Strain-Engineered Ferroelastic Structures in PbTiO3 Films and their Control by Electric Fields.

We study the interplay between epitaxial strain, film thickness, and electric field in the creation, modification, and design of distinct ferroelastic structures in PbTiO3 thin films. Strain and thickness greatly affect the structures formed, providing a two-variable parameterization of the resulting self assembly. Under applied electric fields these strain-engineered ferroelastic structures are highly malleable, especially when a/c and a1/a2 superdomains coexist. To reconfigure the ferroelastic structures and achieve self-assembled nanoscale-ordered morphologies, pure ferroelectric switching of individual c-domains within the a/c superdomains is essential. The stability, however, of the electrically written ferroelastic structures is in most cases ephemeral; the speed of the relaxation process depends sensitively on strain and thickness. Only under low tensile strain-as is the case for PbTiO3 on GdScO3-and below a critical thickness do the electrically created a/c superdomain structures become stable for days or longer, making them relevant for reconfigurable nanoscale electronics or non-volatile electromechanical applications.


INTRODUCTION
Ferroelastic structures, many of them formed by ferroelectric-ferroelastic domain architectures, have attracted significant attention in the last few years. [1][2][3][4][5][6] On the one hand, the polar character of the ferroelectric domains has promoted a wide array of electronic properties-from insulating to highly conducting-at the ferroelectric-ferroelastic domain walls, which can greatly differ from those of the parent material. [7][8][9][10][11][12][13] Unlike the interfaces grown into multilayer structures that are fixed, domain walls can be created, moved, and erased by an electric field. This makes ferroelastic structures attractive for novel applications in reconfigurable electronics.
Additionally, ferroelastic switching and the generation of user-defined ferroelastic-ferroelectric structures by an electric field 5,14 can provide new methodologies for (nano-)electromechanics and piezoelectric devices. 15,16 On the other hand, the electrical switching of ferroelastic structures in epitaxial films may be impeded by elastic constrains imposed by the substrate [17][18][19][20][21] or their elastic pinning to defects, 22 making the ferroelastic domain walls less mobile than their exclusively ferroelectric or magnetic counterparts. It is thus essential to not only engineer new ferroelastic structures, but also to assess the feasibility of the electric-field control of these structures and their stability over time.
Here we focus on the model ferroelectric PbTiO3. This compound offers a rich epitaxial-straindependent domain phase diagram at room temperature 5,23-25 that allows a multitude of ferroelectric-ferroelastic structures. Significant progress in the electrical switching of ferroelastic domain walls between a-and c-domains¾tetragonal domains with polarization parallel to the substrate-film interface and along the out-of-plane direction, respectively¾has been reported, either in PbTiO3 thin films or related Pb(Zr,Ti)O3 films. [26][27][28][29][30][31] Electrical reconfigurability has varied considerably, ranging from a very little 29 to significant annihilation of a-domains (domains with a-axis oriented perpendicular to the plane of the PbTiO3 film). 27 To enhanced the mobility of ferroelastic domain walls, composition gradients have been employed. 30 Another approach recently applied to epitaxial films involves the possibility of modifying superdomains-ferroelastic structures comprised of an agglomerated bundle of ferroelectric domains arranged in a particular pattern 32,33 -by applying an electric field. 5 Examples of superdomains are bundles of 90° stripe domains. 32,33 A complete picture of the ferroelastic switching in PbTiO3 is lacking, especially understanding the interplay between epitaxial strain, thickness, and electric field. In this work, we systematically investigate the thickness dependence and the electrical switching of a wide variety of strained-engineered ferroelastic structures in epitaxial films of this compound. PbTiO3 films, ranging from 20 to 75 nm in thickness, are grown by reactive molecular-beam epitaxy (MBE) onto (110)-oriented rare-earth (RE) scandate single-crystal substrates, where RE = Dy, Tb, Gd, and Sm. We show that the domain configuration can be effectively tuned by altering strain and film thickness simultaneously, which opens the possibility of designing, at will, different ferroelectric-ferroelastic configurations using these two variables. We find that applying an electric field can heavily disrupt the domain ground state found at a particular thickness and strain: the as-grown ferroelastic structures are all highly reconfigurable. We develop an understanding of the mechanisms underlying the ferroelastic-ferroelectric switching, the electrical rearrangement and ordering of ferroelastic structures, and in particular the stability of the electrically written domain and superdomain patterns over time. Our findings pave the way for the design of non-volatile ferroelastic structures that can be harnessed in reconfigurable nanoscale electronic circuitry, 9 in electromechanical applications, 5,29 or even in ferroelectricbased phononic devices. [34][35][36][37]

EXPERIMENTAL SECTION
Thin film growth. PbTiO3 thin films were grown by MBE in a Veeco GEN 10 system using distilled ozone as an oxidant and elemental lead and titanium as source materials. Lead is supplied from a conventional MBE effusion cell, whereas titanium is sublimed from a Ti-Ball TM (Varian Associates, Vacuum Products Division). 38 During growth lead and titanium were continuously codeposited, achieving phase-pure PbTiO3 in the growing film by adsorptioncontrol, where the desorption of the excess lead supplied is controlled automatically by thermodynamics. 39 Typical lead and titanium fluxes were 1.7x10 14 and 1.5x10 13 atoms/(cm 2 ·s), respectively. Distilled ozone, which consists of about 80% O3 and 20% O2, was used as the oxidant. 40 The background pressure of distilled ozone during growth and the substrate temperature were fixed to 9x10 -6 Torr and 600 °C, respectively. The growing film was continuously monitored by reflection high-energy electron diffraction (RHEED) to stay within the adsorption-controlled growth window. 39 After deposition, the films were cooled down at »100 °C/min, in a background pressure of 5x10 -6 Torr of distilled ozone. PbTiO3 films were grown on (110)-oriented orthorhombic DyScO3, TbScO3, GdScO3, and SmScO3 substrates that impose biaxial strains ranging from -0.25% (compressive) to +0.71% (tensile). A 10 nm thick SrRuO3 layer was grown on the aforementioned substrates by MBE immediately prior to the growth of the overlying PbTiO3 without breaking vacuum. These SrRuO3 bottom electrodes were grown by codepositing strontium and ruthenium in an adsorption-controlled regime 41 using a mixture of O3 (»10%) and O2 (»90%) as the oxidant species. Strontium was supplied by an effusion cell, while an electron-beam evaporator was used for ruthenium. The pressure of the oxidant mixture gas and the substrate temperature were 1x10 -6 Torr and 690 °C, respectively.
Thin film characterization. q/2q X-ray diffraction measurements (XRD) were performed using a four-circle diffractometer (PANalytical X'Pert PRO) with Cu Ka1 radiation and the 220 reflections of a four-bounce channel-cut germanium crystal as a monochromator. Reciprocal Space Maps were performed using a four-circle diffractometer (PANalytical Empyrean) with a PIXcel 3D area detector. The surface topography and the ferroelectric domain and superdomain configuration were assessed by atomic force microscopy (AFM) in contact mode and piezoresponse force microscopy (PFM) in dual ac resonance track (DART) mode, respectively,   superdomains (formed by 90° domain walls) are found to increase in size as the lateral size of the dots increases. 33 Here, it is the thickness of the film that augments and affects all types of superdomains (a/c and a1/a2) with all kinds of superdomain walls. Superdomains thus behave as individual ferroic entities to which the same arguments used for ferromagnets, 45 ferroelectrics, 46 and ferroelastics 47 should also apply: the energy cost of adding a superdomain wall increases with film thickness. Furthermore, superdomain walls might have a significantly higher energetic cost than individual domain walls as they impose electrostatic or mechanical incompatibilities, 50 explaining their rapid decrease with increasing film thickness.   37,42,51 In other words, the normal vector of the in-plane base of the unit cell of these domains is tilted with respect to the out-of-plane direction of the film (normal to the substrate interface). We refer to these domains as "tilted" in the sketch in Figure 4.
Conversely, the a-domains forming a1/a2 superdomains do not tilt with respect to the out-ofplane direction, 5 that is, the in-plane base of the unit cell is parallel to the surface of the substrate.
We refer to these a-domains as "non-tilted" in   (Figure 3). This is also corroborated by the PFM images (Figure 2a This rapid thickness-dependent transition of the domain patterns in the tensile-strained PbTiO3 films arises from the rapid increase in the population of c-domains with thickness, as proved by the q-2q XRD patterns (Figure 5a,b). This behavior was predicted to occur in tetragonal ferroelectric films as a mechanism to relieve epitaxial strain. 52 In practice, the thickness trend ( Figure 2) is analogous to the strain trend in going from tensile to compressive strain (Figure 1), giving rise to the same domain pattern evolution: from mainly a1/a2 superdomains to a/c domain architectures. Thus, it is possible to design at will the type of domain architecture and the desired ratio between a/c and a1/a2 superdomains by selecting the appropriate strain and thickness of the PbTiO3 film. to be annihilated. 29 The a/c domain structure thus appears to be quite robust. Yet, by applying an increased voltage (+5 V) to an as-grown region, a significant number of a-domains are erased so long as the electric field is applied ( Figure S4 in Suppl. Info.). Therefore, reconfiguring the a/c domain architecture (which involves ferroelastic-ferroelectric switching) seems to be energetically costlier than just switching the c-domains within the ferroelastic structure (pure ferroelectric switching). Nonetheless, new a-domains appear immediately after the electric field is removed ( Figure S4 in Suppl. Info.), reverting to the same density of a-domains as in the asgrown equilibrium state. Conversely, the pure ferroelectric switching of c-domains within the a/c domain architecture is extremely stable.
When the thickness is reduced (t = 32 nm), applying an out-of-plane electric field causes a noticeably larger annihilation of a-domains (Figure 6c,d)-compared to the thicker filmresulting in long a-domains, similar to what is found in PbZr0.1Ti0.9O3 films. 27 In addition, the electrically written pattern remains after the applied voltage is removed (Figure 6d  Pure ferroelectric switching of the c-domains is thus seen to be robust, whereas the ferroelastic switching of the a/c patterns is not very stable. The a-domains form in order to relieve the accumulated elastic energy, which leads to an equilibrium ferroelastic-ferroelectric state imposed by the epitaxial strain and thickness. When altered, relaxation occurs towards the ferroelastic ground state. This altered state differs more and more from the initial state as the PbTiO3 films get thicker. Relaxation is immediate in the 75 nm thick film and more progressive and incomplete in the 32 nm thick film. The depolarizing field does not depend on thickness and moreover it can be screened over time. In contrast, elastic energy is proportional to the thickness and can never be screened. Therefore, it makes sense that, as films get thicker, elastic forces dominate over electrostatic ones and thus the films revert faster to their original ferroelastic configuration. This finding is important to consider when it comes to designing functional properties at a/c domain walls 9 or non-volatile ferroelastic switching devices based on a/c domain architectures. 29 We now assess the scenario in which a/c and a1/a2 superdomains coexist with almost equal populations as is the case for PbTiO3 (t < 50 nm) on GdScO3. Figure 7a analyzes    When a negative dc bias voltage from the PFM tip is applied (Figure 7b  The stability over time of the written a/c superdomains (both maze-distributed and ordered stripes) is shown in Figure 8. The electric field was applied to the area delimited by the dashed red rectangle. As is evident, the electrically written ferroelastic structures are rather robust. They last for at least several days in this form after the applied voltage is removed. An expansion of the a1/a2 superdomains is evident in the initial hours, which gradually compresses the a/c superdomains. This shows that parts of the a/c superdomains relax into a1/a2 superdomains by moving the superdomain walls, making the former smaller, instead of completely turning the whole superdomain into a1/a2. The latter would appear as a change in the maze-shape or stripeshape superdomain pattern. The expansion of the a1/a2 domains slows down over time and the final stable written structure contains a higher density of a/c superdomains than the as-grown one, as we quantify in the next Section. Hence, it is possible to stabilize long-lasting metastable superdomain configurations in PbTiO3 on GdScO3. On the other hand, the upward-poled cdomains of the stripe-shape pattern are mainly maintained; a few c-domains flip their polarization to the as-grown state after several days (Figure 8b bottom panel).
For thinner films (~20 nm) grown on GdScO3 the domain pattern is fully transformed by applying a vertical voltage into an a/c domain architecture. All of the a1/a2 superdomains are erased as is shown in Figure S6 of the Suppl. Info. It is as if the PbTiO3 were grown on DyScO3.
Moreover, no relaxation of the pattern is seen with time, further establishing the strong stability of the electrically switched ferroelastic structures in PbTiO3 films grown on GdScO3.
The electric-field dependence of a domain architecture dominated by a1/a2 superdomains (PbTiO3 on SmScO3) is shown in Figure 9. During writing the whole domain pattern transforms into an a/c domain architecture, as also occurs when a voltage is applied to PbTiO3 on GdScO3, even though in this PbTiO3 on SmScO3 case we start from a mainly a1/a2 superdomain structure.
Thus, even if the epitaxial strain determines a strong presence of a1/a2 domains, the application of a vertical voltage is able to turn all of them into a/c patterns. This demonstrates the high electrically malleability of the ferroelastic structures in PbTiO3 when different types of superdomains coexist. The electrically written a/c superdomains are, however, rather short lived once the electric field is removed. In contrast to the relaxation that occurs for PbTiO3 on GdScO3, here all of the a/c superdomains revert to a1/a2 superdomains, progressively disappearing over time as shown in Figure 9. Similar rapid reversion to the as-grown equilibrium a1/a2 domain pattern is also found for thinner PbTiO3 on SmScO3 films (see Figure S7 of the Suppl. Info.). Thus, the large tensile strain imposed by the SmScO3 substrate (+0.71%) prevents the written a/c superdomains from lasting, precluding the stabilization of nanoscale ferroelastic structures in this case. Nonetheless, it is worth noting that some residual a/c superdomains after switching look like droplets, similar to the bubble domains found in 180-degree domain configurations. 53 These ferroelastic "bubble superdomains" are a rare feature as these kinds of structures are generally absent in ferroelastic domain configurations. the previous cases where a unique out-of-plane polarization was observed over the whole sample. This may explain the less ordered a/c stripes that can be written on SmScO3. The lack of a unique out-of-plane polarization direction means that regardless of whether a positive or negative dc bias voltage is applied to the as-grown a/c superdomains, the out-of-plane polarization of many of the superdomains will point in the same direction as the external electric field, resulting in a mix between maze-and stripe-shaped a/c superdomains.
Time relaxation of the electrically written a/c superdomains. We quantify the time evolution of the relaxation of the written a/c superdomains into a1/a2 superdomains, both when they become narrower (on GdScO3) and when they disappear (on SmScO3). To do so, we have computed the amplitude of the vertical PFM images of ~50 nm thick films on both substrates to account for the quantity of a1/a2 and a/c superdomains present at each time. The quantity of a1/a2 and a/c superdomains are shown in black and orange in Figure S9 of the Supplemental Info. Figure 10 shows the time dependence of the areal percentage occupied by a/c superdomains in the PFM image, starting at time = 0 when the voltage is applied (which corresponds to 100% of the total area). On both GdScO3 and SmScO3 substrates a rapid decrease in a/c superdomains occurs after the applied voltage is removed, which slows down over time. The relaxation of domains in other ferroic materials tends to follow either an exponential or a power law decay, 3 which suggests that our superdomain structures could display similar trends. The exponential decay was found to fit our data better. The solid orange line in Figure 10 depicts the experimental data fit to the exponential function y = A0exp(-t'/t0) + y0, where y is the percentage of a/c superdomains in the pattern, A0 is a proportional constant which accounts for the initial fraction of a/c superdomains induced by the electric field (at t' = 0), t' is time, t0 is the relaxation time, and y0 is the residual presence of a/c superdomains for t' ® ¥. The A0 and t0 values depend on the elastic energy cost of the superdomains, which in turn depends on thickness and mismatch strain. The larger either of these quantities is, the faster the relaxation will proceed.
The fit matches the data reasonably well, better on GdScO3 than on SmScO3. This may be due to the superdomains disappearing completely on SmScO3 instead of the more gradual shrinking that occurs on GdScO3. The relaxation time¾accounting for how quickly the relaxation process takes place¾is much larger (200% larger) on GdScO3 (t0 ~ 18 minutes) than on SmScO3 (t0 ~ 9 minutes). This reflects the significantly faster conversion of written a/c superdomains into a1/a2 superdomains with increasing tensile strain (as qualitatively revealed in Figures 8 and 9). y0 is found to be slightly larger than the areal occupation of a/c superdomains in the as-grown films for both scenarios. This implies that the relaxation process is incomplete on both substrates and that the final domain configuration after applying the out-of-plane voltage is enriched in a/c superdomains compared to the as-grown scenario.

CONCLUSIONS
In summary, we have systematically investigated the evolution of ferroelastic structures in PbTiO3 films as a function of epitaxial strain, film thickness, and voltage applied by a PFM tip.
The kind of domain architecture does not change with thickness for exclusively a/c domain patterns, but it does when the domain patterns contain a mixture of a/c and a1/a2 superdomains.
Specifically, the presence of c-domains significantly increases with film thickness, promoting the increase of a/c superdomains at the expense of a1/a2 superdomains. We find that the balance between a/c and a1/a2 superdomains can be tipped, not only by strain, but also by thickness, providing an extra degree of freedom to engineer ferroelastic structures. We also show that the ferroelastic structures in PbTiO3 are quite malleable when an electric field is applied. The a/c domain architectures can be completely reconfigured by annihilating most of the a-domains. The stability of the new pattern is, however, short-lived, especially for thicker films. When a/c and a1/a2 superdomains coexist, the out-of-plane electric field turns all a1/a2 superdomains into a/c superdomains. The ferroelectric switching of c-domains is found to be essential to imparting designed a/c superdomain morphologies. Larger tensile strains destabilize the written a/c superdomains. At a biaxial strain of 0.71% (PbTiO3 on SmScO3) these quickly decay-relaxing to a1/a2 superdomains-when the electric field is removed. Only for low tensile strains (e.g., PbTiO3 on GdScO3) are electrically created a/c superdomains stable for days. Our findings demonstrate the feasibility of tailoring stable ferroelastic structures in PbTiO3 films that are relevant to non-volatile electromechanical applications or reconfigurable nanoscale electrical properties.