructures on GdScO₃, where the structural coupling between the PbTiO₃ and SrTiO₃ layers resulted in periodic polar waves in the SrTiO₃,¹³ in SrRuO₃/PbTiO₃ superlattices, the large local deformations of the ferroelectric lattice are accommodated by periodic lattice modulations of the metallic SrRuO₃ layers with very large curvatures.¹⁴ 

At the core of the heterostructure studied here is PbTiO₃, a tetragonal ferroelectric with a polarization developing along the c-axis mostly due to ionic displacements. In PbTiO₃ thin films, the orientation of the polarization and arrangement into domain structures have been theoretically studied,^15–20 and are described by phase diagrams with regions of different domain configurations as a function of epitaxial strain and temperature (see review by Schlom et al.²¹). The domain pattern is also affected by the film thickness²² and electrostatic boundary conditions.^23,24 Complex polarization configurations in PbTiO₃ have recently been reported in PbTiO₃/SrTiO₃ superlattices,^14,25–30 with simultaneous control of these configurations using electric fields and light, giving rise to novel phenomena such as negative capacitance.³¹ When grown on DyScO₃, PbTiO₃ takes the a/c phase, where the polarization forms ordered ferroelastic domains (a/c twins), resulting in distortions of the film surface visible by atomic force microscopy (AFM).^32–35 

Whether through ferroelectric polarization or strain effects, controlling the structure and morphology of the SrRuO₃ thin films is of importance as it will affect the film electronic resistivity via structural and electronic coupling. Here, we study the structural coupling between oxide thin film layers on a set of SrRuO₃/PbTiO₃/SrRuO₃ heterostructures epitaxially grown on (110)_o-oriented DyScO₃ substrates. We establish the direct role that the ferroelastic domain structure in PbTiO₃ plays in the determination of the orthorhombic domain structure in SrRuO₃.

A series of samples was grown by off-axis radio-frequency (RF) magnetron sputtering on (110)_o-oriented DyScO₃ substrates, with the bottom and top SrRuO₃ electrodes of 55 unit cells (u.c.) and a PbTiO₃ film thickness of 23, 45, and 90 u.c. (see Sec. IV A for details of sample growth).

The substrate, DyScO₃, is orthorhombic with room temperature lattice parameters (in the Pbnm space group) a_o = 5.443(2) Å, b_o = 5.717(2) Å, and c_o = 7.901(2) Å.³⁶ It is often useful to also refer to the pseudocubic unit cell, where the lattice parameters can be calculated as a_pc = c_pc = $a o 2 + b o 2 2$ = 3.947 Å, b_pc = c_o/2 = 3.951 Å, α_pc = γ_pc = 90°, and β_pc = 2 ⋅ arctan (a_o/b_o) = 87.187° at room temperature. Here, “pc” subscript refers to the pseudocubic unit cell, while “o” is used to refer to the orthorhombic unit cell. For (110)_o-oriented DyScO₃, the out-of-plane [001]_pc direction is equivalent to [110]_o, while the in-plane directions [100]_pc and [010]_pc are equivalent to $[ 1 ̄ 10 ] o$ and [001]_o, respectively (see the supplementary material, Fig. S1).

The bottom and top electrodes, SrRuO₃, are orthorhombic with bulk room temperature lattice parameters (in the Pbnm space group) a_o = 5.57 Å, b_o = 5.53 Å, and c_o = 7.85 Å,³⁷ corresponding to the pseudocubic unit cell parameters a_pc = c_pc = 3.924 Å, b_pc = 3.925 Å, α_pc = γ_pc = 90°, and β_pc = 90.413°. According to the Glazer notation, octahedral tilting in orthorhombic SrRuO₃ is described by a⁻a⁻c⁺, implying that RuO₆ octahedra are rotated in opposite directions by equivalent magnitude along [100]_pc and [010]_pc (out-of-phase) and in the same direction about [001]_pc (in-phase).^38,39 On (110)_o-oriented DyScO₃ substrate, SrRuO₃ can grow with different possible orientations,^8,12 as described in Fig. 1, and supplementary material, Figs. S1 and S2.

Last, the PbTiO₃ is ferroelectric below a bulk critical temperature of 765 K with a tetragonal structure and lattice parameters a = b = 3.904 Å and c = 4.152 Å at room temperature. The in-plane strain imposed by DyScO₃ on PbTiO₃ films can thus be calculated as $a p c − a 0 a p c =−0.25%$ along a_pc and $b p c − a 0 b p c =−0.16%$ along b_pc, where a₀ is the extrapolated lattice parameter of PbTiO₃ in the room-temperature cubic paraelectric phase, a₀ = 3.957 Å for PbTiO₃. To accommodate this strain,⁴⁰ PbTiO₃ thin films on DyScO₃ at room temperature are expected to be in the a/c-phase, with regions where the c-axis points out-of-plane (c-domains) as well as regions where it points in-plane (a-domains), giving rise to a ferroelastic a/c-domain configuration with 90° domain walls. The latter are parallel to the {101}_pc crystallographic planes and, thus, are inclined at about 45° with respect to the film/substrate interface, as predicted in Ref. 17 and demonstrated experimentally (see, for example, Refs. 33, 34, and 41). In addition to these ferroelastic domains, the electrostatic boundary conditions and depolarization field arising from an incomplete screening of the surface bound charges can lead the c-domains to alternate between “up” (c⁺) and “down” (c⁻) orientations. Although the surface bound charges of our PbTiO₃ films are screened by the top and bottom SrRuO₃ electrodes, this screening is incomplete^42–46 and the depolarization field still plays a role. Such a combination of mechanical and electrostatic constraints can then result in flux-closure structures, as observed in strained PbTiO₃ thin films.^35,45,47,48

Figure 2(a) shows atomic force microscopy (AFM) images for the three SrRuO₃/PbTiO₃/SrRuO₃ heterostructures grown on DyScO₃. The AFM topography images reveal that as the PbTiO₃ layer thickness increases, trenches develop at the surface of the SrRuO₃ top layer in an organized pattern. For the samples with 23 and 45 u.c. thick PbTiO₃ layers, this pattern is hardly visible, and the top SrRuO₃ is smooth. The pattern gets more pronounced and anisotropic with increasing PbTiO₃ layer thickness, with long and deep trenches parallel to the DyScO₃ [001]_o axis, and smaller trenches parallel to the DyScO₃$[ 1 ̄ 10 ] o$ axis, while the surface roughness stays reasonably low [root mean square (rms) roughness values ranging from 157 to 393 pm over surfaces of 10 × 10 μm²].

The pattern that we observe at the surface of the SrRuO₃ top layer is comparable to what has been seen in PbTiO₃ layers grown on DyScO₃ substrates in Ref. 34, attributed to the presence of periodic ferroelastic a/c domains. To extract the period of the distortions visible on the surface of the samples, we calculate the fast Fourier transform (FFT) of the autocorrelation image, as shown in Fig. 2(d) for the sample with the 90 u.c. thick PbTiO₃ layer. Along DyScO₃ [001]_o (red), two periods are visible, P₁ = 77 ± 1 nm and P₂ = 280 ± 3 nm, while along DyScO₃$[ 1 ̄ 10 ] o$ (blue), a unique period P₃ = 335 ± 4 nm is visible. These periods have been illustrated on the topography image of the corresponding sample as yellow (with dimensions P₁ × P₃) and green (with dimensions P₂ × P₃) rectangles. All these values are reported in Table S1 (supplementary material).

To better understand the origin of this pattern visible at the surface of the SrRuO₃ top layer, we turned to cross-sectional scanning transmission electron microscopy (STEM) images. The three samples were cut and prepared for STEM measurements to obtain slices in the plane defined by the [001]_o (horizontal direction) and [110]_o (vertical direction) axes of DyScO₃. STEM images were obtained using bright field (BF), annular bright field (ABF), medium angle annular dark field (MAADF) and high-angle annular dark field (HAADF) detectors along the DyScO₃ $[ 1 ̄ 10 ] o$ zone-axis (see Sec. IV C for more technical details).

The domain walls in the PbTiO₃ layers can be directly seen in the STEM images, as shown in Fig. 3 [(a)–(c) - HAADF images] and in Fig. 6 [(a)–(c) - BF images], while the SrRuO₃ layers appear rather homogeneous. The PbTiO₃ layers in the three samples studied have different domain configurations, where the expected a/c pattern for the thicker PbTiO₃ layer transforms into a flux-closure pattern for the thinner PbTiO₃ layers [see Ref. 35 for a complete x-ray diffraction (XRD) based investigation of ferroelectric domain configuration in an extended series of samples].

To study the local strain induced by these different domain configurations, we turn to Geometric Phase Analysis (GPA).⁴⁹ This is done by taking the FFT of the HAADF-STEM images in Fig. 3, selecting two peaks [here $( 01 1 ̄ ) p c$ and (011)_pc] corresponding to two reciprocal lattice vectors defining the lattice, and getting the inverse Fourier transform containing information about local displacements of the atomic planes along these two vectors. The local strain components are calculated from the derivative of the obtained displacement field: in-plane strain ɛ_yy (along DyScO₃[001]_o), out-of-plane strain ɛ_zz (along DyScO₃[110]_o), shear strain ɛ_yz and rotation ω_yz.

Looking first at the results within the PbTiO₃ layers, we see from the HAADF images and from the GPA maps that the domain patterns vary with PbTiO₃ thickness. For the 90 u.c. thick PbTiO₃ in Fig. 3 (top row), we see large regions with a high out-of-plane strain but low in-plane strain, shear and rotation, corresponding to c-domains, i.e., regions where the polarization is out-of-plane. These regions are separated by narrower features, with high in-plane strain, and rotation, but low out-of-plane strain and shear, corresponding to a-domains, i.e., regions where the polarization is in-plane. These results confirm a typical well developed a/c-phase. For the 45 u.c. thick PbTiO₃ layer in Fig. 3 (center row), the strain map is more complex, with alternating regions with large out-of-plane strain or large in-plane strain close to each interface, and reduced strain at the center of the PbTiO₃ layer, clearly different from an a/c-phase (see the supplementary material, Fig. S4). This pattern is more comparable to the flux closure configuration observed for PbTiO₃ with similar thickness grown without electrodes.⁴⁷ Finally, for the 23 u.c. thick PbTiO₃ layer in Fig. 3 (bottom row), the PbTiO₃ strain maps are more homogeneous compared to the results obtained for the two other samples. This indicates that for this sample, the distortions related to the ferroelectric/ferroelastic domain configuration in the PbTiO₃ layer are small with respect to the homogeneous strain induced by the substrate. The most pronounced contrast is visible in the rotation map and corresponds to a pattern with a period of ∼16 nm, in agreement with the value found by XRD (see the supplementary material, Fig. S3 and Table S1 for comparison).

Concentrating now on the SrRuO₃ layers, we see that the bottom ones are predominantly homogeneous in all three samples. However, this is not the case for the top SrRuO₃ layers, where different contrasts appear for the three different PbTiO₃ thicknesses. While the SrRuO₃ layer on top of the 23 u.c. PbTiO₃ looks rather homogeneous, regions with different shear strain and rotation values alternate in the SrRuO₃ layers grown on top of the 45 and 90 u.c. PbTiO₃ with boundaries propagating along the [001]_pc growth direction.

For the sample with 90 u.c. PbTiO₃, at the interface with each a-domain and above the obtuse angle formed by the a/c domain wall, the rotation is positive (red), while it is negative (green) above the acute angle [Fig. 3(m)]. The rotation then propagates directly to the top surface along the growth direction. A similar modulation of the rotation is also observed in the SrRuO₃ bottom electrode, with positive rotation below the obtuse angle of the a/c domain wall, and negative rotation below the acute angle. However, for the bottom electrode, this modulation is limited to the vicinity of the interface and does not propagate through the whole SrRuO₃ bottom electrode thickness, most likely due to substrate clamping.

For the sample with 45 u.c. PbTiO₃, regions with a positive rotation (red) alternate with regions with a negative rotation (green) [Fig. 3(n)], with a reduced rotation amplitude compared to the sample with 90 u.c. thick PbTiO₃, but with sharper boundaries. The period of this pattern follows the period of the ferroelectric domains underneath.

To better understand the origin of this contrast, one can use the FFT and deduce the orientation of the SrRuO₃ layers from the obtained Bragg peak positions. In the FFT images in Fig. 4, the bright peaks of the pseudocubic lattice are clearly visible, corresponding to {0 k l}_pc planes with k and l integer indices. In addition to these peaks, weaker peaks also appear at positions corresponding to planes with half-integer Miller indices {0 1/2 1/2}_pc highlighted in blue and {0 1/2 1}_pc highlighted in yellow. These peaks come from the orthorhombic unit cell, which is composed of four pseudocubic unit cells, as described in Fig. 1. The position of the additional peaks is a clear indication of the orientation of the orthorhombic unit cell. The peaks corresponding to the {0 1/2 1}_pc planes in the FFT appear when the orthorhombic long axis [001]_o is oriented in-plane, parallel to the [010]_pc axis, and correspond to the X or X′ orientation (note that it is not possible to discriminate between X or X′ in this measurement geometry). The peaks corresponding to the {0 1/2 1/2}_pc planes, on the other hand, are the signature of the orthorhombic long axis [001]_o being oriented in-plane, parallel to the [100]_pc axis, corresponding to Y or Y′ orientation.

By selecting the different half order peaks and reconstructing the images in Fig. 4, we find that the {0 1/2 1}_pc peaks corresponding to X/X′ orientation originate from the substrate and the bottom SrRuO₃ electrode for all three samples, while the {0 1/2 1/2}_pc peaks corresponding to Y/Y′ originate from the top SrRuO₃ electrode. We also note that for the sample with the thickest PbTiO₃ layer, the top SrRuO₃ shows a mixed X/X′ and Y/Y′ character. Although already highlighting differences in the top SrRuO₃ layers for the different samples, this is not enough yet to explain the contrast observed in the strain and rotation maps in the GPA analysis in the SrRuO₃ top layers for the samples with 45 and 90 u.c. thick PbTiO₃ layers. This will be further investigated below, where we show that it is possible to discriminate between Y and Y′.⁵⁰ 

FFT was performed locally on selected regions corresponding to different shear strain and rotation values in the top SrRuO₃ layers of the three samples, as shown in Fig. 5. The regions of interest are selected based on the largest contrast in the GPA rotation maps in Figs. 5(d)–5(f), and give the colored diffraction patterns in (a)–(c) for the sample with 90 u.c. (a), 45 u.c. (b), and 23 u.c. (c) PbTiO₃, respectively, combining the FFT Bragg peaks in red and in green from the two regions. For the samples with 90 and 45 u.c. PbTiO₃, the two diffraction patterns do not overlap perfectly, and a very small horizontal shift can be observed [the $( 02 2 ̄ ) p c$ peak is enlarged for clarity]. For comparison, the diffraction pattern has been simulated for the Y and Y′ orientations by arbitrarily increasing the difference between the a_o and b_o parameters (a_o = 5.62 and b_o = 5.48 in arbitrary units), making the difference in the Bragg peak positions more visible: the difference between Y and Y′ results in horizontal shifts of peaks, as measured experimentally. No shift is observed for the SrRuO₃ top electrode above 23 u.c. PbTiO₃. From this, we can conclude that the contrast seen in the GPA strain and rotation maps for the two samples with the thickest PbTiO₃ layers arises from alternating Y and Y′ domains. Moreover, Fig. 5(d) shows that the transition from Y to Y′ domains for the sample with 90 u.c. PbTiO₃ is gradual with a modulation of the rotation following a sinusoidal behavior between 0.3° and −0.3° with a period of ∼30 nm. In comparison, this transition is much sharper for the sample with the 45 u.c. PbTiO₃ layer, with the modulation of the rotation following a step-like function between 0.15° and −0.2° with a period of ∼20 nm as shown in Fig. 5(e), hinting at the presence of proper twin boundaries between the Y and Y′ domains. Further discussion and a high resolution TEM image of such a twin boundary is shown in the supplementary material, Sec. S4.

We show that the complex tilt pattern of the PbTiO₃ layer is responsible for the deformation of the SrRuO₃ layer deposited on top, resulting in the periodic pattern visible in the topography by AFM. Our STEM measurements highlight how the domain pattern in the PbTiO₃ layer affects the strain state and crystal orientation in the SrRuO₃ top layer, with clear differences for the three samples with different PbTiO₃ layer thicknesses.

We find that the top SrRuO₃ layers show a different behavior for each of the three samples, shown in Fig. 6, while the bottom SrRuO₃ layers systematically have the same orientation as the DyScO₃ substrate (X-orthorhombic orientation), probably pinned by the interfacial continuity of the oxygen octahedral rotation imposed by the substrate.

For the sample with a 23 u.c. PbTiO₃ layer, where no pattern is visible in the topography, we observe a flux-closure type PbTiO₃ domain structure and correspondingly a null or weakly distorted SrRuO₃ structure, homogeneously in the Y-orthorhombic orientation, as shown in Fig. 6 (bottom row).

For the sample with a 45 u.c. PbTiO₃ layer, where a pattern is only weakly observed in the topography, we again have a flux-closure type PbTiO₃ domain structure. However, in Fig. 3, if we compare the out-of-plane (e) and in-plane (h) strain maps close to the interfaces, the strain pattern locally resembles that of the a/c phase [Figs. 3(d) and 3(g)]. This points at a nascent a/c phase near the top interface, allowing a more pronounced deformation that translates into a clearly distorted SrRuO₃ structure that shares the same periodicity as the PbTiO₃. The top SrRuO₃ thus alternates between Y- and Y′-orthorhombic orientations—with a period corresponding to the period of the domain pattern in PbTiO₃. The mechanism that drives the rotation of the top SrRuO₃ is strain-induced: due to the small shear and rotation in the top layer of PbTiO₃, the PbTiO₃/top SrRuO₃ interface is not totally flat (left and right inclination). The formation of Y/Y′ domains is a good way to minimize the interface strain [Fig. 6 (center row)].

Finally, in the sample with the 90 u.c. thick PbTiO₃ layer, where the topography displays noticeable tilts and trenches, the a/c-phase is fully developed, with strong PbTiO₃ lattice heterogeneity that partially imprints on the top SrRuO₃ electrode. Here, the top SrRuO₃ exhibits domains with alternating primary Y- and Y′-orthorhombic orientations, and some X interstitial regions. The positive and negative rotation on the SrRuO₃ correspond to the Y and Y′ domains, as evidenced by the GPA shear strain and rotation maps. In between these Y and Y′ domains, a very tiny X-orientated region is often observed in the FFT. This is typically restrained to a 10 nm width domain at the interface between the Y and Y′ domains, where no rotation was observed on the GPA map. It is different from the case with the 45 u.c. thick PbTiO₃ layer, where sharp interfaces and no X oriented domain were observed between the Y and Y′ domains.

Our work demonstrates that the large structural distortions associated with ferroelastic domains propagate through the top SrRuO₃ layer, creating a modulated structure that extends beyond the ferroelectric layer thickness, allowing domain engineering in the top SrRuO₃ electrode. Since there exists a one-to-one correspondence between the structural and magnetic domains,¹² our approach allows magnetic domain engineering in SrRuO₃ thin films through structural domain engineering to be realized. This work paves a new path toward control of magnetic domains via structural coupling to ferroelastic domains.

The three samples were deposited using our in-house constructed off-axis radio-frequency magnetron sputtering system, equipped with three different guns allowing the deposition of heterostructures and solid solutions of high crystalline quality. PbTiO₃ thin films were deposited at 560 °C, in 180 mTorr of a 20:29 O₂/Ar mixture, at a power of 60 W, and using a Pb_1.1TiO₃ target with 10% excess Pb to compensate for its volatility. SrRuO₃ layers were deposited from a stoichiometric target in 100 mTorr of an O₂/Ar mixture of ratio 3:60 at a power of 80 W. The bottom layer was grown at 640 °C, while for the top layer, the temperature was kept at the growth temperature used for PbTiO₃, i.e., 560 °C, to avoid possible damage of the PbTiO₃ layer. Huettinger PFG 300 RF power supplies are used in power control mode. The sample holder is grounded during deposition, but the sample surface is left floating.

Topography measurements were performed using a Digital Instrument Nanoscope Multimode DI4 with a Nanonis controller.

Cross-sectional slices prepared by a focus ion beam allow the imaging of domain structures by scanning transmission electron microscopy. Experiments were acquired on Nion Cs-corrected UltraSTEM200 at 100 kV operating voltage. A convergence angle of 30 mrad was used to allow high-resolution atomic imaging with a typical spatial resolution of 1 Å. Three imaging detectors in the STEM are used to simultaneously obtain bright field, annular bright field or medium angle annular dark field, and high angle annular dark field images. For ABF-MAADF imaging, the inner-outer angles can be continuously adjusted between 10–20 and 60–120 mrad. Most ABF images were collected with 15–30 mrad and MAADF images with 40–80 mrad angular ranges.

For the high-resolution HAADF images used to extract GPA, to minimize the influence of the sample drift and environmental noise, a series of fast-scan (low exposure time) HAADF images was taken in the same region; afterward, a script based on Gatan DigitalMicrograph software aligned and summed them together. This technique typically used 20 4k × 4k images with 1 µs exposure time per pixel.

GPA is an algorithm that reconstructs the displacement field $u ⃗ ( r ⃗ )$ from HAADF images by measuring the displacement of lattice fringes with respect to a reference lattice here chosen as the substrate. GPA thus allows the local strain present in the different layers to be revealed: in-plane strain $ε y y = ∂ u y ∂ y$ (along [010]_pc, i.e., perpendicular to the growth direction), out-of-plane strain $ε z z = ∂ u z ∂ z$ (along [001]_pc i.e., along the growth direction), shear strain $ε y z = 1 2 ∂ u z ∂ y + ∂ u y ∂ z$⁠, and rotation $ω y z = 1 2 ∂ u z ∂ y − ∂ u y ∂ z$⁠. This is particularly useful for the study of the domain configuration in PbTiO₃, as the polarization is related to the strain from the strong strain-polarization coupling.⁵¹ At room temperature, PbTiO₃ is tetragonal with the polarization pointing along the long tetragonal axis. The strain orientation and amplitude, therefore, indicate the orientation and magnitude of the polarization.

We determine the periodicity of the superstructures in the PbTiO₃ and SrRuO₃ layers by measuring the distances between the additional reciprocal space spots obtained after FFT. The accuracy of the measurement was estimated by considering the diffraction spot extension as the lower and upper limits for the superstructure length estimation.

In-house XRD measurements were performed using a Panalytical X’Pert diffractometer with Cu Kα₁ radiation (1.540 598 0 Å) equipped with a 2-bounce Ge(220) monochromator and a triple axis detector. The θ-2θ scans were analyzed using the InteractiveXRDFit software.⁵² This XRD system is also equipped with a PIXcel 1D detector, used for faster acquisition of reciprocal space maps.

supplementary material contains a detailed description of the orthorhombic orientations, with a schematic diagram showing the pseudocubic representation of the (110)o-oriented DyScO3 substrate and the six possible orthorhombic orientations of the SrRuO3 on the substrate; reciprocal space maps showing the high crystalline quality of the samples studied here and demonstrating the periodic pattern of the PbTiO3 layers; a table summarizing the different periods; and a discussion about the twin boundary observed in the SrRuO3 layer above the 45 u.c. thick PbTiO3 layer. Figure S2 showing the six possible orthorhombic orientations of SrRuO3 on (110)o-oriented DyScO3 substrate can be found in high resolution here.

The authors thank Lukas Korosec and Christian Weymann for their support and discussions.

This work was supported by Division II of the Swiss National Science Foundation under Project Nos. 200021_178782 and 200021_200636. STEM experiments were supported by the EU Horizon research and innovation program under Grant Agreement No. 823717-ESTEEM3. C.-P. Su acknowledges the Taiwan Paris-Saclay doctoral scholarship, which is cost-shared by the Ministry of Education, Taiwan, and the Université Paris-Saclay, France. M.H. acknowledges funding from the SNSF Scientific Exchanges Scheme (Grant No. IZSEZ0_212990).

The authors have no conflicts to disclose.

C.L, M.H., A.G., and J.-M.T. designed the experiment. C.L., M.H., and L.T. grew the samples and conducted the AFM and XRD measurements and analysis. C.-P.S. and A.G. conducted the STEM measurements. I.G., C.-P.S., and A.G. performed advanced STEM analysis. C.L. wrote the manuscript with contributions from all authors. All authors discussed the experimental results and models, commented on the manuscript, and agreed on its final version.

Céline Lichtensteiger: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Chia-Ping Su: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Writing – original draft (equal); Writing – review & editing (equal). Iaroslav Gaponenko: Data curation (equal); Formal analysis (equal); Investigation (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Marios Hadjimichael: Data curation (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Ludovica Tovaglieri: Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Patrycja Paruch: Conceptualization (equal); Funding acquisition (equal); Writing – original draft (equal); Writing – review & editing (equal). Alexandre Gloter: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Jean-Marc Triscone: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available in Yareta at https://doi.org/10.26037/yareta:nt2pqmrilrc77nqy2yzjwdgtdu.