Deterministic Switching of Ferroelectric Bubble Nanodomains · 2020-01-31 · Topological...

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Deterministic Switching of Ferroelectric Bubble Nanodomains

Qi Zhang, Sergei Prokhorenko, Yousra Nahas, Lin Xie, Laurent Bellaiche, Alexei Gruverman, and Nagarajan Valanoor*

Here, the deterministic and reversible transformation of nanoscale ferroelectric bubbles into cylindrical domains using a scanning probe microscopy (SPM) approach is demonstrated. The bubble domains—sub-10 nm spheroid topological structures with rotational polarization—can be erased by applying a mechanical force via the SPM tip. Application of an electrical pulse with a specific combination of amplitude and duration can recreate the bubble domain state. This combination of mechanical and electrical passes is essential for realization of reversible transformation as application of only electrical pulses results in complete erasure of the bubble domain state. Effective Hamiltonian-based simulations reproduce phase sequences for both the mechanical and electric passes and confirm the intrinsic nature of these transitions. This simple and effective pathway for switching between various topological defect states may be exploited for emergent devices.

DOI: 10.1002/adfm.201808573

Dr. Q. Zhang, Prof. N. ValanoorSchool of Materials Science and EngineeringThe University of New South WalesSydney, New South Wales 2052, AustraliaE-mail: [email protected]. S. Prokhorenko, Dr. Y. Nahas, Prof. L. BellaichePhysics Department and Institute for Nanoscience and EngineeringUniversity of ArkansasFayetteville, AR 72701, USADr. L. XieDepartment of PhysicsSouthern University of Science and TechnologyShenzhen 518055, ChinaProf. A. GruvermanDepartment of Physics and AstronomyUniversity of NebraskaLincoln, NE 68588, USA

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.201808573.

In order to fully exploit these emergent phenomena, one must be able to success-fully manipulate the topological defect state in a precise and regulated fashion. These have been demonstrated in mag-netic systems, e.g., the use of magnetic skyrmions[12] as well as magnetic domain-walls[13] for race-track memory. How-ever, controlled switching at the single defect level in ferroelectrics remains a substantive challenge[2c,10,14] even though this has been achieved at the mesoscale.[15] The unambiguous demonstration of deter-ministic switching between various non-trivial ferroelectric topologies, particularly at the single defect level would lead to a unprecedented handle over the emergent properties and hence entirely new cross-

coupled electro-mechanical-optical-polarization functionalities, as outlined by Martin et al.[10] The primary impediment with ferroelectrics is that single topological configurations (i.e., vortex-like or bubble domain states)[5,16] have a size only several unit-cells, which is several orders magnitude smaller than their classical magnetic counterparts. While this drastic size reduc-tion imposes a considerable level of difficulty for manipulation and measurement, it also offers an ideal platform for employing advanced scanning probe microscopy (SPM) approaches. For example, the recent demonstration of rewritable vortex states by an electric field applied through an SPM tip[2c] in BiFeO3 films demonstrates this can be a viable approach to exploit the con-ductive feature of vortex cores to achieve memory function.[8]

Here, we report the deterministic and reversible switching of nanoscale ferroelectric domain topologies (at the single defect level) in an ultrathin ferroelectric PbZr0.2Ti0.8O3 (PZT) sand-wich heterostructures using SPM techniques. Previously, we showed that under specific electrical and mechanical boundary conditions this system could allow spontaneous formation of the bubble domain states – unique sub-10 nm spheroid topo-logical structures with rotational polarization. Our focus here is to demonstrate the controlled reversible transformation between three domain states, namely, i) a c-axis single-domain matrix with downward polarization (i.e., no domain walls), ii) cylindrical domains with sharp 180° domain walls, and iii) ferroelectric bubble domains with fuzzy domain walls.

To achieve this, we first erased the as-grown bubble domains via a “mechanical pass,” by scanning the SPM tip under con-tact mode at the desired region under a purely mechanical force (>200 nN). This is followed by an “electrical pass,” used to nucleate new domains. Under this pass, by applying an elec-trical pulse of specific amplitude and duration we can either

Ferroelectric Topologies

1. Introduction

Topological structures (or defects) in ferroic materials, such as skyrmions,[1] vortices,[2] flux closures,[3] incommensurate curl domains,[4] and bubble domains,[5] have recently attracted attention due to their emergent nature. They can display large current-induced spin-orbit torques,[6] giant electromechanical response,[5] enhanced[7] or ballistic electron transport,[8] chi-rality[9] or colossal optical coefficients,[10] to name just a few of their exciting properties. Often these are distinctly absent in their parent ferroic phases, which provides us with a new para-digm for functional nanodevices.[11]

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recreate bubble domains or generate cylindrical domains. Effec-tive Hamiltonian-based simulations show that the observed state sequence can be explained by a unique property of the as-grown film state—namely, its location in close vicinity of a discontinuous transition line separating bubble and single-domain matrix stability regions in the pressure-bias field phase diagram. The latter allows for intrinsic coexistence of single-domain matrix/bubble states and reproducible switching between the two topological defect states. Thus, we achieve deterministic switching of nanoscale ferroelectric domain topologies in a relatively simple and effective manner.

2. Results and Discussion

The crystallographic details of (001)-oriented epitaxial PZT/STO/PZT sandwich films on La0.67Sr0.33MnO3(LSMO) buffered STO substrate used here can be found elsewhere.[5] For this study, we chose PZT layer fixed at 7 unit cells (u.c.) (≈3 nm) with the STO spacer being 1 u.c. thick. The bubble domains are randomly distributed and with an average size <10 nm, and form as a result of the competition between the imposed epi-taxial compressive strain from substrate (that stabilizes long range ferroelectric order) and appropriate depolarization field (that tries to suppress the polarization). Previously, we revealed that the bubbles are bound by mixed Néel–Bloch-like domain walls and possess rotational or shear polarization, a property nominally forbidden for parent P4mm tetragonal symmetry at bulk scales (Figure 1a). Due to the combination of their extremely small size (<10 nm) and non-180° characteristics of their walls, the domain boundaries are rendered with a blurry or fuzzy contrast in the out-of-plane piezoresponse force micro-scopy (vPFM) amplitude image. For sizes larger than ≈10 nm we observed conventional cylindrical domains with well-defined sharp boundaries (Figure 1b). It is worthwhile to note the dif-ference in the vPFM amplitude profiles between the bubble and

the cylindrical domains. In our previous work we demonstrated for the bubble domains that their size is at the limit of the SPM tip radius. Therefore, the SPM tip is not able to resolve the individual bubble walls clearly; rather the vPFM amplitude pro-file appears as a single depression (i.e., a flattened “U” shape). In contrast the PFM tip is typically clearly able to resolve the cylindrical domain walls. As a consequence, the vPFM ampli-tude cross-section profile across a given cylindrical domain will clearly reveal two depressions along the line scan, each depres-sion corresponding to the location of the inversion domain (in this case 180°) wall. We refer to this here on as a “W” profile.

Previously, we have shown that even under a very weak AC field the bubble domains can easily morph into classical cylin-drical domains and eventually merge to form a mesoscale labyrinthine polydomain network.[5] This transition from the bubble domain to the cylindrical domain state under electrical bias manifests a polarization rotation process, which results in a significant enhancement of the electromechanical response. However, the conversion to the cylindrical domains is irrevers-ible.[5] Thus, in order to fully exploit this enhanced electrome-chanical response, one needs to explore alternate methods that allow the system to reversibly straddle across the boundary between the two topologies.

To achieve this, here we employ a “dual pass” scanning probe approach, which involves a mechanical pass followed by an electrical pass. We exploit the fact that mechanical force alone applied through the SPM tip with no concurrent electric field can change polarization state of a ferroelectric.[17] This mechanical switching of polarization has been proposed to result from the flexoelectric effect of the given thin dielectric film[18] and can be realized by applying a mechanical force to a specific location on a ferroelectric surface through an SPM probe.[17] A recent report[19] suggests that a systematic control of the populations of two different coexisting phases having different directions and magnitudes of their electrical polariza-tion can be accomplished via a dual pass involving i) electric


Figure 1. A sketch illustrating a difference between the PFM signals from the bubble and cylindrical domains. a) Bubble domain and b) cylindrical domain configuration and their corresponding piezoresponse force microscopy (PFM) responses. The blue and orange arrows represent the two dif-ferent polarization directions within the single-domain matrix and the nanodomains, respectively. Note the stark difference between the PFM amplitude profiles between the bubble and the cylindrical domains.



fields and ii) a mechanical mechanism through the simple tra-ditional coupling between stress and strain without invoking flexoelectricity.

Figure 2a,b shows the 2 µm × 2 µm PFM amplitude and phase images of the as-grown film. At this relatively low mag-nification, homogeneously distributed bubble domains with speckled contrast are observed, yielding an ultrahigh domain density of nearly 1012 inch−2. Bubble domains can be clearly seen in a higher magnification image in Figure 2c. Mechanical erasure of these domains has been carried out with a loading force in the range from 200 to 500 nN. Note that a force less than 100 nN has limited effect on the domain evolution without any erasure (see Figure S1, Supporting Information). After scanning back and forth (along slow scan axis) for seven times (Figure 2d), the bubble domains in the scanning regions are successfully erased transforming them into the same down-ward polarization state as the surrounding single-domain matrix (Figure 2e).

Critically, no topography change is observed (see Figure S1, Supporting Information) which confirms that the switching is not due to chemical effects[20] or ferroelastic domains.[21] Such local pressure applied from SPM probe provides energy to switch bubble domains polarization to downward orientation

and also induces a downward state in the surrounding single-domain matrix. As a result, after mechanical switching, this rectangular region in Figure 2c shows slightly higher PFM amplitude than the as-grown single-domain matrix regions. This phenomenon has been confirmed by scanning on film surfaces under different tip forces, as shown in Figure S1 (Sup-porting Information).

We have also demonstrated that these bubbles do not disappear upon annealing in oxygenated environments and cooling back to room temperature (see supplementary materials in ref. [5]). Furthermore, high-resolution electron energy-loss spectroscopy (EELS) mapping (see Section S2, Supporting Information) do not reveal distinct unambiguous Ti+3 regions or pockets. The corresponding high-resolution strain maps (also discussed pre-viously in ref. [5]) reveal strong shear displacements in the loca-tion of the bubble but no discontinuity in strain in the vertical and lateral profiles (i.e., perpendicular or along the thickness respectively). This suggests that the bubbles are not a simple manifestation of defects. Indeed, based on previous reports,[22] a rather complex correlation between the topological defect and lattice point-defects exists. A full study of the screening mecha-nisms, especially with the role of defects will be reported else-where as it lies outside the focus and scope of this paper.


Figure 2. a) vPFM amplitude and b) vPFM phase images of PZT/STO/PZT thin film in a scan size of 2 µm × 2 µm; the amplitude z scale bar indi-cates a relative value here. c) PFM amplitude and phase images of the pristine PZT/STO/PZT thin film showing bubble domains (dark contrast in the amplitude image) homogeneously distributed in the single-domain matrix with the downward polarization; d) After scanning back and forth (along slow scan axis) several times, the bubble domains under the tip are successfully switched to a net downward polarization state (similar to the single-domain matrix). e) PFM amplitude and phase images of the same PZT/STO/PZT thin film after mechanical writing under a contact force of 200 and 500 nN. White boxes indicate the mechanical writing region where the bubble domains were erased successfully.



Once mechanical erasure has been accomplished, we then move to the next step, i.e., the writing function. It is well known that under an external bias pulse, nucleation and growth of switched domains are strongly dependent on pulse width and amplitude.[23] Thus, the first task was to identify electrical pulse amplitude and width parameter space that would create either nanoscale bubble or cylindrical domains. Details of the optimized conditions that are able to nucleate bubble domains are given in the experimental section. Chiefly, when the bias height and pulse width are fixed at +2.5 V and 0.01 s, a bubble-like domain with fuzzy domain boundaries is created. Using a slightly lower bias (i.e., at +2.25 V) or shorter pulses (i.e., 0.005 s), no visible domains can be observed for either PFM amplitude or phase. The domain size as a function of the pulse amplitude and pulse width is shown in Figure S3 (Supporting Information).

Figure 3 is a series of vPFM amplitudes that display this domain evolution process. The as-grown bubble domains are shown in Figure 3a. Figure 3b is the vPFM amplitude image of the same region as above but after mechanical writing using a force of 500 nN. The next step is domain nucleation under tip-induced electric field. Figure 3c is the panel of the vPFM ampli-tude images captured immediately following the application of pulse with fixed height of +2.5 V but under varying pulse

widths while Figure 3e shows the PFM amplitude of the same region after a 20 h relaxation period. Note that no scanning was done during this 20 h interval. Finally, Figure 3d,f shows the vPFM amplitude line profiles of the domains imaged in Figure 3c,e, respectively. The PFM figures have been precisely aligned for the desired positions in Figure 3, and the zoom-out details are given in Figure S4 (Supporting Information). The corresponding domain evolution process is also schematically depicted in Figure 4.

For applied pulse times longer than 0.05 s domains with clear domain walls are observed (left side of Figure 3). Typical “W” feature (characteristics of cylindrical domain wall as shown in Figure 1b) found in their corresponding PFM amplitude line profile (Figure 3d) confirms the existence of cylindrical domains, as sketched by Figure 4a. With the reducing pulse width, the nucleated domain size decreases from ≈35 ± 5 nm (in diameter) for pulse periods 0.2 s to ≈15 ± 5 nm when the pulse is reduced to 0.05 s. When the pulse duration is decreased below 0.02 s, domains of ≈10 nm in size are formed with their PFM amplitude line profile exhibiting a single dip (Figure 4b), which is similar in magnitude to those shown by the cylin-drical domains (Figure 4a). Thus, it is likely that the domains created by the pulses shorter than 0.02 s, are still cylindrical domains but with extremely small diameter, such that their

lateral size is at PFM probe resolution limit, as sketched in Figure 4b. In contrast, the dip in the PFM amplitude line profile for the domain nucleated at 0.01 s is very shallow; in fact, the size and PFM amplitude of the new domain from 0.01 s pulse is similar to the as-grown bubble domains (as depicted by the sketch of Figure 4c,d). No decay in this dip was observed even after 20 h (Figure 3f). Thus, the nucleated domain for smallest pulse, namely, 0.01 s is likely to be a bubble domain.

For domains recreated using pulses greater than 0.02 s, regardless of the initial domain morphology, all relax into a fuzzy domain state within the next 20 h (Figure 3e). The amplitude line profiles (Figure 3f) reveal that the “W” features disappear and are replaced with a single-flattened “U” dip but with higher net amplitude. The amplitude of the domain nucleated under a 0.01 s pulse remains as is with no discernable decay. The two peaks for the 0.02–0.05 s domains are for two single fuzzy domains in transi-tion after relaxation, but not the walls. The nucleated and relaxed domain size as a func-tion of applied bias pulse width is plotted in Figure S3b (Supporting Information). Note that the relaxation time is even shorter (<3 h), for domains created using 0.1 s or shorter pulse widths. Once these domains return into fuzzy state, they remain stable and do not vanish. This suggests that these domains with fuzzy domains walls, viz., bubble domains are energetically the most


Figure 3. a–d) Domain erasure, recreation, and e,f) relaxation process. a) As-grown bubble domains were first b) erased under seven times mechanical force (500 nN) scan, followed by c) nucleation under +2.5 V pulsed bias with various pulse widths (0.5–0.01 s, from left panel to right panel). PFM amplitude cross-sectional line profile plot (d) shows the amplitude change of recreated domains in panel (c). The walls of cylindrical domains can be resolved as “W” shape (for domains recreated using pulses 0.05 s and above), while no clear wall features can be observed for domains nucleated under 0.01 and 0.02 s pulse widths. e) Irrespective of their initial applied pulse widths, all domains relax to the fuzzy state after 20 h. f) No cylindrical wall features can be observed in the PFM amplitude cross-sectional profile of relaxed domains. Scale bar: 50 nm.



stable state. The full details of relaxation process are beyond the scope of this study and will be reported in the future.

We next explored if we could cycle these bubble domains through a mechanical, and then electrically induced transi-tion to test the reversibility of the whole process. As shown in Figure 5, after all bubble domains were erased by scanning under a tip force of 500 nN (Step 1, Figure 5a), a +2.5 V, 0.01 s pulse was applied to the sample at a selected point (Step 2, Figure 5b). A bubble domain is created with size comparable to the as-grown ones (see the original region in Step 1 or 2 for reference). This newly grown bubble domain could again be erased mechanically by scanning with the tip under a high loading force of 500 nN (Step 3, Figure 5c), suggesting that the manipulation process is repeatable. Since the recreated bubble domains are fairly stable with time (as discussed above), the disappearance of new bubble domains in Step 3 cannot be the result of relaxation. Indeed, for the case of where Step 3 was not performed, the nucleated bubble domain remains stable for the entire duration of the experiment. Note that no topog-raphy change is observed through the whole process, thus this repeated erase and write procedure does not cause any plastic deformation of the surface. These results above now give us a clear picture of the landscape of the entire possible transitions as depicted in Figure 6.

To further explore the observed switching paths, we have performed first-principles based simulations using the effective Hamiltonian model of PbZr0.4Ti0.6O3 ultrathin films.[24] Rather

than modeling all the layers of the fabricated heterostructure, we have focused our atten-tion only on the upper PZT layer. The experi-mentally observed as-grown bubble state is reproduced by performing the Metropolis Monte Carlo temperature annealing from 500 K down to 250 K with the temperature steps of 25 K under the bias electric field of −0.43 V nm−1 (−4300 kV cm−1). At each tem-perature, we have performed 10 000 Monte Carlo sweeps, which was largely sufficient for relaxation purposes. The resulting 3D distri-bution of the [001] components of the local mode vectors uz is shown in Figure 7a where one can clearly observe the spherical shape of the bubble domains. The distribution of uz corresponding to the obtained configuration within the middle (001) plane of the super-cell is presented in Figure 7b.

To reproduce the “mechanical pass,” we then subjected the obtained “as-grown” state (Figure 7a,b) to an increasing uniaxial stress applied perpendicular to the film’s surface. In these simulations, the stress was assumed to be spatially homogeneous. Although this approximation does not take into account the real stress distribution exerted by the PFM tip,[25] it nevertheless allows to under-stand the effect of local pressure in the area beneath the tip where η33 can be considered uniform. For example, homogeneous stress simulations have already allowed to obtain

theoretical insight into experiments where stress was exerted by PFM tip.[19] At each value of the applied stress the system was relaxed during 10 000 Monte Carlo sweeps. The obtained results show that until reaching the stress value of σ* = 0.92 GPa the bubble state remains stable, while above σ* the bubbles are suppressed in favor of a homogeneously polarized state (single-domain matrix) in agreement with experimentally observed transition. The spatial mappings of uz corresponding to the single-domain matrix state under an applied stress of 4 GPa is shown in Figure 7c,d.

Finally, the simulated “electrical pass” consisting in releasing the applied pressure and applying an external electric field E (added to the bias field value) resulted in a re-entrance into the bubble state for E > 0.03 V nm−1, therefore reproducing the experimentally observed transition from single-domain matrix to bubble state under the electrical pass (Figure S5, Supporting Information). Once again, for both structural relaxations (with external stress released and under applied external electric field) we have performed 10 000 sweeps.

The gathered numerical results corroborate the revers-ibility of the writing/deletion of the bubble domains under external electrical/mechanical passes, respectively, and sug-gest an insight into the switching mechanisms. Namely, the heterostructure system lies at the boundary between mono-domains (or cylindrical domain) and bubbles, and applying stress or electric field can get the system to go from one state to another.


Figure 4. Schematic description of domain evolution under bias pulse. a) When the pulse width is above 0.05 s, a cylindrical domain is created with clear “W” shape domain wall feature in the cross-sectional PFM amplitude line profile. b) When the pulse width decreases pulse to 0.02 s, an extremely narrow cylindrical domain is created such that PFM tip is not able to resolve the domain walls. In this case, a “U” shaped amplitude cross-sectional profile is obtained but the dip in the PFM amplitude is similar to the 0.5 s case. In cases (c) and (d) when the pulse width is reduced to below 0.02 s, the cylindrical domains transform into bubble domains with fuzzy domain walls. In this case the PFM amplitude displays a very shallow dip in its line profile with a flattened “U” shape.



It is known that the bubble domain state in thin films, a bridge between stripe and monodomain phases, is stabilized by application of electric field[24a] or by partial screening of bound charges[26] under a moderate, substrate-induced, compressive strain. Indeed, the extreme cases of complete screening pro-motes monodomain and absence of screening favors stripes, while the moderate strain enables rotation of dipoles away from the tetragonal directions featured at the boundary of bubble domains. Interestingly, both screening and applied electric field

effects appear to be very similar in nature if the depolarizing field Ed is perceived as an “external” one, albeit self-consistent with the state of the system (dependent on the out-of-plane polarization component). Specifically, since the residual depo-larizing field is proportional to (β − 1)⟨uz⟩,[24a] it can be readily seen that the change of β simply translates into adjusting such, self-exerted, “external” field. In the case of the sandwich het-erostructure both mechanisms come into play—the intrinsic bias electric field resulting from structural asymmetry plays the role of external field, while the intermediate STO layer along with imperfect screening at the sandwich interfaces reduces the effective screening β, and the combination of these effects results in a stable bubble domain structure. The effect of external stress is also well known[27]—positive stress stiffens the on-site potential, therefore effectively reducing equilib-rium dipole magnitudes. In fact, in the absence of the built-in bias voltage, large enough external positive stress would have inevitably resulted in suppression of any dipolar order. How-ever, intrinsic bias breaks the symmetry and allows for polar state at applied pressures above σ* (the corresponding state is equivalent to paraelectric state under applied external field). Then, being closer to a monodomain state than to a bubble configuration, the system transits to a metastable monodomain configuration after the pressure is released. Finally, subsequent application of an external electric field takes the system back to an equilibrium bubble domain state.[24a]

Note that these simulations did not find any cylindrical domain under these passes, which contrasts with the experi-mental case. Such feature i) may be due to our supercell not


Figure 6. Schematic of reversible manipulation for topological domain transition.

Figure 5. Reversible mechanical–electrical switching of the bubble domains. For each step the PFM amplitude is displayed on the bottom left with corresponding PFM phase to the immediate right. a) Step 1: the as-grown bubble domains are erased by mechanical force of 500 nN. b) Step 2: a new bubble domain is created by applying a +2.5 V pulse (0.01 s) in the mechanically switched region via an SPM probe, the voltage was applied from sample (bottom electrode) to the probe. c) Step 3: the new electrically written domain can be erased again by a second mechanical pass of 500 nN. Each scan size is 200 nm × 400 nm.



being large enough to see such cylindrical domains, which is consistent with the fact that these latter domains have sizes larger than 10 nm; but more importantly, ii) can also be taken as a further proof that the true ground state of the investigated systems are indeed bubble domains rather than cylindrical domains (as consistent with relaxation measurements).

3. Conclusion

In summary, controllable and reversible transformation of the topological domain structures in ultrathin PZT/STO/PZT heterostructures has been demonstrated. An SPM-tip based dual mechanical-electrical writing process is used to realize the deterministic transition between three topological states, namely, bubble, cylindrical, and single-domain matrix. The bubble domains can be precisely erased into single-domain matrix under an applied tip force and reversely recreated via short electrical pulses applied to the same tip. The domain size and topological states can also be manipulated by tuning the pulse width or bias amplitude. We anticipate these find-ings will now provide a pathway toward the exploitation of

topological domain transitions in ferroelectrics for advanced device applications.

4. Experimental SectionFilm Synthesis: Epitaxial PbZr0.2Ti0.8O3 (PZT)/SrTiO3/PbZr0.2Ti0.8O3

sandwich heterostructures were deposited on (001)-oriented stepped SrTiO3 substrates (Shinkosha Co., Ltd, Japan). La0.67Sr0.33MnO3 (LSMO) was used as bottom electrode in a thickness of 15 nm. Both LSMO and sandwich films were deposited using a pulsed laser deposition system (Neocera Co., Ltd, USA). The details of the preparation process have been reported previously.[5]

Piezoresponse Force Microscopy: The ferroelectric domain structure was investigated using a commercial scanning probe microscope (SPM, Cypher S, Asylum Research, USA). Conductive Cr/Pt coated silicon cantilevers (Budget sensor ElectricMulti75-G, Bulgaria) were used for domain imaging, mechanical switching, domain creation, and PFM hysteresis loop measurement. The force applied on the film was controlled by tuning the deflection (or set point) of tip toward the sample surface. The contact force and AC amplitude for domain reading are ≈50–100 nN, and ≈200–300 mV, respectively.

Mechanical Writing (Domain Erasure) and Domain Nucleation by Scanning Probe Microscopy (SPM) Tip: Mechanical erasure of the bubble domains was carried out by repeated scanning in a 15 × 200–300 nm2


Figure 7. 3D distribution of the [001] components of the local mode vectors uz (panel (a)) and the distribution of uz within the middle (001) plane of the supercell (panel (b)) at 250 K as obtained from temperature annealing simulations. Panels (c) and (d) show the corresponding 3D and cross-sectional distributions obtained after the simulated “mechanical pass” at uniaxial stress value of 4 GPa.



area with an SPM tip under a loading force in the range of 200–500 nN. The AC amplitude was set to zero during mechanical writing process. To find the optimized bias conditions for bubble domain nucleation, a series varying bias heights (+2.5 V to +3.5 V for a fixed pulse width of 0.01 s) and varying bias pulse widths (0.01–0.5 s for a fixed bias height of +2.5 V) were applied to a given region following the mechanical switching of polarization. When a bias above +2.5 V (i.e., +2.75 V to +3.5 V) was applied, cylindrical domains with distinct domain walls evidenced by the double-dip in the vPFM amplitude are produced. When the bias height was reduced to +2.5 V, a bubble-like domain with fuzzy domain boundaries was created. Using a slightly lower bias (i.e., at +2.25 V), no visible domains can be observed for either PFM amplitude or phase. Thus, the bias was fixed at +2.5 V and varied the pulse width from 0.01 to 0.5 s to observe the domain-growth kinetics.

Transmission Electron Microscope (TEM) and Electron Energy Loss Spectroscopy (EELS) Analysis: EELS was performed on a Thermo Fisher Themis G2 60–300 transmission electron microscope with Gatan Quantum system. The experiment was performed with the convergence angle of the incident electron beam ≈18 mrad and the collection angle of ≈30 mrad. Dual-EELS mode with a dispersion of ≈0.1 eV per channel was applied to simultaneously obtain both the zero-loss and the core-loss spectra, with the dwell time of core-loss spectra ≈0.1 s. In order to improve the signal/noise ratio of the spectrum, an EELS map of the heterostructures was first acquired and then processed by aligning the spectrum with respect to the zero-loss peak and integrating along the direction parallel to the interface.

Numerical Simulations: First-principles-based simulations were performed using the effective Hamiltonian model of PbZr0.4Ti0.6O3 ultrathin films. The upper PZT layer of the fabricated sample is mimicked by a 56 × 56 × 5 supercell with periodic boundary conditions along [100] and [010] crystallographic directions and partial electric screening at free boundaries along the [001] axis. The Hamiltonian has the following form

,

{ } ( )

eff ons ,,

,,

,

*0

*

H h J D u u q u u

c Z a Z ai i i i j i ji j i j i i i i

i i i vi i i ii di i

u

f v E E u E u

∑ ∑ ∑∑ ∑ ∑ ∑

σ η

η η σ β( )( ) ( )( )= + + +

+ + ⋅ − + ⋅ + ⋅

α β α β α βαβγ

γ α β

αβα β

(1)

where ui denotes the local mode attributed to the ith unit cell—a dimensionless vector proportional to its electric dipole moment (di = aZ*ui, where Z* and a are local mode Born effective charge and lattice parameter respectively). Variables σi describe alloying configuration (taking values of +1 or −1 depending on whether the corresponding B-site i is occupied by Zr or Ti) and iηγ denotes the γ component of the unit cell strain tensor in Voigt notation. The latter is split into sum of homogeneous and inhomogeneous contributions. This equation describes imperfect screening of bound charges modeled by linear mixing of dipole-dipole interaction terms[26,28] for open-circuit (⟨Ed⟩ term) and short-circuit ( ,

,Di jα β term) boundary conditions,

respectively (β = 0 corresponds to absence of screening, while β = 1 describes the case of complete screening). Since such approach introduces the compensating screening potential on both film’s surfaces in a symmetric way, we have further introduced a bias electric field E0 pointing from the top interface downward along the [00-1] direction so as to account for structural asymmetry stemming from interface difference of the fabricated heterostructure. Such bias field is added to the external field E and its value of −0.43 V nm−1 (−4300 kV cm−1) was chosen so that the equilibrium state at 250 K corresponds to a phase of bubble domains at the realistic value of β = 0.8 used in current simulations. Other energy terms of the employed effective Hamiltonian model include on-site energy—sum of fourth-order polynomials hons(ui,σi) in local mode components that describes crystalline anisotropy due to perovskite unit cell structure. Specifically,

ons2 4

,2

,2

,2

,2

,2

,2

h

u u u u u ui i i i

i i x i y i x i z i y i z u i i

u u

f u

κ σ δκ α σ δαγ σ δγ σ( ) ( )

( ) ( )( ) { }

= + + ++ + + + +

(2)

The effect of alloying was also taken into account in hons(ui,σi) by introducing for each unit cell i an Ising variable σi taking values of +1 or −1 depending on whether the corresponding B-site is occupied by Zr or Ti. These variables were used to introduce local change of unit cell volume, change of stiffness (δκ and δα), and crystalline anisotropy (δγ), as well as appearance of local forces fu({σi}) due to compositional breaking of local cubic symmetry. The distribution of Zr and Ti atoms was assumed to be random. Moreover, the Hamiltonian included short-range interactions (up to third nearest neighbors) described by anisotropic ,

,Ji jα β tensor; long-range electrostatic interactions computed

using Ewald summation technique ( ,,Di j

α β term); electrostriction (qαβγ coefficients) and elastic energy (cαβ denotes elastic constants tensor in Voigt notation) stemming from homogeneous and inhomogeneous lattice deformations.[24b-d,26,28] The inhomogeneous deformations of each unit cell were derived from displacement vectors vi mapped on A sites of the lattice. These vectors were also subjected to local forces fv depending on the local distribution of σi variables as a result of alloying. Epitaxial conditions were mimicked[26] by fixing the in-plane homogeneous strain (η11 = η22 and η12 = η21 = 0) and allowing relaxation of the remaining strain tensor components. The set of ab initio obtained parameters for PZT used in this study can be found in ref. [24c].

Supporting InformationSupporting Information is available from the Wiley Online Library or from the author.

AcknowledgementsThe research at the University of New South Wales (UNSW) was supported by an Australian Research Council (ARC) Discovery Project and partially supported by the Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies (project number CE170100039) and funded by the Australian Government. S.P., Y.N., L.B., and N.V. thank the financial support of the DARPA Grant No. HR0011727183-D18AP00010 (TEE Program). Y.N. and L.B. also acknowledge support of the ARO grant W911NF-16-1-0227. A.G. acknowledges support of the Nebraska Materials Research Science and Engineering Center (MRSEC, grant DMR-1420645).

Conflict of InterestThe authors declare no conflict of interest.

Keywordsbubble nanodomains, mechanical switching, scanning probe microscopy, ultrathin ferroelectric films

Received: December 3, 2018Revised: April 15, 2019

Published online:

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