Polar Vortexes and Charged Domain Walls in a Room Temperature Magnetoelectric Thin Film

Multiferroic domain walls are an emerging solution for future low-power nanoelectronics due to their combined tuneable functionality and mobility. Here we show that the magnetoelectric multiferroic Aurivillius phase Bi 6 Ti x Fe y Mn z O 18 (B6TFMO) crystal is an ideal platform for domain wall-based nanoelectronic devices. The unit cell of B6TFMO is distinctive as it consists of a multiferroic layer between dielectric layers. We utilise atomic resolution scanning transmission electron microscopy and spectroscopy to map the sub-unit-cell polarisation in B6TFMO thin films. 180˚ charged head-to-head and tail-to-tail domain walls are found to pass through > 8 ferroelectric-dielectric layers of the film. They are structurally similar to BiFeO 3 DWs but contain a large surface charge density (σ s ) = 1.09 |e|per perovskite cell, where |e| is elementary charge. Although polarisation is primarily in-plane, c-axis polarisation is identified at head-to-tail domain walls with an associated electromechanical coupling of strain and polarisation. Finally, we reveal that with controlled strain engineering during thin film growth, room-temperature vortexes are formed in the ferroelectric layer. These results confirm that sub-unit-cell topological features can play an important role in controlling the conduction properties and magnetisation state of Aurivillius phase films and other multiferroic heterostructures.


Introduction
Layered oxide thin films such as the Bi2O2(Am−1B mO3m+1) Aurivillius phase (AP) offer a flexible template for designing new multiferroic devices [1,2]. APs are a promising ferroelectric material with strong polarisation [3], and fatigue-free energy storage performance [4][5][6]. The rare possibility of room temperature magnetoelectric coupling is achieved in APs by simply substituting the structure with magnetic ions [7][8][9][10][11]. The room temperature magnetoelectric multiferroic property indicates that this material system has a very clear potential for future low energy devices such as a charge-to-spin conversion node in magnetoelectric-spin orbit logic for recurring neural networks [12,13].
Bi6Ti2.8Fe1.52Mn0.68O18 (B6TFMO) is an example of an ion-substituted AP with experimentally proven reliable magnetoelectric switching [14,15]. B6TFMO can be thought of as a 2D nanostructured framework, with 5 PK-cells of ferroelectric (FE) BiFeO3 (BFO) sandwiched between dielectric (DE) Bi2O2 layers. Mn and Ti are substituted for Fe at some "B sites" and the preference for these magnetic cations to concentrate in the central PK-cell of the B6TFMO structure causes true room temperature ferromagnetism (FM), as opposed to the antiferromagnetic room temperature BFO [16]. The fundamental physics and growth conditions governing magnetoelectric properties are still not fully understood and thus methods to improve these results are difficult to plan. As the multiferroic-dielectric heterostructure is at the sub-unit cell scale [17,18] , probing any changes within this heterostructure requires the characterisation technique to be at atomic scale spatial resolution.
Initial aberration corrected scanning transmission electron microscopy (STEM) and spectroscopy revealed the preferential Mn cation segregation at the central PK layers across all samples [19]. In the regions where out-of-phase boundaries (OPBs) and associated stacking default defects were present, the magnetic Mn and Fe ion partitioning increased. It has been suggested that OPBs suppress the ferroelectricity [20], while their high structural disorder and elevated magnetic ion density increases the magnetic spin [9,21]. Thus, inducing higher OPB densities could result in improved magnetoelectric measurements and device efficiency. In this study, we focus on the role these OPB defects play in the formation of charged domain wall (DW) and polar vortexes. We map out the pico-meter scale atomic column shifts and unit cell deformation as demonstrated previously for other ferroic materials [22][23][24][25][26], revealing the direct link between OPBs and polar topological solitons in AP thin films.

Results and Discussion
The samples were grown by liquid injection chemical vapour deposition as described in reference [15]. Figure 1 shows a model of the five-layered B6TFMO unit cells alongside an atomic resolution scanning transmission electron microscopy (STEM) high-angle annular dark-field (HAADF) image of the structure. The FE-DE heterostructure within the B6TFMO unit cell leads to distinctive FE behaviour, where oppositely polarised PK-cells co-exist side by side within the FE-layer as demonstrated in Figure 1(b). The PK-cell is pseudo-cubic with a FE dipole forming analogous to that in BiFeO3 (BFO). The outer PK-cells bonded to the DE layer are hyper-tetragonal and thus highly strained along the c-axis (ɛyy) compared to BFO, BiTiO3 or PbTiO3 unit cells. At these outer PK-cells the polarisation is larger and always points towards the DE layer forming a "mirror plane". At the 3 PK-cells in the centre of the layer the ɛyy strain relaxes and thus the polarisation state has a shallower potential well [27]. In other words, with less ɛyy strain present, polarisation direction is largely determined by electrostatic stress and has a lower energy cost for switching. In line with the reduced dimension effects of thin lamellae seen in other ferroelectrics [28], the central and intermediate PK-cells prefer to have an in-plane polarisation, left or right as in Figure 1(b). Accordingly, AP has been observed to strongly favour in-plane polarisation macroscopically, measured as 50 μC cm −2 in B6TFMO [14]. AP DWs have previously been viewed on a microscale and from the surface by piezoresponse force microscopy (PFM) but only FE switching across dielectric layers has been observed by STEM HAADF, where the dipole experiences an interruption rather than a continuous rotation across PK-cells [3,29]. The conventional approach to map out atomic resolution polarisation is by reversing the measured B-site displacement from STEM HAADF images. This is a reliable technique for AP materials and is used throughout this paper [29].
The large yellow arrows in Figure 1  Nominally charged DWs have been observed in other AP materials such as 4-layered Bi5Ti3FeO15 but only from the surface by PFM [3]. In Figure 1(c) we observe an atomic resolution vertical DW passing through multiple AP unit cells. Net polarisation here is headto-head (H-H) oriented and rotates 180˚ across the DW. The DW is thus strongly charged [30].  This calculated σ s is of the same order as that found at strongly charged DWs in other perovskites [31]. As charge is likely to be spread across the DW width for 5-8 PK-cells, rather than confined to a 2D surface, a more realistic number for charge density (ρ) would be ρ = Measuring the electric field influence on the magnetisation through magnetoelectric coupling and the exact screening charge at the DW will be the subject of future research.  lowest energy polarisation state is to point to one of the "corner" Bi atoms of the PK-cell [29].
This appears to contribute to the angled orientation of the domain wall, seen throughout the figures in this study. The yellow traced domain wall position is approximated as running between the inflection point of the polarisation in the outer PK-cells. The 5-8 PK-cells of inhomogeneous net polarisation is similar in width to charged DWs in BiFeO3 but quite large for a FE domain wall [34]. This infers a lower exchange energy allowed by a lower anisotropy cost. That is to say, the central PK-cells seem to be more "polarisable" than structurally harder FE's with thinner DWs such as PbTiO3 [35]. The anisotropy cost of the DW is studied by examining rotation and ɛyy strain maps in Figure 2 [34]. The lack of strain difference between domains confirms that there is little anisotropy cost, allowing for a semi-continuous rotation of the polarisation i.e.
However, in this case, the PK-cell retains a larger c/a ratio than pseudo-cubic bulk rhombohedral BFO so the effect is deemed unlikely. The demonstrated "structural softness" is consistent with a large magnetoelectric effect [38]. Furthermore, the relatively low anisotropy associated with the domain wall indicates that switching is determined only by the electrostatic energy, with no elastic energy cost. These results imply that charged DWs in B6TFMO are likely to be highly mobile with low dielectric loss.
While in bulk BFO, c = a = 3.96 Å, epitaxial strain (ɛxx) can result in rhombohedral and tetragonal phases with c/a ratios up to 1.13 and 1.27 respectively [39]. Fascinatingly, the measured a spacing in B6TFMO (range: 3.68 Å to 3.99 Å, uncertainty +/-0.1 Å , average: 3.835 Å,) includes the a spacing of LaAlO3 at 3.79 Å on which the rhombohedral (a > 3.79 Å ) and tetragonal (a < 3.79 Å) BFO phases can co-exist [39,40]. This implies that individual PK-cells in B6TFMO can exist flexibly in local rhombohedral or tetragonal phases. The natural a spacing of the (Bi2O2) 2+ DE layer is calculated to be 3.80 Å. The average a value agrees exactly with previous AP measurements, falling between the natural DE layer and PK-cell a values [41].   Figure 4) there is a clear indication of oxygen depletion at the DW. Oxygen vacancies are common in perovskites, and normally found even at H-T DWs purely due to the strain field present, without needing to provide electrostatic screening [45,46]. A further illustration of the interplay between strain and polarisation is shown in Figure 4, where a FE polarisation vortex is identified. The feature can be seen in atomic level detail in Figure 4(c). The vortex occurs as a form of 180° polarisation transition between tail-to-tail (T-T domains). As such, the vortex must be charged to the same extent as the H-H DW in Figure   2, with average = 1.09 e per PK-cell. Although the DW width is similar to the H-H case in Figure 2, the defined vortex polarisation suggests the charge density is concentrated at the vortex core [47], further increasing the relative conductivity difference versus the domain.
The required positive charge may be provided by either oxygen vacancies or a local change in Two of these vortexes occur in a region of the B6TFMO film containing "out-of-phase boundary" (OPB) defects, as shown in Figure 4(a,b). OPBs are common boundary defects occurring in materials of high structural anisotropy, such as the Aurivillius phases, and are characterized by displacement by a fraction of a lattice parameter (c/x) between two neighbouring regions parallel to the c-direction [48].. They appear as a "step" in the DE and Vortexes and vortices are more traditionally associated with ferromagnetic domains, where there is no anisotropy cost to extend the transition of the magnetisation direction, thus lowering the exchange energy at the DW [49]. FE vortexes/vortices have previously been identified in thin films of BFO and PbTiO3 multilayers [50][51][52][53][54][55] but remain a novel occurrence.
To examine the strain state of the vortex we compare the c-axis strain map (ɛyy) in Figure 4(d) to the PK-cell polarisation in Figure 4 Table 1.

FE Layer
Charged DW present between OPBs?
These results offer a detailed insight into the ferroelectric behaviour of B6TFMO and AP materials. However, at the nanoscale, there remains significant questions to be answered.  [60]. Answering these questions is extremely important in realising electric field control of magnetisation and magnetoresistance. Quantifying the relationship will be the subject of future work. Bi6Ti2.8Fe1.52Mn0.68O18.

Electron Microscopy:
Cross-sections of the B6TFMO films were prepared using a FEI Dual Beam Helios NanoLab 600i focused ion beam (FIB) and were mounted on a Cu based TEM grid. The sample was thinned via the FIB Ga beam first at 30kV and 93 pA, and then 5kV and 43pA. The samples were then further thinned and polished to sub> 30nm using a Fischione 1020 Ar ion based plasma cleaner prior to STEM imaging and EDX/EELS analysis. Energy filtered images acquired at 300 kV on an FEI Titan TEM with Gatan Tridiem Energy Filtering system demonstrated that thicknesses of the regions used for imaging were <30 nm. Imaging and analysis was performed on a NION UltraSTEM 200 operating at 200 kV. A Gatan Enfinium and GMS 2.0 was used for EELS acquisition and analysis.
Atom position finding and 2D Gaussian refinement were completed with the Atomap Python package [62]. Image analysis and mapping, as well as polarisation vector analysis, were completed using the TEMUL Toolkit Python package [63]. Supplementary material strain analysis was carried out by geometric phase analysis using the Stem Cell program [64].