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Manipulation of polar vortex chirality in oxide superlattices

Topological polar vortices that are the electric analogues of magnetic objects, present great potential in applications of future nanoelectronics due to their nanometer size, anomalous dielectric response, and chirality. To enable the functionalities, it is prerequisite to manipulate the polar states and chirality by using external stimuli. Here, we probe the evolutions of polar state and chirality of polar vortices in PbTiO3/SrTiO3 superlattices under electric field by using atomically resolved in situ scanning transmission electron microscopy and phase-field simulations. We find that the adjacent clockwise and counterclockwise vortex usually have opposite chirality. The phase-field simulations suggest that the rotation reversal or axial polarization switching can lead to the chirality change. Guided by which, we experimentally validate that the vortex rotation direction can be changed by applying and subsequently removing of electric fields, offering a potential strategy to manipulate the vortex chirality. The revealed details of dynamic behavior for individual polar vortices at atomic scale and the proposed strategy for chirality manipulation provide fundamentals for future device applications.


Introduction
Polar vortex, a topological structure with electric dipoles continuously rotating around a stable core, exhibits new emergent ordering and properties [1][2][3] and thus attracts extensive research attention [4][5][6][7] . Such vortices have been theoretically predicted and experimentally realized in low dimensional ferroelectrics [8][9][10] . Recently, the vortex array was discovered in (PbTiO3)n/(SrTiO3)m superlattices (PTO/STO, where n and m are the number of unit cells for PTO and STO, respectively) with alternating clockwise and counterclockwise rotations of electric dipoles 1 . Their small size makes them ideal storage units for high density memory applications 2,4,11 and the anomalous dielectric behavior or negative capacitance, has great potential for nanoelectronics to overcome the Boltzmann tyranny 4 . Moreover, these vortices carry chirality 12 , providing a new order parameter for these complex oxides and thus enabling possible novel functionalities and devices by using it.
In order to enable these applications of the polar vortex, it is prerequisite to manipulate the ferroelectric order parameters and/or the vortex chirality. The theoretical investigations 13,14 have predicted the evolution path from the vortex to trivial ferroelectrics under external electric fields, i.e., clockwise and counter-clockwise vortices melt to form a/c domain. Experimentally, Damodaran et al. 6 has demonstrated the interconversion between vortex and ferroelectric a1/a2 domains under electric field by atomic force microscopy (AFM). Using in situ transmission electron microscopy (TEM), Du et al. 15 showed a local transformation from vortex into dipole wave and c domain by applying non-contact bias and the transitioned states sustained even with the removal of electric bias, while Nelson et al. 16 have found the vortex response to the applied electric fields through a reversible transition to a/c domain or a-domain.
Besides the electrical field driven phase transition, Chen et al 17 . observed mechanical stress can also cause similar phase transition between topological polar state and trivial a-domain. Recently, Li et al observed a ultrafast collective polarization dynamics driven by terahertz-field electrical field 18 .
Despite of great progress on switching pathways and polarization dynamics for vortex, the chirality manipulation of polar vortex has been rarely explored in experiments. The chirality of polar vortex is determined by both the rotation direction and the axial-component of polarization along the vortex tube direction 12 . Theoretically, the switching of vortex rotation is predicted either by a curled electric field 19,20 or by deliberately designed geometry of nanostructures (such as notched nanodots, asymmetric nanorings and void nanoplatelet) [21][22][23] , which, however, is somewhat impractical for to current technologies due to the difficulties in control of such a distribution of electric fields or fabrication of these complicated nanostructures.
Experimentally, characterization of chirality in polar vortex, however, is extremely difficult. To date, the transmission electron microscopy is the only approach to directly probe the rotation direction and radial-component polarization for individual polar vortex 2 , while the axial-component polarization has never been directly characterized in experimental studies, not to mention tracking their evolution under external stimuli.
Here, by combining the phase field simulations and atomically resolved in situ scanning transmission electron microscopy (STEM) methods, we probe the dynamic evolutions and chirality of individual polar vortices in PbTiO3/SrTiO3 superlattices under electric field. We find that the adjacent clockwise and counterclockwise vortices usually have opposite chirality. We directly observe the rotation of chiral vortex can be changed during switching and back-switching events under simple electrical fields.
Based on our phase field simulations, the rotation reversal is accompanied by the chirality reversal. Besides, we also reveal the detailed switching pathways and find that the vortex core can move laterally into a/c domain stripes and then become a mono non-chiral c-domain, which is in excellent agreements with phase field simulations. Our work reveals the reversible switching pathways of individual vortices at atomic scale and demonstrates the ability to electrically tune the vortex rotation, which may open a new strategy to control the chirality and further utilize it as a new order parameter for novel device applications.  Fig. 3). Such small values are difficult to extract from quantitative analysis of electron microscopy images 25 , which explains why previous electron microscopy studies rarely discussed the chirality 15,17,26 . It is even harder to detect the axial polarization component for the in situ TEM experiments that generally suffer relatively large vibrations and instabilities due to the introduction of the contacting probe and applied fields. Thus, we performed the in situ experiments from the crosssection view operated under lower magnification dark-field and atomically resolved HAADF modes to track the evolution of rotation direction. Furthermore, we extract the displacement maps (Fig. 1g, h) and out-of-plane lattice constant (Fig. 1i) from the atomically resolved HAADF image (Fig. 1d), which is schematically illustrated in Fig. 1f. From these maps, for each unit cell the core positions and possible domain wall positions can be located and the rotation direction can be identified 27 . Particularly, the vortex core lies in the boundary of the upward and downward out-of-plane displacement regions (Fig. 1g, h) similar to the dark-field TEM image and it can be also reflected in the lattice mapping with much better signal to noise ratio (Fig. 1i) as the polarization is highly correlated with the lattice. Therefore, the evolution of rotation direction for each vortex during in situ biasing can be reliably tracked by multiple parameters (e.g., dark field TEM image, out-of-plane polarization mapping, and lattice c mapping) in decent atomically resolved images. reveals that surrounding the fully switched region there is an intermediated phase zone where the pristine dark doted contrast became into tilted stripes, which indeed is a feature of a/c domains as we discuss details below. Removal of electric fields results in spontaneous back-switching to form the vortex array (Fig. 2i).

Results
More importantly, we observe that in some regions the vortex rotation can be reversed during switching and back-switching events, which is expected to lead to chirality switching given unchanged axial-components. The subtraction of Fig. 2g and 2i acquired before and after electric bias results in obvious nonuniform contrast in the marked region (Fig. 2j), indicating the occurrence of rotation change, which is further confirmed by the enlarged view of the same region with the rotation sense denoted by the arrows (bottom row of Fig. 2g, i, j), while the rest region remains almost the same after removing the bias.
In order to determine the vortex position more accurately, we perform atomically resolved in-situ TEM experiment. Figure 3a, d are the atomically resolved HAADF-STEM images acquired before and after electric fields for the exactly same region that is tracked by a deliberately made mark (red circle) using electron beam (Methods). With the same label rule in Fig.1d and e, the rotation direction of the clockwise and counterclockwise vortices are labeled by the curved arrows from the out-of-plane displacement distribution (Fig. 3b, e) 27 and out-of-plane lattice mapping (Fig. 3c, f)

Competing interests
The authors declare that they have no competing interests.

Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Thin Film Growth
The bottom electrode layer of ~10 nm SrRuO3 was grown on (110)o-DyScO3 substrates followed by the growth of the (PbTiO3)n/(SrTiO3)n superlattice films by a pulsed laser deposition (PLD) system (PVD-5000) using a KrF excimer laser (λ=248 nm). During the growth of SrRuO3, the substrate temperature was kept at 690 ℃ with an oxygen pressure of 80 mTorr and a laser energy of 390 mJ pulse −1 , and when the substrate temperature was cooled down to 600 ℃, the n uc-thickness PbTiO3 and

TEM Sample Preparation
TEM cross-sectional samples were polished to about 30 micrometers made by conventional mechanical methods and then transferred to ion-beam milling process in Gatan PIPS 695 system with an acceleration voltage of 3 kV for a quick milling followed by the final 0.1 kV to reduce the damage.

STEM Characterization and analysis
Atomic resolution HAADF images were obtained in a double aberration-corrected JEOL Grand ARM 300 CFEG with collection semi-angle [54, 220] mard and convergence semi-angle 18 mrad. STEM images were filtered by a HRTEM-filter plugin to remove the zero-frequency and high-frequency noise. The polarization map was done by calculating the offset between A site and B site using a Matlab code based two-dimensional Gaussian algorithm. Geometric phase analysis images were obtained by a free FRWRtools plugin for the Digital Micrograph software.

In situ (S)TEM.
In situ TEM experiments were carried out using a customized holder from ZepTools Technology Company on JEOL ARM 300F, allowing us to get atomic resolution even under the applications of electric fields because of the good stability of the holder. Electric bias was applied to the PTO/STO films with the scanning tungsten tip acting as a top electrode and the conductive SRO layer serving as the bottom electrode. In situ experiment was carried out in TEM mode for the dark-field and electron diffraction. Dark-field images were acquired under two-beam condition with (002)pc selected for the optimal image condition. The atomic HAADF-STEM images were acquired under the application of electric fields with a dwell time of 4 µs per pixel.
In STEM mode, whether the electric fields are applied to the samples can be judged from the current values. The markers were made by focusing the electron probe on a specific location for a few minutes.

Phase Field Modeling
In order to study the chirality of the polar vortices and its evolution under an electric field, a phase field model is employed to simulate the polarization evolution in ferroelectric superlattice. In the phase field model, the free energy is the sum of Landau free energy, domain wall energy, elastic energy and electric energy. The total free energy of the PTO/STO ferroelectric superlattice has the following form 30 : in which , and denote the Landau coefficients, is the gradient coefficient, is the elastic constant, is the electrostrictive coefficient and is the vacuum permittivity. All values of the above coefficients at room temperature can be found in the previous papers [31][32][33] . As for , the relative dielectric constant of the background material, is set to 66 and 300 for PTO and STO respectively. , and represent the polarization, strain and electric field, respectively. The repeating subscripts in equation (1) imply summation over the Cartesian coordinate components ( = 1, 2 and 3).
In this study, the temporal evolution of the domain structure is obtained by solving the time-dependent Ginzburg-Landau (TDGL) equations 34 : where L, r, and t denote the kinetic coefficient, spatial position vector, and time