Strain modulation of TaO4 planarity in tantalates ultrathin films: surface states engineering.

Ultrathin films of perovskites have attracted considerable attention once they fit in numerous applications. Over the years, controlling and tuning their properties have been attainable when biaxial strain is applied. Through ab initio DFT calculations, (110) ultrathin (Na,K)TaO3 films were submitted to biaxial tensile and compressive strain. Intrinsically, surface Ta shallow states emerge into the bandgap since the (110) cleavage breaks its octahedral symmetry to create TaO4 units. Removal of ligands along the x-y plane stabilizes dx2-y2 orbitals, which decrease in energy due to lower electrostatic repulsion. Such stabilization is maximized when biaxial tensile increases the TaO4 planarity towards a square planar symmetry. Accordingly, the corresponding electronic levels move further into the bandgap. Conversely, compressive biaxial strain intensifies electrostatic repulsion, closing the TaO4 tetrahedra, and surface states move to higher energy zones. The reported strain-driven modulation might be applied in different applications, as photocatalysis, ferroelectricity, and spintronics.

properties tuned and controlled when strain (stress) is induced 17,18 . The effects of biaxial strain have been frequently explored due to the surprising responses obtained when it comes to properties' modulation, which ranges from induction of dielectric anomalies 19 to bandgap engineering 20 . To control the amount of induced strain, substrates with different mismatches with the films are usually employed 21 . The application of an electric field to a piezoelectric substrate has also been used to induce biaxial strain and modulate specific properties 22 . Additionally, developed synthesis methodologies have granted refined control of surface particle size as well as surface area and morphology in thin films, not to mention the fact that characterization techniques that are usually difficult to be implemented for nanoparticles (scanning probe microscopy, for instance) can be readily used in 2-D materials 23,24 . Therefore, studying the influence of surface BO x arrangements on ultrathin films should provide clear evidence of their role in controlling electronic properties.
Recently, several experimental reports have driven their attention to the synthesis of ABO 3 thin films, such as NaTaO 3 24,25 and KTaO 3 [26][27][28] , on different substrates and heterostructures. Amazingly, angstroms-thick perovskites ultrathin films have already been achieved [29][30][31][32] , which supports reliable theoretical and experimental comparisons. Furthermore, the modulation of perovskite properties by means of biaxial strain is also widely reported and highly relevant to various applications. Magnetic, electrical, and transport properties, for example, react significantly to strain and can therefore be tuned 33,34 . Strain-induced lattice deformation (octahedral tilting) 35 as well as photoluminescence features 36 have also shown considerable changes upon biaxial strain. Here, through ab initio density functional theory 37,38 , we have systematically studied the effects of biaxial strain on (110) cubic (Na,K) TaO 3 ultrathin films, emphasizing how the geometric arrangement of surface-exposed TaO 4 tetrahedra influence their electronic structure. Shallow surface states of Ta e g orbitals are located below the conduction band (CB) and can be pushed either into or out of the bandgap as strain is applied and TaO 4 planarity varies. Biaxial tensile strain increases Ta-O bond distances and the unit planarity, stabilizing e g orbitals and shifting surface states into the gap. The opposite movement is produced when biaxial compressive strain reduces Ta-O bond distances and makes TaO 4 units less planar. To the best of our knowledge, the aforesaid structural-electronic connection has not been reported hitherto and allows bandgap states engineering, which is desirable in many different fields.

computational Details
Our calculations have run on Vienna Ab Initio Simulation Package (VASP) 39,40 , with electron-ion interactions described by projector augmented-wave (PAW) 41 pseudopotentials. For electrons exchange-correlation interactions, the generalized gradient approximation (GGA) within the PBE functional 42 has been used. To sample the Brillouin zone, k-points meshes were generated following the Monkhorst-Pack 43 scheme. During geometry optimizations, plane-wave cutoff energy of 520 eV and electronic energy convergence for self-consistent iterations of 10 −8 eV were set, aiming at accurate results.
In order to have a reference from which ultrathin films could be built using a slab approach, we have first optimized KTaO 3 (KTO) and NaTaO 3 (NTO) cubic Pm3m bulk structures, performing 11 × 11 × 11 k-points integrations. The equilibrium lattice parameters were a 0 KTO = 4.04 Å and a 0 NTO = 3.98 Å, which are in agreement with experimentally reported values 44,45 . Typical semiconductor band structures (Fig. 1S) with a Γ-R indirect bandgap of 2.07 eV (KTO) and 2.26 eV (NTO) have been obtained. Despite being well-known that GGA underestimates the bandgap when compared to experimental data 45,46 , it agrees with other similar theoretical studies 47,48 .
Ultrathin KTO and NTO films were constructed by replicating the bulk and cleaving it in the (110) direction. Thus, 12 layers thick (~31 Å) films that expose such a surface were relaxed with a 15 Å vacuum to minimize image self-interactions from periodic boundary conditions. The k-points integration was performed up to a 5 × 1 × 5 grid. To simulate in-plane epitaxial strain, the interplane x-z lattice constants were changed up to −4% and 4% for compressive and tensile strain, respectively. We designated the strain as , where α KTO,NTO is the strained lattice parameter and a 0 is the bulk optimized lattice parameter.

Results and Discussion
According to the equilibrium structure of the films, biaxial strain may induce changes in both structural (bond angles, bond distances, crystallinity, etc.) and electronic properties (bandgap, electronic states, Fermi level, etc.). Strain-free, tensile σ = 4% (α KTO = 4.02 Å, α NTO = 4.14 Å), and compression σ = −4% (α KTO = 3.88 Å, α NTO = 3.82 Å) converged structures are displayed in Fig. 1. For both KTO and NTO, strain-free films are more stable than those under tensile and compressive strain (Fig. 2S). Despite exposing polar terminations with non-zero formal charges, no surface reconstruction has been observed. Therefore, an electronic reconstruction mechanism will compensate the polarity induced by the cleavage. KTO structures retain their cubic lattice and relaxation occurs by changes in the interlayer spacing along the y-axis. NTO films, in turn, relax by similar mechanisms but also allow the rotation of internal TaO 6 and surface TaO 4 units. Note that under biaxial compression, the film acquires a more orthorhombic character while the bulk cubic group spacing can be partially recovered under tensile. A closer look at surface layers reveals a common feature presented by both films upon relaxation. Under biaxial compression (σ < 0%), Ta-O bond distances decrease and TaO 4 tetrahedral units become less planar, whereas under biaxial tensile strain (σ > 0%), Ta-O bond distances increase and so does their planarity. We here call planarity (P L ) an average of in-plane O-Ta-O angles so that the upper planarity limit corresponds to both x and z plane angles being 180°.
Since surface states are crucial in the electronic structure of low dimension materials, we have plotted the projected density of states on the potassium (K) s, oxygen (O) p, and tantalum (Ta) d orbitals in Fig. 2. As in bulk, the valence band maximum consists of O 2p states and the conduction band minimum is mostly Ta 5d levels with a slight O 2p contribution, which indicates d-p (π) hybridization states. Nevertheless, a metallic character is observed in all films as a consequence of their polarity, which induces electronic reconstruction by filling up conduction states. It is interesting to note that there are spin up well-localized energy states near the CB which appear to be shallow and within the bandgap, especially under tensile. The layer resolved projected density of states (LRPDOS, Fig. 3S) confirms that such states are derived from surface TaO 4 units. Under compressive conditions where σ < 0%, these states migrate to higher energy regions, eventually entering the CB energy zones. When tensile acts on the system, σ > 0%, the opposite behavior is observed and they move to lower energy zones within the material's bandgap. Oppositely, when tensile is applied, σ > 0%, they move into the bandgap. Black dashed lines represent the Fermi levels, and the plots were aligned according to their electrostatic potential.
The band structure of the films (Fig. 3) helps in describing such TaO 4 surface states, pointing out their energy difference (ΔE) regarding the CB. A complete plot of both P L and ΔE as functions of σ can be seen in Fig. 4 (all the related data is in Table 1S). It turns out that for σ = 0% both KTO and NTO surface states are already separated from the CB by a total of ΔE = 0.08 eV for the former and ΔE = 0.21 eV for the latter, which characterizes them as shallow states within the bandgap. The planarity values of TaO 4 surface tetrahedra are P L = 77.4% (KTO) and P L = 79.1% (NTO). When the tensile limit of σ = 4% is achieved, such planarity rises to 80.7% and 81.5%, respectively. Accordingly, ΔE increases to 0.33 eV (KTO) and 0.30 eV (NTO), which sets the levels even further into the gap. On the other hand, when the compression limit of σ = −4% is reached, P L of surface TaO 4 units reduces to 70.4% for KTO and 71.5% for NTO. This approximates surface states and the CB, resulting in a significant bands overlap for KTO, and reducing ΔE to 0.05 eV for NTO. The above results shall be explained in two different but complementary discussions: (i) the reason why surface Ta d states lie below the CB; (ii) the way biaxial strain changes the position of such states.
As for the first, we have to consider the consequences that cleaving atomic bonds triggers on an initially TaO 6 octahedral (O h ) symmetry existing in bulk KTO and NTO. As part of a group five transition metal, the five-fold degenerated Ta d orbitals are split by the ligand field of six oxygen atoms approaching along the axes, forming a set of doubly-degenerated e g (d z 2 and − d x y 2 2 ) and triple-degenerated t 2g (d xy , d yz , d zx ) orbitals. Being oxygen a π-donor ligand, charge transfer occurs through π bonds due to lateral overlap of ligand O 2p and Ta t 2g orbitals, which causes their energy to decrease. On the other hand, e g orbitals rise in energy since their interactions with ligand orbitals are mostly repulsive (σ*) 49 . Consequently, in the TaO 6 bulk arrangement, the CB is composed by Ta t 2g -Op (π*) bands followed by a higher lying set of Ta e g -O p (σ*) bands. Cleaving the crystal in order to reduce  www.nature.com/scientificreports www.nature.com/scientificreports/ the unit coordination to TaO 4 removes two oxygen ligands. In such cases, the absence of ligands along the axes stabilizes the corresponding e g orbital, reducing their repulsive interactions 50 . Therefore, e g orbitals shall lower in energy but now with the degeneracy broken since d z 2 and − d x y 2 2 will not be equally stabilized. For instance, changes in the ligand field as it moves from octahedral to a square planar symmetry are generally described as a consequence of removing two ligands along the z-axis, which stabilizes d z 2 orbitals electrostatically and increases the energy of − d x y 2 2 orbitals that now suffer the greatest repulsion 51 (Fig. 4S). For the proposed thin films, the (110) cleavage removes two cis oxygen atoms, leaving initially 'butterfly' TaO 4 complexes on the surface. Such a cleavage cut out half of − d x y 2 2 interactions, while the main electrostatic repulsion in z remains the same, as illustrated in Fig. 5(a). The O-Ta-O angles may acquire variable values, changing the TaO 4 planarity so that tetrahedral (T d ), square planar (D 4h ), and intermediate symmetries are allowed. In the studied structures, relaxation induces intermediate values of planarity to reach the structure equilibrium, balancing electrostatic and steric interactions. Figure 5(b) reveals the e g nature of surface states near the CB, confirming the stabilization of − d x y 2 2 orbitals caused by the (110) cleavage. The small contribution of d z 2 states result from a slight stabilization of its central lobe that reduces in energy when two weak antibonding interactions are removed.
As for the way that biaxial strain changes the position of surface Ta d states, an individual investigation of isolated TaO 4 units is required. We have calculated TaO 4 tetrahedral groups with different spatial arrangements in 20 Å vacuum supercells (oxygen atoms were saturated with hydrogen to mimic their coordination in both bulk and films). In addition to the configurational case of the strain-free KTO film, we have also calculated TaO 4 units with the coordinates and hence planarity in which they are found on KTO film surfaces when σ = ±4%. In the left panel of Fig. 5(c), starting from the strain-free tetrahedra (σ = 0%, d xy ( )   Table 2S. The central panel of Fig. 5(c) illustrates the weakening or strengthening of repulsive interactions between antibonding Ta e g -O p orbitals when tensile or compression is applied, respectively. The consequence in the material's electronic structure is depicted on the right panel. The projected density of states reveals that as a (110) cleavage is performed in the cubic bulk, − d x y 2 2 and d z 2 states are stabilized and appear occupied (spin-up) below the Fermi level after structural relaxation. If biaxial tensile strain is applied in the x-z plane, Ta-O bonds will stretch, repulsive d-p interactions along such axes will decrease, and e g orbitals are stabilized. Conversely, biaxial compression along x-z brings atoms close together, repulsive d-p interactions increase, and e g orbitals rise in energy.
Finally, we note the fact that the electronic structure of ultrathin KTO films appears to be more sensitive to changes in surface TaO 4 planarity than NTO films. As shown in Fig. 4 (left y-axis), the planarity of superficial TaO 4 groups in both films respond very similarly to biaxial strain. Showing an essentially linear variation, the P L increases under tensile and decreases under compression, following basically the same slope. On the other hand, the linear coefficient is smaller for the KTO film than for the NTO one, what indicates that the initial planarity of the former is intrinsically lower than that of the latter. Since potassium has an extra electron shell compared to sodium, and hence a larger atomic radius, the repulsion felt by the superficial K-Ta-O arrangement is greater than in the case of Na-Ta-O, which initially prevents KTO-TaO 4 groups from being as planar as NTO-TaO 4 ones. As the electrostatic interactions are stronger for KTO, it was expected that its electronic structure would change more sensibly upon strain, as shown in Fig. 2. The exact influence of A-site cation on this type of process is still under investigation, nevertheless.
We also suggest that there are upper and lower limits of planarity that biaxial strain is able to induce. Despite the almost linear behavior of P L as a function of strain, too high tensile values stretch Ta-O to such an extent that the TaO 4 coordination might be broken. In turn, too high compressive values maximize electrostatic and steric repulsions. For the KTO film, for instance, the repulsion at σ = −4% is such that potassium atoms start a exsolution-like process and are "expelled" from the surface of the film, TaO 4 planarity values decrease drastically, and the electronic structure changes considerably. When the maximum tensile is achieved, in turn, both films tend to the similar planarity values and to the same ΔE maximum of ~0.30 eV from which greater P L is only achieved if more severe strain that irreversibly destabilizes the system is applied.

Conclusions
In conclusion, the (110) cleavage in cubic KTaO 3 and NaTaO 3 crystals made to obtain ultrathin films modifies the Ta d orbitals degeneracy and local electrostatic interactions to such an extent that shallow surface states can be manipulated by biaxial strain. Cleaving the crystal in such direction naturally induces − d x y 2 2 orbitals stabilization and introduces them near the CB. We systematically investigated and showed that biaxial tensile or compression modifies surface TaO 4 planarity, and therefore the energy of electronic defect states. Biaxial tensile pushes them further into the material's bandgap while compression moves them towards the CB. As the behavior is generically the same for both different tantalates, we report a practical way of tuning their electronic properties through biaxial strain. Our results elucidate meaningful structural-electronic relationships that can be readily harnessed to control and engineer bandgap energy states. Although further investigation is required to connect such results with tactile applications, the proposed engineering may be widely desirable. For photocatalysis (the main application of NaTaO 3 nanostructures), for instance, the alignment of CB and VB states with the water redox potentials is a major challenge and usually achieved by doping. Such strain-driven modulation may be effective and rule out the use of foreign materials. Concerning less explored applications, as spintronics, the magnetic characteristics of the system can be useful for building spin filters or similar devices.