Complete Selective Switching of Ferroelastic Domain Stripes in Multiferroic Thin Films by Tip Scanning

BiFeO3 is a rare single‐phase multiferroic which shows coupled ferroelectricity, ferroelasticity and antiferromagnetism at room temperature. Many fantastic properties of BiFeO3 are regulated by its domain structure. While (001) rhombohedral BiFeO3 thin films can possibly develop up‐to eight degenerate states of two‐variant 71° ferroelastic domain stripes, complete selective control of all possible switching paths between these states has not yet been achieved. Here, combining phase field simulations and scanning probe microscopy experiments, we demonstrated such a complete selective control. The tip bias and the built‐in field were shown to affect the volume fraction of the 71°, 109° and 180° switched domains in rhombohedral BiFeO3 thin films under single‐point loading. Meanwhile, tip scanning further broke the symmetry of the nucleated domains, leading to different switched domain patterns. We then grew BiFeO3 thin films with a specific two‐variant 71° ferroelastic domain state and showed that such a state could be deterministically switched into the other seven two‐variant domain states by collaborative controlling tip scanning and tip bias in scanning probe microscopy experiments. These results should deepen our current understanding on the domain switching kinetics in BiFeO3 thin films and indicate they are promising platforms for developing configurable electronic and spintronic devices.

In the ground state, BFO exhibits a rhombohedral (R) phase with a spontaneous polarization along [111] pseudocubic direction.As a result, there are up to eight (four) possible ferroelectric (ferroelastic) variants of the R-phase BFO.[22][23][24][25][26] Under the action of external stimuli, R-phase (or weakly distorted) BFO can generally exhibit 71°, 109°and 180°switching, defined by the polarization switching angle.While 180°switching is purely ferroelectric, 71°or 109°switching induces ferroelastic strains and a rotation of the magnetization plane. [11,27]Controllable 71°and 109°switching and the ferroelastic domain patterning in BFO are the key to realization of magnetoelectric coupling.
][30][31][32][33][34] For example, Cruz et al. found in BFO films on (001) SrTiO 3 (STO) that 180°switching was favorable at low tip bias, while 71°and 109°switching occurred at higher tip bias. [28]Balke et al. utilized the lateral tip motion to break the symmetry of domain nucleation and growth under the rotationally invariant SPM tip field and achieved a deterministic control of ferroelastic switching in BFO thin films. [29]Consequently, the two domain variants of the switched patterns form along the slow scan direction and opposite to the fast scan direction of the SPM tip motion.Based on a similar idea but making use of a tip-force-induced trailing flexoelectric field, Park et al. realized a deterministic selection of 71°and 180°switching in monodomain R-phase BFO thin films by controlling the SPM scan direction. [30]Based on this selective switching, Gross et al. effectively manipulated the antiferromagnetic order in a BFO thin film through magneto-electric coupling. [31]Recently, Chen et al. proposed a method for selectively controlling 71°and 180°switching paths in R-phase BFO thin films by combining out-of-plane electric field and in-plane trailing field, [32] meanwhile we reported a facile manipulation of four switching paths in R-phase BFO thin films by solely varying the scanning tip bias. [33]espite of these progresses and the fact that R-phase BFO thin films can possibly develop up-to eight degenerate states of twovariant 71°ferroelastic domain stripes, complete selective control of all the possible switching paths between these states has not yet been achieved.So far, the reported deterministic switching of R-phase BFO thin films has been limited to four states. [29,32,33]At the same time, there has been limited analysis of the combining effects of multiple controlling variables (e.g., tip scanning motion, tip bias, and built-in field) on the evolution of ferroelastic domain stripes in R-phase BFO thin films during tip scanning.The existing literature works mainly revealed the tip-scanninginduced domain switching of BFO thin films under the effect of single controlling variable.In this work, we investigated the tipscanning-induced domain switching of R-phase BFO thin films with two-variant 71°ferroelastic stripes under the combining effects of multiple controlling variables, including tip scanning motion, tip bias, and built-in field.Based on phase field simulations and SPM experiments, we demonstrated a complete selec-tive control of switching paths between eight states of two-variant 71°ferroelastic domain stripes.Domain switching kinetics of Rphase BFO thin films under tip scanning was first investigated by phase field simulations.It showed that tip bias and the built-in field would affect the relative volume fraction of the 71°, 109°and 180°switched domains under single-point loading.Moreover, tip scanning broke the symmetry of the nucleated domains and led to different domain evolution processes under tip scanning.We then grew R-phase BFO thin films with a specific two-variant ferroelastic domain state by pulse laser deposition (PLD).Via a collaborative control of tip scanning and tip bias in the SPM experiments, we successfully switched the pristine two-variant domain state into the other seven degenerate states in a deterministic way.We emphasize that the revealed domain switching of R-phase BFO thin films under the combining effects of tip scanning motion, tip bias and built-in field is much more complicated than the scenario reported in the literature and cannot be simply explained by the trailing field.Our results deepen our understanding on the domain switching kinetics of BFO thin films in SPM experiments and indicate their great potential in developing configurable electronic and spintronic devices.

Simulations of the Domain Switching in BFO Films under Scanning Tip Bias
In this section, domain switching in R-phase BFO thin films under scanning tip bias is investigated by phase field simulations.To first gain a preliminary understanding of the effect of scanning tip bias on the domain switching kinetics of R-phase BFO thin films, we recall its analogy in our daily life-the effect of a rainbow tip pencil scribing in different directions on a white paper (Figure 1a).As the rainbow tip pencil combines multiple colors on the tip, it can draw out lines with various colors dependent on the scribing direction.The effect of scanning tip bias on BFO thin films is similar.At the ground state, the polar axis of R-phase BFO is oriented along the ⟨111⟩p pseudocubic diagonals, with eight degenerate ferroelectric variants (denoted as r − 1 , r − 2 , r − 3 , r − 4 , r + 1 , r + 2 , r + 3 and r + 4 ) (Figure 1b).Accordingly, BFO can exhibit ferroelastic (71°and 109°) and ferroelectric (180°) switching, defined by the polarization switching angle.Due to the multiple states, the tip bias can trigger multiple domain nuclei and the subsequent domain growth dependent on the scanning direction, similar to how a rainbow tip pencil scribing in different directions can produce different colors.Despite the similarity of these two phenomena, it should be emphasized that the domain switching behaviors of BFO films under scanning tip bias are expected to be much more complicated due to the sensitivity of the polarization state of the BFO films themselves to the tip bias.Consequently, the domain switching kinetics of BFO films is not only affected by the tip scanning direction but also by the magnitude of tip bias.This provides us the possibility to achieve a complete switching of ferroelastic domain stripes in BFO thin films by tip scanning.
We first simulate the domain switching in BFO thin films with a single r − 3 domain under a tip bias of -25 V located at the middle of the simulation region (that is what we call single-point loading).Two cases are considered: i) the BFO film is without a  ).Meanwhile, for both cases (without built-in field and with built-in field), the relative volumes of the switched domains are not the same, except those are constrained by symmetry (like r − 2(4) and r + 2(4) ).Specifically, out-of-plane 71°switching (r − 3 →r + 1 ) is found to be the most favored switching in both films, with the switched r + 1 domain penetrating through the film thickness.Out-of-plane 109°switching (r − 3 →r + 2 and r − 3 →r + 4 ) is more favored than out-ofplane 180°switching (r − 3 →r + 3 ).Moreover, the in-plane 71°and 109°switching (i.e., r − 3 →r − 2 , r − 3 →r − 4 and r − 3 →r − 1 ) are found to be less favored than those out-of-plane switching.However, by comparing the switched domain patterns of two cases, one can see that the existence of a negative built-in field (which increases the out-of-plane switching barrier) can increase (decrease) the relative volume faction of the in-plane (out-of-plane) switched domains.Such a built-in field is common in real films due to the asymmetric interface environments and manifests itself in the ferroelectric hysteresis loops.Note also that other factors including the tip bias, film thickness, as well as the bias-loading time affect the relative volume faction of the switched domains, [29,33] we will explore the influences of these factors on the domain switching of BFO thin films under scanning tip bias in a near future work.
Then we simulate the domain switching in BFO thin films without a built-in field under area poling by a scanning tip. Figure 2a depicts the simulation results of domain switching in BFO thin films with a single r − 3 domain under scanning tip bias of -25 V. Panel (i) shows the switched domain pattern under a single-point loading, the same as shown in panel (i) in Figure 1c.To investigate the effect of tip scanning motion on the domain switching, we simulate four typical scanning configurations, corresponding to the four quadrants of the switching diagram as shown in Figure 2a.Here, the fast scan direction is defined as the trace direction with tip bias on (tip bias is off during retrace).More details about the tip scanning are shown in Figure S1 (Supporting Information).To see it more clearly, in panel (ii) of Figure 2a, we illustrate the tip motion of the first scanning configuration (corresponding to the first quadrant) where the fast scan is along (1 10) p and the slow scan is along (110) p .For this case, at the beginning, the tip is located at the start point (64, 64) (labeled by a white star) and at the end, the tip is located at the end point (192, 192) (red star).For each scanning configuration, we take a square poling area (128 nm ×128 nm) with the tip subsequently scanning over 16 × 16 points.The loading time at each tip location is set to be 1000 steps.Figure 2a shows that the switched domain pattern after tip scanning is dominated by outof-plane 109°switched domains (i.e., r + 2 and r + 4 ), and the domain evolution is mainly determined by the slow scan direction.Specifically, when the slow scan direction is along (110) p (i.e., the first and second quadrants), domain patterns with r + 2 domain dominated is favored; when the slow scan direction is reversed (i.e., the third and fourth quadrants), domain patterns with r + 4 domain dominated is favored.Figure 2b further shows the simulation results of domain switching in BFO thin films with a single r − 4 domain under scanning tip bias of -25 V.For this case, the switched domain pattern after scanning is dominated by those switched domains in direction with the slow and fast scan directions (e.g., r + 1 and r + 2 domains are dominated for the scanning in the first quadrant), and the domain evolution is determined by both the slow scan and fast scan directions.
Note that the above results are understandable, considering that the tip scanning breaks the symmetry of the nucleated domains.It tends to help growth of those domains nucleated behind the tip by covering the domains in front of the tip.This tip scanning effect, together with the relative stability of the nucleated domains under single-point loading, results in the final switched domain pattern after area poling.Based on such a picture, one can expect that the domain evolution is determined by those domains in the same direction with the slow and/or fast scan di-rections.As in the above simulations, the BFO films are without built-in field and out-of-plane switched domains are more stable than in-plane switched domains, the following domain patterns after tip scanning are expected: (a) pattern with r + 1 and/or r + 2 domains dominated (the first quadrant); (b) pattern with r + 2 and/or r + 3 domains dominated (the second quadrant); (c) pattern with r + 3 and/or r + 4 domains dominated (the third quadrant), and (d) pattern with r + 1 and/or r + 4 domains dominated (the fourth quadrant).Moreover, the difference between results shown in Figure 2a,b is a clear outcome from the symmetry breaking effect by the tip scanning motion.
In Figure 3, we further show the phase field simulation results of domain switching in BFO thin films with a built-in field of −2 × 10 8 V m −1 under area poling by a scanning tip of -25 V. Similar to the investigation shown in Figure 2, here we consider two cases: BFO thin films with (a) a single r − 3 domain or (b) a single r − 4 domain.For each case, four different scanning configurations defined by the fast and slow scan directions of the tip are simulated.The simulation settings are the same as Figure 2. Comparing the results of Figure 3 with those of Figure 2, one can see that as the negative built-in field increases (decrease) the relative volume faction of the in-plane (out-of-plane) switched domains, the switched domain patterns after area poling is dominated by in-plane 71°switched domains.Specifically, for case of initial r − 3 domain (Figure 3a), it is found that r − 2 and r − 4 domains are dominated, and the domain evolution is mainly determined by the slow scan direction, i.e., the dominated domain is in direction with the slow scan direction.For case of initial r − 4 domain (Figure 3b), r − 1 and r − 3 domains are found to be dominated.In this case, the domain evolution is mainly determined by the fast scan direction, i.e., the dominated domain is in direction with the slow scan direction.These results are also consistent with the previous proposed physical picture: the symmetry-breaking effect by tip scanning and the relative stability of the nucleated domains under single-point loading, together determine the final switched domain pattern under tip scanning.As indicated by the results of Figures 2  and 3, for BFO thin films with a pristine two-variants ferroelastic stripe domain pattern (e.g., r − 3 / r − 4 ), it is possible to switch it into the other seven two-variant domain states in a deterministic way.

Experiments of the Domain Switching in BFO Films under Scanning Tip Bias
In the following, we perform SPM experiments to explore domain switching in R-phase BFO thin films under scanning tip bias.The schematic of the SPM experimental setup is shown in Figure 4a.The as-grown BFO thin films have atomically flat surface with terrace-like morphology, and they show a robust switchable polarization.The out-of-plane polarization of the as-grown BFO thin films is uniformly pointing downward to the substrate (see Figure S2, Supporting Information), indicating the existence of a built-in electric field.The domain structure of the as-grown BFO thin films mainly consists of 71°ferroelastic stripe domain with two variants, r − 3 and r − 4 , as shown by the in-plane PFM phase image in Figure 1b (more PFM results are shown in Figure S3, Supporting Information).In consistence with the previous The film is assumed without a built-in field.For each case, four different scanning configurations are simulated, as defined by the fast and slow scan directions, corresponding to the four quadrants of the depicted switching diagram.The tip motion of the first quadrant where the fast scan is along (1 10) p and the slow scan is along (110) p is schematically shown in panel (ii) of (a).For this case, at the beginning, the tip is located at the start point (64, 64) (white star) and at the end, the tip is located at the end point (192, 192) (red star).For each scanning, we take 16 × 16 location points.The loading time at each tip location is set to be 1000 steps.
simulations, the BFO thin film is placed in the global Cartesian coordinate system with x axis along the [1 10] p axis, y axis along the [110] p axis, and z axis along the [001] p axis.The fast scan direction of SPM tip is defined to be the trace direction with tip bias on (and the tip bias is off during retrace).The fast scan direction is either parallel or antiparallel to x axis, and the slow scan direction is either parallel or antiparallel to y axis.
We first investigate the domain switching BFO films under scanning tip bias of -8 V.The obtained switching diagram summarizing the results of four typical scanning configurations is depicted in Figure 4c.For each scanning configuration, (i) the in-plane PFM amplitude image, (ii) the in-plane PFM phase image (the corresponding out-of-plane PFM phase image is shown in the inset) and (iii) the schematic domain pattern within the scanning area are included.The area of the scanning region is taken to be 3 × 3 μm 2 , as indicated by the dashed box.The red gradient arrow denotes the fast scan direction, and the blue gradient arrow denotes the slow scan direction.For this tip bias, out-of-plane switching is not observed, but in-plane switching occurs.When the slow scan direction is consistent with that of the initial variant r − 4 and the fast scan direction is opposite to that of variant r − 3 (i.e., the second quadrant in Figure 4c), the domain pattern after scanning is still r − 3 / r − 4 .Note that although the domain pattern remains the same, it has undergone reconstruction.We denote this case as switching path 1.When the slow and fast scan directions are consistent with the directions of r − 3 / r − 4 variants (i.e., the first quadrant in Figure 4c), the domain pattern after scanning changes to be r − 1 / r − 4 .This switching path is denoted as path 2. When the slow scan direction is opposite to that of variant r − 4 and the fast scan direction is consistent with that of variant r − 3 , the switching path 3 from r − 3 / r − 4 to r − 1 / r − 2 is selected, as shown in the fourth quadrant in Figure 4c.Further, when both the slow and fast scan directions are opposite to the directions of r − 3 / r − 4 variants (i.e., the third quadrant in Figure 4c), the switched domain pattern mainly consists of r − 2 / r − 3 variants.Therefore, the BFO film exhibits four differ-ent switching paths under scanning tip bias of -8 V, with each switching path selectable by a specific scanning configuration.Note that the switched domain pattern after scanning consists of two domain variants with one along the slow scan direction and the other opposite to the fast scan direction.This is similar to the observation in a previous experiment, [29] however, our case does not involve out-of-plane switching.Moreover, the experimental switching diagram is not entirely consistent with previous simulations which show that domain variants consistent with the slow and fast scanning directions are favored.This indicates At the end, we would like to discuss the potential key elements to realize complete switching of the ferroelastic domains in R-phase BFO thin film.First of all, the eight ferroelectric variants of the R-phase BFO thin film should have similar stability, so that the film can develop eight degenerate or quasidegenerate two-variants 71°ferroelastic domain states. [22,35]This requires those factors (e.g., the shear strain arisen from the substrate miscut and the built-in field) that would break the degeneracy of the eight variants to have minimal effects. [36,37]Second, the tip bias should significantly moderate the relative stability of the switched domain variants.This might further require suitable built-in field, film thickness and loading time (i.e., scanning speed) as shown by our phase field simulation. [33]n summary, combining theoretical simulations and experiments, we investigated the tip-scanning-induced domain switching of R-phase BFO thin films with two-variant 71°ferroelastic stripes under the combining effects of multiple controlling variables, including tip scanning motion, tip bias, and built-in field.Phase field simulation results show that the tip bias and the builtin field affect the relative volume fraction of the 71°, 109°and 180°switched domains in BFO thin films under single-point loading, meanwhile the tip scanning further breaks the symmetry of the nucleated domains and leads to different switched domain patterns after tip scanning.We then perform SPM experiments on the domain switching kinetics of PLD-grown Rphase BFO thin films with a specific two-variant ferroelastic domain state.It is found that, at a relatively low tip bias, changing the scanning direction of the tip can lead to four types of twovariant ferroelastic domain patterns without switching of the outof-plane polarization.At a relatively high tip bias, another four types of two-variant ferroelastic domain patterns with switching of the out-of-plane polarization are observed.Therefore, eight possible switching paths have been completely demonstrated via the collaborative control of tip bias and tip scan.These results should deepen our current understanding on the domain switching kinetics in BFO thin films and indicate they are promising platforms for developing configurable electronic and spintronic devices.

Experimental Section
Phase Field Simulations: 3D phase field simulations were performed to understand the ferroelectric(elastic) domain switching kinetics in (001) R-phase BFO thin films under scanning tip bias.In the phase field model, the spontaneous polarization field P(r) = (P 1 , P 2 , P 3 ) is chosen as the order parameter field to represent the ferroelectric(elastic) domain structure.The system's total free energy includes contributions from the Landau bulk free energy, gradient energy, elastic energy, electrostatic energy and surface energy: [38,39,40] F = ∭ V [  ij P i P j +  ijkl P i P j P k P l +  ijklmn P i P j P k P l P m P n where ij ,  ijkl and  ijklmn are coefficients of the Landau polynomial under stress-free boundary conditions, g ijkl are the gradient energy coefficients, c ijkl are components of the elastic stiffness tensor,  ij and  0 ij are the total strains and eigenstrains, E i is the electric field,  b is the background dielectric constant and  S i are surface coefficients, respectively.The eigenstrains  0 ij are related to the polarization through  0 ij = Q ijkl P k P l with Q ijkl being the electrostrictive tensor.
The electric field and mechanical strain fields of the film satisfy the electrostatic and mechanical equilibrium equations, respectively: where  is the electrostatic potential.In practice, the film is clamped by the substrate and is free of traction at the top surface.For simplicity, in the model, in-plane misfit strains are applied to the film by constraining the macroscopic in-plane deformation of film, whereas the top and the bottom surfaces of the film are set to be free of traction.Note that this treatment would only bring a minor effect on the domain structure as the substrate effect on the film is mainly came from the misfit strain.Moreover, electrical short-circuit condition is applied at the bottom surface of the film.The tip bias is applied by setting a Lorentz-like distribution potential profile at the top surface of the film.The surface potential profile has the form,  surf =  0 R 2 tip ∕(r 2 + R 2 tip ), where r denotes the distance between a specified point on the top surface of the film and the tip center, R tip describes the width of the applied potential distribution, and ϕ 0 is the maximum electric potential at the top surface of the ferroelectric. [41,42]The electrostatic and mechanical equilibrium equations are solved by Fourier transform (FFT) technique based on the Khachaturyan's microscopic elastic theory and the Stroh's formalism of anisotropic elasticity. [43,44]The evolution of polarization field is captured by the time-dependent Ginzburg-Landau (TDGL) equations which are numerically solved via a Euler iteration method.The BFO thin films are discretized by a grid of 256Δ × 256Δ × 8Δ with Δ = 1.0 nm.
Experimental Methods: Epitaxial BFO thin films, with a thickness of ≈40 nm, were directly grown on 0.7% Nb-doped (001) STO (NSTO) single crystal substrates by PLD.The PLD system used a 248 nm KrF excimer laser with a uniform laser energy density of 1.2 J cm −2 and a pulse frequency of 3 Hz.Throughout the deposition process, the substrates were maintained at 720 °C under an oxygen pressure of 0.15 mbar.Following 8000 laser pulse depositions, the films were annealed at 650 °C in the PLD chamber for 10 min in order to reduce oxygen vacancies and then cooled down to room temperature at a rate of 5 °C min −1 under 100 mbar oxygen pressure.
The structure of the BFO thin films were characterized by X-ray diffraction (XRD, PANalytical X' Pert PRO) with Cu-K  radiation at room temperature (2 range: 10-50°).The surface topography of the samples was investigated by the atomic force microscope (AFM) mode of Asylum Research MFP-3D Scanning Probe Microscope (SPM).The polarization state of the samples was manipulated and characterized by piezoelectric force microscopy (PFM) based on the same SPM system.The dual AC resonance tracking PFM (DART-PFM) mode was employed to reduce the crosstalk between changes in sample-tip contact stiffness.In all the SPM measurements, a high voltage holder was used to ensure a large enough voltage variation range, and conductive probes with boron doped diamond coating (Adama innovations, AD-2.8-As) were adopted.The probes have a typical curvature radius of 10 ± 5 nm, a nominal spring constant of 2.8 N m −1 and a free-air resonance frequency of 65 kHz.

Figure 1 .
Figure 1.a) A schematic showing the effect of rainbow tip pencil scribing in different directions on a white paper.b) Schematic of the eight ferroelectric domain variants of R-phase BFO and the possible switching paths.c) Phase field simulation results of domain switching in BFO thin films with a single r − 3 domain under a tip bias of -25 V located at the middle of the simulation region.(i) The case without a built-in field.(ii) The case with a built-in field of −2 × 10 8 V m −1 .The loading time is set to be 1000 steps.d) The (110) p cross-section images of the two evolved domain patterns shown in (c).e) The (1 10) p cross-section images of the two evolved domain patterns shown in (c).
built-in field, and (ii) the BFO film is subjected to a built-in field of −2 × 10 8 V m −1 .The loading time of the tip bias is set to be 1000 steps.The top-view images of the evolved domain patterns of the two cases are shown in panels (i) and (ii) in Figure 1c, respectively.The corresponding (110) p and the (1 10) p cross-section images of the two evolved domain patterns are shown in Figure 1d,e, respectively.It shows that the negative tip bias can trigger all the possible switching paths, including the in-plane 71°switching (i.e., r − 3 →r − 2 and r − 3 →r − 4 ), in-plane 109°switching (r − 3 →r − 1 ), out-of-plane 71°switching (r − 3 →r + 1 ), out-of-plane 109°switching (r − 3 →r + 2 and r − 3 →r + 4 ), and out-of-plane 180°switching (r − 3 →r + 3

Figure 2 .
Figure 2. Phase field simulation results of domain switching in BFO thin films with a) a single r − 3 domain or b) a single r − 4 domain under scanning tip bias of -25 V.The film is assumed without a built-in field.For each case, four different scanning configurations are simulated, as defined by the fast and slow scan directions, corresponding to the four quadrants of the depicted switching diagram.The tip motion of the first quadrant where the fast scan is along (1 10) p and the slow scan is along (110) p is schematically shown in panel (ii) of (a).For this case, at the beginning, the tip is located at the start point (64, 64) (white star) and at the end, the tip is located at the end point(192, 192) (red star).For each scanning, we take 16 × 16 location points.The loading time at each tip location is set to be 1000 steps.

Figure 3 .
Figure 3. Phase field simulation results of domain switching in BFO thin films with a) a single r − 3 domain or b) a single r − 4 domain under scanning tip bias of -25 V.The film is assumed under a built-in field of −2 × 10 8 V m −1 .For each case, four different scanning configurations are simulated.The simulation settings are the same as Figure 2.

Figure 4 .
Figure 4. a) Schematic experimental setup of SPM poling and PFM measurement of (001) R-phase BFO thin films with pristine 71°ferroelastic stripe domain patterns.b) in-plane PFM phase image of the as-grown BFO film.c) The switching diagram of BFO film under scanning tip bias of -8 V.For each scanning configuration, the following are depicted: (i) the in-plane PFM amplitude image, (ii) the in-plane PFM phase image (the corresponding out-of-plane PFM phase image is shown in the inset) and (iii) the schematic domain pattern within the scanning area.

Figure 5 . 6 .
Figure 5.The switching diagram of BFO film under a scanning tip bias of -10 V.For each scanning configuration, the following are depicted: (i) the in-plane PFM amplitude image, (ii) the in-plane PFM phase image (the corresponding out-of-plane PFM phase image shown in the inset), and (iii) the schematic domain pattern within the scanning area.

Figure 6 .
Figure 6.Schematics of polarization switching paths obtained by collaborative control of tip bias and tip scanning in this work.a) Low tip bias.b) High tip bias.