ATiO$_{3}$/TiO (A=Pb, Sn) superlattice: bridging ferroelectricity and conductivity

TL;DR

This study uses first-principles calculations to explore ATiO3/TiO superlattices, revealing anisotropic conductivity and potential ferroelectric control, and proposes a method for designing novel materials through layered combinations.

Contribution

It introduces a computational approach to design superlattices with tailored ferroelectric and conductive properties by layering perovskites and metal oxides.

Findings

Superlattice exhibits strong anisotropic conductivity.

Ferroelectricity can potentially control conductivity.

Structural phases evolve with epitaxial strain.

Abstract

We propose to insert TiO layers to perovskite ATiO$_{3}$ to form a superlattice and use first-principles calculations to investigate its basic properties. Our computational analysis shows that the structure, which consists of repeated ATiO_{3} and TiO layers, has strong anisotropic conductivity. The structure immediately suggests a possible control of its conductivity by ion displacements related to its intrinsic ferroelectricity. In addition, we have obtained the structural information of its low-energy phases with the aid of phonon calculation and examined their evolution with epitaxial strain. Since the number of possible combinations is huge, we have therefore suggested an approach to mix perovskites and simpler metal-oxides to build materials with novel properties.

Tables

Table 1. Table 1: Structural information of the ATiO 3 -TiO (A=Sn,Pb) superlattice after relaxation. Note the rocksalt TiO has a lattice constant of 4.177 Å and the energy unit is meV per formula.

Space group		$a$(Å)	$b$(Å)	$c$ (Å)	$\alpha$	$\beta$	$\gamma$	Energy
SnTiO3/TiO	$P4/mmm$	4.0067	4.0067	7.8791	90	90	90	172.6
	$P4mm$	4.0069	4.0069	7.9261	90	90	90	156.4
	$Pmm2$	4.0116	4.0117	7.9178	90	90	90	22.9
	$Amm2$	4.015	4.015	7.9039	90	90	89.33	22.4
	$Pm$	4.011	4.012	7.9193	90	89.98	90	22.8
	$Cm$	4.013	4.013	7.9125	89.98	89.98	89.54	0
PbTiO3/TiO	$P4/mmm$	4.012	4.012	7.8964	90	90	90	37.4
	$P4mm$	4.013	4.013	7.8974	90	90	90	37.3
	$Pmm2$	4.023	4.000	7.8946	90	90	90	5.6
	$Amm2$	4.012	4.012	7.8950	90	90	89.88	0
	$Pm$	4.023	4.000	7.8957	90	89.99	90	5.4
	$Cm$	4.012	4.012	7.8946	89.98	89.98	89.87	0.1

Full text

I Introduction

The crystal structure of a material is one of the most important factors that determines its properties. For ferroelectric and piezoelectric materials, strain engineering has been used to enhance their performances (Helmolt_1993, ; Locquet_1998, ; Lee_2000, ; Bea_2009, ; Schlom_2014, ; Nakashima_2017, ; Zhang_2018, ) by tuning the in-plane lattice constant and ion displacements, and its influence on structural properties and polarization has been extensively studied. In addition to applying strain, combing ferroelectricity with other functionality (e.g., conductivity) in a single structure can potentially induce their mutual control, crucial for technological applications. The most important example is probably the LaAlO3/SrTiO3 heterointerface, where the polarity discontinuity creates high-mobility electron gas (Ohmoto2004, ) that enables the conductivity, which is rather surprising since both materials are insulators. Later, Lee et al replaced the polar LaAlO3 with a polarizable gel, resulting in continuously tunable electron density on the interface (Lee2011, ).

Researchers have proposed other superstructures to go beyond perovskite (ABO3) by combining it with other oxides. One well known combination is a perovskite interfacing with its constituent oxide where an extra rocksalt AO layer is added (with some in-plane shift) to $n$ layers of ABO3 ($n=1,2,3\dots$), resulting in the An+1BnO3n+1 structure (Fennie_2005, ; Ruddlesden_1958, ) [see Fig. S1 (a) in the supplemental material (Supplemental, )], referred to as the Ruddlesden-Popper (RP) phase, which has been experimentally realized (Haeni_2001, ; Haislmaier_2016, ) and its ferroelectric nature investigated for, e.g., Sn2TiO4 and Pb2TiO4 (Fennie_2005, ; Zhang_2014, ). In addition, Aurivillius-type layred structure has also been investigated (Li_2010, ; Yang_2012, ; Yuan_2014, ) and recently proposed for energy storage (Tang2019, ).

One may wonder if tunable conductivity can be achieved by mixing perovskite with simpler metal-oxides. Such a possibility indeed exists by inserting extra BO layers into a perovskite (which means TiO for ATiO3). While the misfit strain between ATiO3 and TiO can be huge, given the recent discovery of giant polarization in highly strained ($\sim 16.5\%$ tensile strain) crystal structure (Zhang_2018, ), the ATiO3/TiO superlattice is plausible and worth first-principles investigation to establish its basic properties. Furthermore, while perovskites junctioned with TiO2 have been explored to optimize their photoelectrochemical, photocatylitic, and dielectric properties (Jang_2017, ; Zeng_2018, ), the use of TiO lacks any prior investigation.

In this work, we investigate superlattices made of ATiO3/TiO (A = Pb, Sn) with and without epitaxial strain. The superlattice is built by stacking the $\left(001\right)$ planes of simple metal-oxdes, resulting in the AO-TiO2-$2$TiO-TiO2 structure, which has 12 atoms in each unit cell shown as the dotted-line-enclosed region in Fig. 1 (a), noting that the TiO layer has two Ti atoms and two O atoms in one unit cell. The general formula for such a superlattice is (ATiO3)n(2TiO)m(TiO2) ($n=1,2,3\dots$ $m=1,3,5\dots$), different from the RP structure (An+1TinO3n+1) as shown in Fig. S1 (Supplemental, ). The TiO layer has been properly shifted in the $x$-$y$ plane to allow the oxygen atoms to sit above the Ti atom of ATiO3, maintaining the TiO6 octahedra that strengthens the bonding of the TiO and TiO2 layers, where edge-sharing oxygen octahedra can be seen in Fig. 1 (b) and (c). The specific arrangement of oxygen octahedra likely deactivates their tilting. In addition to the structural novelty of the superlattice, TiO is known to be stable and metallic (Denker1966, ; Ahuja1996, ; Ciftci2009, ) and nano TiO cyrstal is a type-II superconductor (AM2018, ) while ATiO3 (A $=$ Pb, Sn) is an insulator with strong ferroelectricity. Therefore, the proposed superlattice is an ordered structure formed by repeating different functional units, following the recently proposed research paradigm (Chen_2019, ). In this paper, we will investigate their structural and electronic properties using first-principles calculations. As we will show, such a structure bridges ferroelectricity and conductivity that is potentially tunable by the relative number of the TiO and the ATiO3 layers.

II Method

In first-principles calculations, the atomic positions and lattice constants are relaxed until both the force on an ion and the stress fall below 0.005 eV/Å using the projector augmented plane wave (PAW) method as implemented in the GPAW software package (Enkovaara_2010, ). The localized density approximation (LDA) is used with a cut-off energy of 750 eV to ensure the convergence. A $4\times 4\times 2$ Monkhorst-Pack (Monkhorst1976, ) sampling is used for the $k$-space integration. The used valence orbitals are: Sn (5$s$ 5$p$ 4$d$), Pb (6$s$ 6$p$ 5$d$), Ti (3$s$ 3$p$ 4$s$ 3$d$) and O (2$s$ 2$p$). All the crystal structures are created using Atomic Simulation Environment (ASE) (Larsen_2017, ) and visualized with VESTA (Vesta2011, ). With such a setup, we first obtained the tetragonal structures of SnTiO3 and PbTiO3, which are compared to literature (Xue_2015, ), showing excellent agreements (see Tab. S1(Supplemental, )). The initial lattice constants of SnTiO3 and PbTiO3 with ions in their ideal positions ($P4/mmm$ symmetry) have the lattice parameters of $a=3.79$, $c=4.175$ Å (Matar_2009, ), and $a=3.89$, $c=4.15$ Å (Zhang_2018, ), respectively, whereas the rocksalt TiO has a lattice constant of $a=4.17$ Å (Wang_2017, ) with the $Fm\bar{3}m$ symmetry, indicating a stretching of the perovskite part in the $x$-$y$ plane when its lattice is coherently kept with TiO. We note, under external epitaxial strain, the lattice mismatch between ATiO3 and TiO can be adjusted.

III Results and Discussion

We use Phonopy (phonopy, ) to perform phonon calculation on the original superlattice ($P4/mmm$ symmetry (P4mmm, )) in order to obtain unstable phonon modes and construct low-energy structural phases accordingly. To this end, the lattice constants of the structure are optimized but ions are fixed on their initial (ideal) positions. We have used a $2\times 2\times 2$ supercell (96 atoms) to get accurate results on the high-symmetry points (e.g., $\Gamma$, $X$, $R$, and $M$ points in the Brillouin-zone). Figure 2 shows that the phonon dispersion has the strongest instability at the $\Gamma$ point [$\bm{k}=(0,0,0)$], providing clues to the most likely structural phases. We note the $\Gamma$ point instability is inherent to many ferroelectric perovksites including PbTiO3 and SnTiO3.

Based on the phonon spectrum and common ferroelectric phases of perovskites, we obtained several structural phases of the ATiO3/TiO superlattice by displacing Ti in the perovskite layer along the high-symmetry directions, forming the $P4/mmm,P4mm,Pm,Amm2,Pmm2$, and $Cm$ phases (Dieguez_2008, ). The overall symmetry of the superlattice is checked both before and after their structural relaxation. Table 1 displays the information of the relaxed SnTiO3/TiO and PbTiO3/TiO, which have the $Cm$ and $Amm2$ phase as the ground state, respectively. The perovskite part of the relaxed ATiO3/TiO experiences a tensile strain of about $3$-$5\%$ while the TiO part undergoes a compression of about $4\%$. The tensile strain forces the ATiO3 component into a pseudocubic structure ($a=b\simeq c/2$). The in-plane lattice constants of SnTiO3/TiO and PbTiO3/TiO are rather close since the rigid TiO layer is unable to compress further. Except the $P4mm$ and $P4/mmm$ phases, the structural phases have close energies, indicating that the ion displacement inside the $x$-$y$ plane is preferred. In addition, the SnTiO3/TiO has a stronger tendency to stay in the $Cm$ phase with a nonzero polarization along $z$, an inherent property to SnTiO3(Wang_2018, ).

Table S2 (Supplemental, ) provides the ion displacements (in fractional coordinates) for the $Cm$ and $Amm2$ phases, showing large displacements of ions in the $x-y$ plane and relatively small shifts in the $z$ direction. It also indicates that SnTiO3/TiO has larger ion displacements than PbTiO3/TiO. Due to its smaller ionic size, the Sn atom exhibits a much larger (10 times larger) displacement than the Pb atoms. To further confirm that the $Cm$ ($Amm2$) phase is the ground state, we have also constructed other configurations suggested by the $\Gamma$ point phonon eigenvector, removed all the symmetry constraints, and relaxed the structure again; but no new structural phases with lower energy were found.

Let us now turn to the electronic properties of ATiO3/TiO. Since PbTiO3 and SnTiO3 are insulators, it is important to know how the TiO layer alters the electronic band structures. For TiO, we have calculated its band structure, agreeing well with literature (Denker1966, ; Ahuja1996, ; Ciftci2009, ), confirming that TiO is a conductor (see Fig. S2 (Supplemental, )). Figure 3 displays the electronic band structure of PbTiO3/TiO (left column) and SnTiO3/TiO (right column). Figure 3(a) shows that the electronic band structure of PbTiO3/TiO in its original $P4/mmm$ phase, which clearly demonstrates that the superlattice is still a conductor, while the $\Gamma$ to $Z$ line (related to the superlattice growth direction) is slightly above the Fermi level. Figure 3(b) shows the band structure when the ions are also relaxed. This structure is still a conductor, but the $\Gamma$ to $Z$ line has dropped below the Fermi level. While such a change is small, it implies a strong influence on the conductivity along the growth direction. For the lowest energy state we have found (with the $Amm2$ symmetry), Fig. 3(c) shows that the $\Gamma$ to $Z$ line again rises above the Fermi level, but remains very close to it.

The electronic band structure along the $\Gamma$-$Z$ line shown in Figs. 3(a-c) indicates that the conductivity along the superlattice-growth direction can be quite sensitive to ion displacements. This connection is potentially important given the fact that both PbTiO3 and SnTiO3 are ferroelectric, a feature arising from their ion displacements. Moreover, in all the three cases shown in Figs. 3(a-c), the $\Gamma$ to $Z$ line is special in its flatness, indicating a huge electron/hole effective mass along the superlattice-growth direction, resulting in strong anisotropic conductivity. Figures 3(d-f) show that SnTiO3/TiO has similar behaviors on the $\Gamma$ to $Z$ line with some minor variations comparing to PbTiO3. Similar behavisor with the Ruddlesden-Popper double-layered perovskite La3Ni2O7 has been reported in recent years (Lee2014, ; Mochizuki2018, ).

Finally, let us briefly discuss epitaxial strain effects on ATiO3/TiO. We replicate the biaxial epitaxial strain by fixing the in-plane lattice constant. The misfit strain is calculated with $\varepsilon=\left(a-a_{0}\right)/a_{0}$ where $a_{0}$ is the optimized lattice constant of the superlattice without the in-plane constraint. The energies of the structural phases versus the epitaxial strain are shown in Fig. 4, where the $P4mm$ and $P4/mmm$ phases are omitted due to their much higher energy. Figure 4(a) shows that SnTiO3/TiO has the $Cm$ phase as the ground state for a wide range of mistfit strain until $a=4.10$ Å ($\simeq 2.15\%$ tensile strain) when the $Amm2$ phase becomes most stable. Figure 4(b) shows a similar behavior for the PbTiO3/TiO where the $Cm$ is most stable phase until $a=4.05$ Å ($\simeq 0.95\%$ tensile strain) (Cm_is_lower, ). Over the whole misfit strain range, the $Pm$ [with polarization direction $(u,0,w)$ ] and $Pmm2$ [$(u,0,0)$] phases are close in energy to the $Amm2$ [$(u,u,0)$] and the $Cm$ [$(u,u,w)$] phases while their ion displacements are in different directions. Figure S3 shows the $\left(c/2\right)/a$ ratio for ATiO3/TiO, which is adopted to compare to the $c/a$ of simple ATiO3, decreases with the in-plane lattice constant. The $\left(c/2\right)/a$ of SnTiO3/TiO remains higher than that of PbTiO3/TiO since the tetragonality of the parent SnTiO3($1.13)$ (Parker_2011, ) is larger than PbTiO3($1.065)$ (Saghi-Szabo_1998, ).

The proposed superlattice is composed of perovskite ATiO3 and TiO layers. As a matter of fact, there are other layered metal-oxides in addition to the RP phase (cava_page, ). The Aurivillius phase was first proposed by Aurivillius with the general formula (Bi2O2)(An-1BnO3n+1), where A and B are cations (Kendall1996, ). It can be thought of as alternating layers of Bi2O2 and perovskites whose ferroelectric, magnetic, and dielectric properties have been extensively studied in the past (Yang_2012, ; Yuan_2014, ; Li_2010, ). The Dion–Jacobson series has the general formula A*′* (An-1BnO3n+1), where A*′, A and B are cations (Choy2001, ; Fennie_2006, ). This structure has an intermediate layer of A′* atoms (often alkali metal) between perovskite blocks (Fennie_2006, ). More recently, Tsujimoto et al managed to remove more oxygens from conventional perovskite SrFeO3-x, producing a structure with alternating layers of FeO2 and Sr (Tsujimoto2007, ). The superlattice we proposed here are different from these known layered structures.

There are many simple oxides and perovskites to choose from to build the proposed superlattice. For instance, possible monoxides with the rocksalt structures include MgO ($a=4.217$ Å), MnO ($a=4.446$ Å), NiO ($a=4.178$ Å), CoO ($a=4.263$ Å), and NbO ($a=4.2101$ Å). Among them, NbO is metallic (Tao2011, ; Dhamdhere_2016, ) and NiO and CoO are antiferromagnetic. Such combinations have the potential to generate novel materials with special properties. Since the growth of the RP phase has already used techniques like reactive/hybrid molecular beam epitaxy (Haeni_2001, ; Haislmaier_2016, ), the growth of the proposed superlattice does not seem particularly difficult, also noting that TiO does not add any new element to ATiO3. The ATiO3/TiO superlattice can be fabricated by alternating growth of the ATiO3 and TiO layers using oxide molecular beam epitaxy (O-MBE) (Mochizuki2018, ), pulsed laser deposition (PLD), or atomic layer deposition (ALD) methods. Monitoring with the in situ reflected high energy electron diffraction (RHEED), the thickness of both the ABO3 and the TiO layers, as well as their periodicity, can be precisely controlled. The epitaxial strain can be induced by properly selecting single crystal perovskite substrates. For instance, the BaTiO3 (001) and $(1-x)$PbMg1/3Nb2/3O3-$x$PbTiO3 substrates can induce tensile strain while the SrTiO3 (001), LaAlO3 (001) substrates can induce compressive strain.

IV Conclusion

In summary, we have proposed a superlattice with TiO layers inserted into the perovskite PbTiO3 or SnTiO3, investigated their structural and electronic properties, finding that they are anisotropic conductors with tunable conductivity that is sensitive to ion displacements. Such a feature can couple conductivity to ferroelectricity, enabling the control of conductivity with electric field or strain. Furthermore, the proposed structure is automatically a micro-multilayer ceramic capacitor and can have large permittivity due to the Maxwell-Wagner effect. We finally note that, in growing such superlattice, there is no constraint on the ratio between the number of ATiO3 layers and the TiO layers, which can be used to tune special properties of the resulting superlattices.

Acknowledgements.

This work is financially supported by the National Natural Science Foundation of China, Grant No. 11974268, 11574246, and U1537210. D.W. also thanks support from the Chinese Scholarship Council (201706285020).