High mobility of isolated three-fold polar vertices by electric fields

doi:10.21203/rs.3.rs-1770124/v1

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High mobility of isolated three-fold polar vertices by electric fields

https://doi.org/10.21203/rs.3.rs-1770124/v1

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Recently various topological polar structures have been discovered in oxide thin films. Despite the increasing evidence of their switchability under electrical or mechanical fields, the dynamic property of an isolated one, which is usually required for applications such as data storage, is still absent as they are always formed as arrays in thin films and evolve together due to strong interactions with their neighbors. Here, we show the controlled nucleation and high mobility of isolated three-fold vertices under an applied electric field. At PbTiO₃/SrRuO₃ interfaces, nanosized three-fold vertices are formed. A two-unit-cell thick SrTiO₃ layer provides critical electrical boundary conditions for the formation of three-fold vertices. Utilizing the SrTiO₃ layer and in situ TEM electrical testing system, we found isolated three-fold vertices can move a long distance along the interface under electric fields in a controllable and reversible manner. Microstructural evolution details of the nucleation and propagation of isolated three-fold vertices are further revealed by phase-field simulations. This work demonstrates the high mobility of isolated three-fold vertices, shedding light on the extraordinary dynamic properties of isolated topological polar structures.

A variety of topological polar configurations have been created in complex oxides by precisely mediating the electrical and mechanical boundary conditions^{1, 2, 3}. For example, vertices (meeting points of two or more domain walls)^{4, 5, 6}, vortices (require a non-zero polarization curl)⁷, polar skyrmions⁸ and polar merons⁹ have been synthesized in (PbTiO₃)_n/(SrTiO₃)_n superlattices or directly written in ferroelectrics by scanning probe techniques. These topological structures host unique properties which allow the development of novel electronics including negative capacitance field-effect transistors^{10, 11} and high-density non-volatile memories¹².

Practical applications of topological structures require the ability to manipulate them by using external stimuli and comprehensive understanding of their dynamic properties^{13, 14, 15}. To date, extensive theoretical and experimental studies have been carried out to explore the evolution of topological structures under electric and mechanical fields^{16, 17, 18, 19}. For example, in PbTiO₃/SrTiO₃ superlattices, reversible phase transition between flux-closure arrays and trivial ferroelectric phase driven by either electrical or mechanical fields have been observed²⁰. In such a similar system, vortex arrays switch to out-of-plane and in-plane polarization by electric fields and mechanical loading, respectively^{21, 22}. However, in these studies, these topological structures in the oxide superlattice always appear as arrays and thus the switching of them exhibits a collective behavior, usually involving multiple topological structures. For instance, one clockwise vortex is always sandwiched between two anticlockwised ones in a PbTiO₃ layer⁷, and similar for flux-closure domains⁶. Under external fields, they usually emerge and disappear simultaneously^{20, 21, 22}. Therefore, the dynamic property of isolated topological polar structures under external stimuli is little known and the ability to control individual topological polar structures which is critical for practical applications, e.g., data storage, for which one-by-one writing and erasing is required, is still challenging.

In this work, we choose the three-fold vertex as a model system to study dynamic properties of isolated topological polar structures. Three-fold vertices are intersections of a 180° domain wall and two 90° domain walls in ferroelectrics^{5, 23} (Supplementary Fig. 1). They consist of smoothly rotated dipoles at the meeting point of domain walls, thus are considered as a type of topological polar structures^{2, 23}. The winding number which is employed to characterize topological structures^{24, 25}, is calculated to be $+\frac{1}{2}$ for three-fold vertices (Supplementary Fig. 1). Although three-fold vertices have been observed before^{4, 5, 6}, the dynamic behavior of isolated ones under electric fields has never been reported. The observation of isolated three-fold vertices at ferroelectric films⁴ suggests the possibility to explore dynamic properties of isolated ones while the other topological polar structures such as vortices and polar skyrmions usually appear as arrays in (PbTiO₃)_n/(SrTiO₃)_n superlattices^{7, 8}. However, the main challenge is that three-fold vertices are usually generated on insulating substrates, for which the polarization charge at the interface is not completely screened²⁶. Therefore, it is difficult to apply an electric field to study the dynamic behavior of three-fold vertices due to the lack of the bottom electrode.

Here, we demonstrate the controlled formation and motion of isolated three-fold vertices in a PbTiO₃ thin film on DyScO₃ with a SrRuO₃ buffer layer by an applied electric field. We elaborately use the atomic-thin diffusion layer SrTiO₃ to induce incomplete screening while remain the SrRuO₃ as the bottom electrode to achieve the application of external electric field. Under electric fields, 180° domain walls expanding to the interface, leading to the formation of isolated three-fold vertices. We directly observe a long-range motion of isolated three-fold vertices along the interface in a controllable and reversible manner. Phase-field simulations verify the role of SrTiO₃ layer and reveal microstructural evolution details of the nucleation and propagation of isolated three-fold vertices. These results elucidate the high mobility of isolated three-fold vertices and suggest extraordinary dynamic properties of isolated topological polar structures which may enable new applications.

Formation and characterization of isolated three-folds vertices. For this work, 100-nm-thick PbTiO₃ thin films were deposited on single-crystal (110)_o DyScO₃ substrates (the subscript O indicates orthorhombic) with 50-nm-thick SrRuO₃ as the bottom electrode. Figure 1a shows a schematic of an isolated three-fold vertex. A cross-sectional view of the PbTiO₃/SrRuO₃ interface is shown in Fig. 1b by a dark-field TEM image. The typical a/c domain patterns and two vertical 180° domain walls are observed by diffraction contrast imaging. In the enlarged images in Fig. 1b, small triangular prisms with ~ 45° tilted domain walls indicate the existence of nanometer-scale three-fold vertices at interfaces. The atomic structure of isolated three-fold vertices was obtained by atomic-resolution high-angle annular dark-field (HAADF) image in Fig. 1c and further analyzed with a home-developed code^{27, 28}. One 180° domain wall and two 90° domain walls were denoted by white dashed lines. The out-of-plane and in-plane lattice parameters of three-fold vertices were measured at the unit-cell scale and mapped in Fig. 1d and e, respectively (a careful calibration has been performed with DyScO₃ substrates as the reference). The spatial variation of lattice parameters across the three-fold vertex are shown in Supplementary Fig. 2 corresponding to dashed boxes in Fig. 1d and e. The in-plane lattice parameters of triangular 90° domain is suppressed to 405 pm compared with 415.8 pm in typical 90° domains²⁹. Besides the suppression of in-plane lattice parameters, the lattice rotation in the triangular 90° domain is also revealed by measuring the angle of the Pb sublattice in Fig. 1f. The contrast in the triangular prism indicates a wave-like lattice rotation. By wave-like lattice rotation and suppressed in-plane lattice parameters, the triangular prism smoothly fit into basic domains at atomic scale.

The formation of isolated three-fold vertices is further verified by phase-field simulations through considering the properties of the interface as we discuss below. The simulated domain structure presented in Fig. 1g shows the formation of a pair of isolated three-fold vertices at the intersections of the 180° domain walls and the PbTiO₃/SrTiO₃ interface. The maps of polarization arrangements of two isolated three-fold vertices as well as their in-plane lattice deformation are shown in Fig. 1h and i, which agree well with our experimental measurements in Fig. 1e. The triangular 90° in-plane domain within each three-fold vertex serves as a transition region between the downward and upward domains, which greatly reduces the dipole bound charges at the PbTiO₃/SrTiO₃ interface.

Atomic structure of PbTiO ₃ /SrTiO ₃ interfaces. To figure out the underlying mechanism why three-fold vertices formed at a ferroelectric/electrode interface, we analyzed the atomic structure and elemental distribution of the interfaces. Figure 2a shows the atomic structure of PbTiO₃/SrRuO₃ interfaces. The corresponding atomic-resolution energy-dispersive X-ray spectroscopy (EDS) mapping in Fig. 2b suggests the diffusion of Ti into SrRuO₃. The substitution of Ru by Ti generates a two-unit-cell SrTiO₃ layer at interfaces which is marked by dashed white lines. Since SrTiO₃ is insulating, it may impair the perfect screening of polarization charges at interfaces. Figure 2c shows a map of relative displacement vectors of Ti cations relative to the center of surrounding Pb cations, which reflects the polarization distribution. A profile of polar displacements in Fig. 2d shows the suppression of polarization within about 6 unit cells from the interface while the transition layer is just 1.5 unit cells in PbZrTiO₃/SrRuO₃ interfaces according to the previous study³⁰. In addition, the displacement between cations even exists in SrTiO₃ and SrRuO₃. Therefore, the wider transition layer and displacements in SrTiO₃ and SrRuO₃ indicate the imperfect screening of depolarizing field induced by the diffused SrTiO₃ layer. The residual depolarizing field provide proper electrical conditions for the formation of three-fold vertices^{31, 32, 33} This hypothesis is verified by phase-field simulations of a comparison between the polarization distributions in systems with and without a 0.8 nm-thick SrTiO₃ layer, as shown in Fig. 2e and f, respectively. As seen, the three-fold vertex is only formed within the PbTiO₃ film possessing a SrTiO₃ transition layers on top of the electrode, whereas the film without a SrTiO₃ layer demonstrates a clean 180° domain wall without any additional polarization structures at the interface. The result proves the critical role of the SrTiO₃ layer, which is also consistent with previous studies of BiFeO₃ on insulating and conducting substrates²⁶.

Electric-field-driven motion of isolated three-fold vertices. Since the atomic-thin SrTiO₃ layer at interfaces induces the formation of isolated three-fold vertices, we elaborately employed this to dynamic property of isolated three-fold vertices under electric fields by in situ TEM electrical testing system. The in situ TEM tests allow us to directly observe the domain structure at interfaces and track their evolution in ferroelectric films^{34, 35}. Figure 3a depicts the probe-based electrical testing system. A tungsten tip acts as the top electrode to apply a bias on PbTiO₃ films while the SrRuO₃ electrode is grounded. The distribution of electric fields in ferroelectric films has been simulated (Supplementary Fig. 3). A chronological diffraction contrast TEM image series in Fig. 3b to 3g shows the domain structure evolution under varying electric fields. Figure 3b presents the initial state of PbTiO₃ films with typical a/c domain patterns. The polarization in PbTiO₃ films is downward as illustrated in Fig. 2d. When a negative voltage is applied, a 180° domain with upward polarization appears (Supplementary Movie 1). Nanoscale isolated three-fold vertices formed where 180° domain walls meet interfaces as shown in Fig. 3c. The three-fold vertices are distinguished by small triangular domains with ~ 45° tilted domain walls as shown in enlarged images. When the voltage increases from negative 6 volts to zero, the isolated three-fold vertices remain at interfaces in Fig. 3d, indicating their non-volatile property.

In addition, when the opposite electric field is applied, 180° domain walls move in the opposite direction from Fig. 3d to 3f. The nearly synchronous motion of 180° domain walls and three-fold vertices along the interfaces can avoid the large derivation of 180° domain walls from the symmetric permitted axis. Because tilted 180° domain walls are charged and thus energetically unfavorable³⁶. Finally, two three-fold vertices coalesce and 180° domain walls leave the interface in Fig. 3g. We measured the distance d between two isolated three-fold vertices. In Fig. 3h, we plot d and applied voltage U as functions of time to quantitatively analyze the switching process. The distance between two isolated three-fold vertices is up to ~ 134 nm. Therefore, the generation and motion of three-fold vertices is controlled by an applied voltage in a reversible manner. The creation and motion of isolated three-fold vertices are repeatable (Supplementary Fig. 4 and Movie 2).

Phase-field simulations of dynamic properties of isolated three-fold vertices. The nucleation and propagation of isolated three-fold vertices in the PbTiO₃ film are reproduced by phase-field simulations in Fig. 4a-f. Starting from a downward polarization state same as the experiments, a voltage bias of a probe tip is applied at the top surface of the PbTiO₃ film. Under an increasingly negative voltage bias, a new domain with upward polarization nucleates near the tip, forming 180° domain walls (see Fig. 4a for the domain structure). The new domain grows vertically towards the substrate and then reaches the PbTiO₃/SrTiO₃ interface at − 8 V, as accompanied by an instant nucleation of a region of in-plane polarization between the bottom front of the 180° domain walls and the interface (Fig. 4b), with its polarization configuration presented in Fig. 4g. This leads to the formation of two isolated three-fold vertices (Fig. 4c) whose polarization distribution are related to each other by a mirror symmetry as shown in Fig. 4h. The two isolated three-fold vertices further move apart along the interface (Fig. 4d) under the negative voltage bias. The process can be reversed upon the application of an opposite voltage, in which the two isolated three-fold vertices move towards each other (Fig. 4e) and finally coalesce, recovering the original state of the PbTiO₃ film (Fig. 4f). The simulated nucleation and reversible motion of the isolated three-fold vertices agree well with the experimental observations. Isolated three-fold vertices do not vanish during the motion indicating their high stability. The microstructure evolution under electric fields not only verify the high mobility of isolated three-fold vertices but also provide further details of the nucleation process.

For electric-field-induced three-fold vertices at interfaces, both electrical and mechanical boundary conditions are important. In electrical, the appearance of a SrTiO₃ layer impairs perfect screening of metallic SrRuO₃ electrode. When 180° domain walls end at interfaces, the formation of three-fold vertices with triangular 90° domains can reduce polarization charges at interfaces. Phase-field simulations further prove the critical role of SrTiO₃ layer for electric-field-induced three-fold vertices. Form a mechanical perspective, a tensile strain from DyScO₃ substrates provides proper mechanical boundary conditions for the formation of three-fold vertices. The in-plane lattice mismatch between DyScO₃ and PbTiO₃ is 1.3%, calculated by the following formula³⁷.

$$f=\frac{{{a_2} - {a_1}}}{{({a_2}+{a_1})/2}} \times 100\% =1.3\%$$

where a₁ is the in-plane lattice parameter of PbTiO₃ films, 390.4 pm, and a₂ is the in-plane lattice parameter of DyScO₃, 395.6 pm³⁸. We also characterized the atomic structure of 180° domain walls at PbZrTiO₃/SrTiO₃ interfaces for comparison (Supplementary Fig. 5). The in-plane lattice mismatch between PbZrTiO₃ and SrTiO₃ is negligible, i.e. 390.4 pm in PbZrTiO₃ and 390.5 pm in SrTiO₃³⁹. Without the tensile stress, a sharp 180° domain wall appears at PbZrTiO₃/SrTiO₃ interfaces without three-fold vertices (Supplementary Fig. 5). Therefore, the two-unit-cell thick SrTiO₃ layer not only mediate the screening of depolarizing field, but also maintain the strain field from substrates. These results demonstrate the possibility of employing interface engineering to fabricate isolated topological polar structures by applied electric fields.

The dynamic property of isolated structures is critical as they may be regarded as single functional elements. Many impressive progress has been made in exploring dynamic behavior of topological structures by state-of-art electron microscopy and other techniques^{18, 19, 20, 40}. During the collective switching process, these topological structure arrays are almost fixed at their locations in superlattices. In contrast, our results demonstrate the highly mobile feature of isolated three-fold vertices. Isolated three-fold vertices are capable to move a long distance along the interface which enables the design of novel devices like electric racetrack memory^{12, 41}. The high mobility of isolated three-fold vertices suggests the dynamic property of isolated topological polar structures may be extraordinary. However, this field is still poorly understood compared with their counterparts in magnetics. In magnetics, many isolated topological structures have been proven to be highly mobile and controllable under external stimuli. For example, isolated magnetic skyrmions can be generated and driven by current⁴². The skyrmion Hall effect has also been discovered by driving the motion of isolated magnetic skyrmions⁴³. In situ TEM combined with interface engineering offers an effective tool to determine the dynamic properties of isolated topological polar structures.

In summary, our work demonstrates electric-field-controlled formation and high mobility of isolated three-fold vertices. We elaborately use the atomic-thin diffusion layer SrTiO₃ to induce incomplete screening that is prerequisite to generate three-fold vertices at PbTiO₃/SrRuO₃ interfaces, and meanwhile achieve the application of external electric field. These isolated three-fold vertices are high mobile under electric fields in a controllable and reversible manner. The nucleation and long-range motion of isolated three-fold vertices are reproduced by phase-field simulations. This work demonstrates the possibility of manipulating isolated topological structures via interface engineering and electric fields. The highly mobile nanoscale three-fold vertices suggest extraordinary dynamic property of isolated topological polar structures and provide new possibilities for applications.

Film Growth. The 100-nm-thick PbTiO₃ thin films were grown on single crystal (110)_o DyScO₃ substrates buffered with ~ 50-nm-thick SrRuO₃ electrodes using pulsed laser deposition method, as well as the Pb(Zr_0.2Ti_0.8)O₃ films on (001) SrTiO₃ substrates. A KrF excimer laser (λ = 248 nm) was focused on the targets with an energy density of ~ 2.5 mJ cm^− 2 and repetition rate of 10 Hz. During the growth of the SrRuO₃, the temperature and the oxygen pressure were kept at 700 ℃ and 100 mTorr, respectively. To avoid the easy evaporation of the lead in PbTiO₃ thin film at high temperature, the target with 5% excess lead was used and the temperature for the subsequent growth of PbTiO₃ thin film was decreased to 650 ℃ at the same oxygen atmosphere. After the deposition process, an in situ post annealing process with the same temperature and high oxygen pressure environment of ~ 300 Torr for 30 min was adopted to effectively eliminate the oxygen vacancies of the sample. Finally, the sample was slowly cooled down to room temperature with a ramp rate of 5 ℃ min^− 1.

Sample preparation and Characterization. TEM samples were prepared by conventional mechanical polishing and subsequent argon ion milling in a Precision Ion Polishing System 691 (Gatan). The procedure for ion milling consisted of two steps. During the first stage, the guns were operated at 4 keV and at angles of 6° and − 6°. During the second stage, the guns were operated at 1 keV for 5 min and at angles of 3° and − 3°, and lowered further to 0.1 keV for 2 min for final surface cleaning. Diffraction contrast TEM experiments were carried out using a FEI Tecnai F20 microscope. Samples were tilted off the zone axis and imaged in the bright field or dark field with two-beam alignment condition using a g = (101) vector. High-angle annular dark-field (HAADF) images and energy-dispersive X-ray spectroscopy (EDS) images in this work were obtained using probe aberration-corrected FEI Titan Cubed Themis G2 operated at 300 kV in Electron Microscopy Laboratory of Peking University. Atom positions were determined by simultaneously fitting two dimensional Gaussian peaks to a perovskite unit cell using a home-developed code. Polar displacements of the Ti cations were measured relative to the center of the surrounding Pb cations in HAADF images. Annular bright field (ABF) images were recorded at 300 kV in JEM ARM300CF (JEOL Ltd.). The convergence semi-angle for imaging is 24 mrad, collection semi-angles snap is 12 to 24 mrad for ABF.

In situ study. In situ TEM experiments were carried out on a FEI Tecnai F20 microscope operated at 200 kV with a PicoFemto double-tilt TEM-STM holder provided by ZEPTools Technology Company. A tungsten tip acted as the top electrode which was precisely controlled by a piezoelectric system. The switching processes were recorded with a OneView camera (Gatan). The imaging rate was set at 10 frames per second in order to get a better contrast.

Phase-field simulations. In the phase-field model, the time evolution of the polarization field P(x) and mechanical displacement field u(x) are described by the time-dependent Ginzburg-Landau equation and the elastic equilibrium equation, respectively⁴⁴, i.e.,

$$\frac{{\partial {\mathbf{P}}}}{{\partial t}}= - {L_P}\frac{{\delta F}}{{\delta {\mathbf{P}}}}$$

$$\frac{{\delta F}}{{\delta {\mathbf{u}}}}=0$$

F[P, u] is the total free energy of the system formulated as a function of the polarization field P and the mechanical displacement field u with expressions the same as those in Refs.⁴⁵. L_P is the kinetic coefficient of polarization. A semi-implicit Fourier-spectral method⁴⁶ is employed for the numerical simulations.

The simulation system of the ferroelectric film consists of 4 layers, including a 4 nm-thick vacuum top layer, a 100 nm-thick PbTiO₃ film layer, a 0.8 nm-thick SrTiO₃ transition layer, and a 35.2 nm-thick substrate layer (i.e., the total vertical size of the system is 140 nm). The in-plane size of the system is taken as 200 nm. An electrostatic boundary condition of a specified voltage applied by the probe tip is employed at the top surface of the PbTiO₃ film⁴⁷. A grounded electrostatic boundary condition is employed at the top plane of the substrate layer (which connects to the bottom of the SrTiO₃ layer). For the separate study of a film without a SrTiO₃ transition layer, the PbTiO₃ layer and the substrate layer are directed connected, where a grounded electrostatic boundary condition is employed at their interface. The material constants of PbTiO₃ and SrTiO₃ adopt the same values as those in Ref.⁴⁸.

Winding number calculations. The winding number is contour integral of the variation of polarization orientation along a closed loop. The winding number n of three-fold vertices is calculated with the following Eq. 2⁵:

$$n=\frac{1}{{2\pi }}\oint\limits_{C} {\Delta \theta \cdot dr}$$

where θ is polarization orientation measured anticlockwise from horizontal direction. $\Delta \theta$ is the orientation difference between of two neighboring points. The winding number of the three-fold vertex is $+\frac{1}{2}$. We assume 180° domain wall has no contribution because of collinear polarization vectors⁴⁹. A flux-closure structure (a pair of three-fold vertices) has a winding number + 1 which is equal to the sum of these two three-fold vertices. This agrees with the conservation property of winding numbers²⁵.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (52125307, 52021006), the Key R&D Program of Guangdong Province (2018B030327001, 2018B010109009). Tiannan Yang and Long-Qing Chen are supported as part of the Computational Materials Sciences Program funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0020145. The phase-field simulations were performed on the Extreme Science and Engineering Discovery Environment (XSEDE) supported by National Science Foundation grant number ACI-1548562.

Author Contributions: M.L. carried out TEM experiments, analyzed the data and wrote the manuscript under the direction of P.G.; T.Y. and L.-Q.C. carried out phase-field simulations. P.C., X.M. and J. Z. assisted with TEM characterization. Y-J.W, H.-J.L., and Y.-L.H. grew the samples under the direction of Y.C.; R.Z., X.L. and R.S. assisted with data analysis.

Competing Interests: The authors declare that they have no conflict of interest.

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