# New class of planar ferroelectric Mott insulators via first principles
design

Chanul Kim  Department of Applied Physics and Applied Mathematics, Columbia
University, New York, New York 10027, USA  Hyowon Park  Department of Physics,
University of Illinois at Chicago, Chicago, Illinois, 60607, USA  Chris A.
Marianetti  Department of Applied Physics and Applied Mathematics, Columbia
University, New York, New York 10027, USA<EMAIL_ADDRESS>
###### Abstract

Inorganic perovskite oxide ferroelectrics have recently generated substantial
interest for photovoltaic applications; however, existing materials suffer
from excessive electronic band gaps and insufficient electric polarization.
The recent resurgence of hybrid perovskite ferroelectrics addresses the
aforementioned deficiencies, but they are highly unstable against
environmental effects and an inorganic resolution may still be optimal. Here
we use first-principles calculations to design a low band gap, planar
ferroelectric by leveraging the complexity of layered double perovskite oxides
AA′BB′O6. We exploit A$\neq$A′ size mismatch, a nominally empty $d$-shell on
the B-site, and A cations bearing lone-pair electrons to achieve a large
ferroelectric polarization. Additionally, B${}^{\prime}\neq$B is chosen to
achieve full charge transfer and a Mott susceptible filling on the B′-site,
yielding a low band gap. These principles are illustrated in BaBiCuVO6,
BaBiNiVO6, BaLaCuVO6, and PbLaCuVO6, which could be realized in layer-by-layer
growth. This new class of materials could lead to stable, high-efficiency
photovoltaic.

##  I Introduction

Ferroelectric oxides have emerged as a candidate for applications in
photovoltaic devices, which separate photo-excited electron-hole pairs via the
internal electric field of the ferroelectricFridkin (1979). Recent progress in
domain engineering of ferroelectric oxides has demonstrated above-bandgap open
circuit voltagesYao  _et al._ (2005); Yang  _et al._ (2010), in contrast to
classic p-n junction photovoltaicShockley and Queisser (1961). Furthermore,
ferroelectric oxides are tolerant to various environments and can be
fabricated using cost efficient methodsGrinberg  _et al._ (2013); Cao  _et
al._ (2012). However, their power conversion efficiencies (PCE) have been
quite limited until recently, despite decades of exploration in this class of
materialsYuan  _et al._ (2014); Grinberg  _et al._ (2013); Zhang  _et al._
(2013); Nechache  _et al._ (2014). The limitation of many existing
ferroelectric oxides is a large electronic band gap (ie. $\geq$ 3$eV$)Yuan
_et al._ (2014), which is typical of $d_{0}$ systems where the gap is between
the oxygen $2p$ and the nominally empty transition-metal $d$ states. Band gaps
of this magnitude are problematic, as they cannot capture a significant
component of the visible spectrumShockley and Queisser (1961). An additional
limitation is the extremely low photo-current observed in most ferroelectric
oxidesYuan  _et al._ (2014), and this problem was long hindered by a lack of a
detailed mechanistic understanding. However, the application of shift current
theory has provided significant insight into this phenomenon, and it is
apparent that strong polarization and covalency are necessary ingredients for
enhancing the photocurrentYoung and Rappe (2012); Young  _et al._ (2012).

In order to circumvent the aforementioned limitations, one must simultaneously
engineer a low band gap, a large ferroelectric polarization, and strong
hybridization. Indeed, designing a lower band gap in ferroelectric oxides has
drawn a large degree of attentionChoi  _et al._ (2009, 2012); Basu  _et al._
(2008); Grinberg  _et al._ (2013); Zhang  _et al._ (2013). One possible route
to smaller band gaps is to utilize Mott or charge-transfer insulators, as in
the well-known case of BiFeO3Choi  _et al._ (2009) where an optical band gap
of 2.7$eV$ is realized. While the gap is still excessive in this case, this is
a promising direction that can be furthered in the context of alloys. In
particular, one can explore the double perovskite A2BB′O6 in order to combine
both aspects of band insulators (ie. nominal $d_{0}$ valence) with Mott
insulators (ie. nominal $d_{n}$ valence) to achieve a high degree of
tunability of the band gap. A large ferroelectric polarization in the presence
of strong hybridization can be achieved via the second order Jahn-Teller
effect, as is often realized when A-site cations contain lone-pair electrons
and or when B-site ions are in a nominal $d_{0}$ valence. Furthermore, the
magnitude of the ferroelectric polarization can be further enhanced by
employing size mismatch on the A/A′-sites, particularly when one of the
cations is lone-pair activeSingh and Park (2008); Takagi  _et al._ (2010a, b);
Shishidou  _et al._ (2004). In order to maximally exploit all aforementioned
mechanisms, one can consider the more general double perovskite AA′BB′O6Young
_et al._ (2015); Rondinelli and Fennie (2012); Mulder  _et al._ (2013). Such
compounds can be realized in experiment via chemical synthesisZubko  _et al._
(2011); Fukushima  _et al._ (2011); Knapp and Woodward (2006); Grinberg  _et
al._ (2013) and potentially via layer-by-layer growth such as Molecular Beam
Epitaxy (MBE) and Pulsed Laser Deposition (PLD)Ohtomo  _et al._ (2002); Hwang
_et al._ (2012); Nechache  _et al._ (2014). One prominent experiment was the
chemical synthesis of [KNbO3]1-x[BaNi1/2Nb1/2O3-δ]x, with $x\approx$ 0.1,
whereby the large band gap of KNbO3 (ie. 3.8  $eV$) is reduced to 1.39 $eV$;
though the polarization is reduced from 0.55$Cm^{-2}$ to 0.19 $Cm^{-2}$, the
photocurrent is still $\sim$ 50 times that of the classic ferroelectric
(Pb,La)(Zr,Ti)O3Grinberg  _et al._ (2013). Another example with A=A′ is
Bi2FeCrO6, resulting in a band gap of 1.43 - 2.51 $eV$, depending on cation
ordering, and a $\sim$8$\%$ power conversion efficiency (PCE)Nechache  _et
al._ (2014). However, there is also a significant reduction of ferroelectric
polarization, which is detrimental for photovoltaic performance. The preceding
examples illustrate the potential of enhancing photovoltaic performance via
band gap reduction, though the ferroelectric polarization was excessively
suppressed in these cases, which likely degrades the PCE. Therefore, first-
principles approaches can be a powerful avenue to more broadly explore this
vast phase space, and design low band gap materials which do retain large
ferroelectric polarization with strong hybridization.

Engineering double perovskites from first-principles has received some
attention within the literature. Previous studies have explored BB′
combinations resulting in d0/d10 valence states, but these scenarios always
result in large band gapsTakagi  _et al._ (2010a, b); Roy and Vanderbilt
(2011). Expanding to Mott physics, $d_{n}$/$d_{m}$ scenarios have been
successful in attaining low band gapsSingh and Park (2008) but experimental
results reveal relatively small polarizations (ie. 0.2 $Cm^{-2}$ ) and the
origin of ferroelectricity is AA′ size mismatch which is not as favorable in
terms of hybridizationLi  _et al._ (2010). Another promising direction is BB′
combinations resulting in $d_{0}$/$d_{n}$ valencies, which may result in low
band gapsChen  _et al._ (2013). However, it has been suggested that the nature
of the BB′ ordering will be critical to realizing a polarization associated
with the $d_{0}$ ionKnapp and Woodward (2006), with rock salt ordering being
highly unfavorable. This argument is consistent with the lack of polarization
in rock salt ordered double perovskite A2MWO6 ($M$=Ni,Mn,Cu,etc) as determined
in experimentMu oz  _et al._ (2002); Azad  _et al._ (2002); Iwanaga  _et al._
(2000); Khattak  _et al._ (1976).Therefore, it is desirable to pursue layered
ordering of BB′. Furthermore, octahedral tilting competes with the second
order Jahn-Teller distortion associated with the $d_{0}$ siteZhong and
Vanderbilt (1995), and having a layered ordering of AA′ with large size
mismatch can frustrate octahedral tiltingAbakumov  _et al._ (2013).

In this letter, we design a new class of materials where we utilize all of the
aforementioned mechanisms simultaneously to achieve a low electronic band gap
and a large ferroelectric polarization with strong hybridization. We employ at
least one A-type ion with lone pair electrons (ie. Bi3+ or Pb2+). In order to
maximize AA′ size mismatch, the A′ ion is chosen to have a different valence
than the A-type. In particular, Bi3+ is paired with Ba2+ while Pb2+ is paired
with La3+, where the selection was dictated by maximizing the size of the
A-type ion in the respective valence state. We realize full charge transfer
with select BB′ pairs having valence dn/d0, which results in a low band gap.
Given our AA′ selections, nominal valence counting dictates (BB′)+7, and one
of these ions should be $d_{0}$. Therefore, we select vanadium as the $d_{0}$
ion, which must exist in the 5+ valence, in conjunction with various B ions in
the 2+ valence. Vanadium is chosen over, for example, Ti4+ or Nb5+ for several
reasons. First, V5+ is smaller than Nb5+ and Ti4+,Shannon (1976) which will
lead to a larger polarization. Second, having a $d_{0}$ B′5+ion dictates a
nominal B2+-type ion that is more susceptible to being a Mott insulator for
the later transition metals, which are necessary in order to ensure full
charge transfer (ie. sufficient electronegativity differences). Therefore, for
B-type ions we choose Ni2+ and Cu2+. These physically motivated choices are
permuted to search for optimal properties, and we additionally explore the
validity of these underlying rules. A final condition is that we restrict this
study to layered ordering of AA′ and BB′ ions, due to the potential for
realization via layer-by-layer growth, such as MBE and PLD. We begin with a
detailed exploration of BaBiCuVO6, which will serve as our prototype, and then
generalize to other possible permutations.

##  II Method

We utilized density functional theory calculations implemented in the Vienna
ab initio simulation program (VASP)Kresse and Hafner (1993, 1994); Kresse and
Furthmüller (1996); Kresse (1996), which employs a plane-wave basis and
projector-augmented wave (PAW) potentialsBlöchl (1994); Kresse (1999).
Correlation effects on the 3$d$ orbitals are treated within the local spin
density approximation (LSDA) + $U$ methodAnisimov  _et al._ (1997). The LSDA +
$U$ method requires the definition of the on site Coulomb repulsion U, and we
do not include an on site exchange interaction J given that this is accounted
for within LSDAPark  _et al._ (2015). We explore a wide of range of values for
$U$, given that this is still an open methodological problem. All results were
obtained using $6\times 6\times 6$ Monkhorst - Pack k-point mesh centered at
$\Gamma$ and a 500 eV plane wave cutoffMonkhorst and Pack (1976). The
tetrahedron method is used for Brillouin zone integrationBlöchl  _et al._
(1994). In order to find the ground state structure, we have explored several
octahedral rotation patterns and computed phonon dispersion curves. Phonons
were computed using the PHONOPY code and a $2\times 2\times 1$ supercell with
forces obtained from self-consistent total energy calculations using the
finite displacement method.Togo  _et al._ (2008) The lattice parameters and
atomic positions were relaxed at the LSDA+$U$ levels until the total energy
changed by less than 10-5 eV per unit cell and the residual force were smaller
than 0.01 eV per $\AA$. Born effective charges and the ferroelectric
polarization were computed within the modern theory of polarizationKing-Smith
and Vanderbilt (1993); Resta (1994). The endpoints of the ferroelectric path
are defined using a 180∘ in-plane rotation centered at the vanadium atom.
Nudged elastic band is performed to determine energy barrier of the
ferroelectric pathHenkelman  _et al._ (2000). Ionic Radii are given by Shannon
for different coordination and charge statesShannon (1976). All images of
crystal structures were generated using VESTA codeMomma and Izumi (2008).

##  III Results

###  III.1 Reference structures and spontaneously broken symmetries

In order to elucidate the origin and nature of the ferroelectric polarization
in layered AA′BB′O6, we consider three reference structures. The first
reference structure, referred to as $R_{o}$, consists of placing the atoms on
the ideal perovskite lattice and then allowing full relaxations of the lattice
parameters while only relaxing the atoms in the z-direction (space group
$Cmm2$, see Figure 1a). The second reference structure, $R_{\mathbf{q}=0}$,
corresponds to fully relaxing $R_{o}$ with respect to lattice parameters and
all internal coordinates within the unit cell (space group $Cm$, not
pictured). The third reference structure, $R_{\mathbf{q}=\pi,\pi,0}$,
corresponds to creating a supercell with lattice vectors
$\bm{(1/\sqrt{2},1/\sqrt{2},0),(1/\sqrt{2},-1/\sqrt{2},0)}$ and $\bm{(0,0,1)}$
in terms of $R_{o}$, and then fully relaxing lattice parameters and all
internal coordinates (space group $Pc$, see Figure 1b). These structures allow
one to determine the role of $\mathbf{q}=0$ relaxations and octahedral
rotations. It should be noted that even the highest symmetry reference $R_{o}$
contains a static polarization in the z-direction, though an in-plane
ferroelectric polarization can still be formed by spontaneously breaking
$C_{4v}$ symmetry via the destruction of a mirror plane upon degenerating to
$R_{\mathbf{q}=0}$ or $R_{\mathbf{q}=\pi,\pi,0}$.

We begin by examining the Ro structure for BaBiCuVO6 (see Figure 1a, 1b). In
this case, we observe a large structural relaxation of both the Ba and Bi
towards the Cu-O2 layer, presumably due to the large nominal 5+ charge
associated with the V ion. This strong distortion will be seen in all
subsequent structures, irrespective of octahedral rotations and other further
symmetry breaking. While there is a polarization in the $z$-direction
associated with this A/A′ ordering and the subsequent z-direction distortion,
this is not relevant for our interests as this ordering is static and could
not practically be switched. The main question is therefore how symmetry is
spontaneously broken relative to this reference.

In figure 2, we have computed phonon spectra for the three reference
structures of BaBiCuVO6 (see Methods Section). In the Ro structure there are
many soft-modes, including at the $\Gamma$-point, reflecting the unstable
nature of this highest symmetry structure (see Figure 2a). In the Rq=0
structure, all of the $\Gamma$-point instabilities have been removed as this
structure is a fully relaxed degeneration of the Ro structure (see Figure 2b).
This effect is pictorially illustrated in the comparison of the planar
projections of Figures 2f and 2g. However, there are still strong in-plane
instabilities shown in the phonons, which correctly suggests that there is
some lower energy tilting pattern of the octahedron. In the Rq=π,π,0
structure, it is demonstrated that all in-plane instabilities have been
removed (see Figure 2c), and the resulting structure is illustrated in the
planar projections of Figure 2h and 2i. However, the Rq=π,π,0 structure still
has a small instability in the z-direction of reciprocal space. By doubling
the unit cell in the z-direction and allowing for full atomic relaxations, we
have determined that this instability only causes a very small structural
distortion that does not substantially affect the physics (ie. the energy gain
is $\approx 1meV$ per f.u.). Therefore, Rq=π,π,0 is a sufficient approximation
for our ground state structure.

Having established how the symmetry degenerates, we now use the Born effective
charges to give an approximate layer-resolved ferroelectric polarization,
referenced by Ro. The main contribution to the polarization comes from large
displacements within the Bi-O and V-O2 layers, which arise from the second
order Jahn-Teller effect associated with the lone-pair electrons and $d_{0}$
configuration, respectively. In the Rq=0 structure, the polarization is
$\bm{\mathbf{P}=0.435\mathbf{i}+0.237\mathbf{j}}$ Cm-2 , demonstrating that a
large polarization is formed even in the absence of any possible octahedral
tilts. The layer-resolved analysis further provides the polarization of Bi-O
layer and V-O2 layer, resulting in
$\bm{\mathbf{P}=0.248\mathbf{i}+0.110\mathbf{j}}$ Cm-2 and
$\bm{\mathbf{P}=0.165\mathbf{i}+0.110\mathbf{j}}$ Cm-2, respectively. In the
Rq=π,π,0 structure, the magnitude of the polarization remains similar though
the direction changes yielding
$\bm{\mathbf{P}=0.354\mathbf{i}+0.354\mathbf{j}}$ Cm-2, which can further be
split into $\bm{\mathbf{P}=0.189\mathbf{i}+0.189\mathbf{j}}$ Cm-2 for the Bi-O
layer and $\bm{\mathbf{P}=0.127\mathbf{i}+0.127\mathbf{j}}$ Cm-2 for the V-O2
layer. Therefore, octahedral tilts do perturb the direction of the
polarization. It should be noted that the polarization in the Bi-O layer is
aligned in the same direction as the polarization in the V-O2 layer, giving
rise to a very large in-plane polarization. The possibility of antialigning
the Bi-O and V-O2 layers was explored, but this could not be stabilized in our
calculations.

Figure 1: $|$ Reference structures for layered BaBiCuVO6.  (a)  Reference
structure Ro, where the atoms have been placed on an ideal perovskite lattice
and subsequently re laxed only in the z-direction. As illustrated, this
structure retains C4v symmetry, though it is unstable. (b)  Reference
structure Rq=π,π,0, which allows for ful l relaxation of all
$\mathbf{q}=(\pi,\pi,0)$ distortions and lattice strains.  Figure 2:  $|$
Phonons of successive reference structures  The phonons of reference
structures for BaBiCuVO6 are presented in panel (a) ,(b), (c) corresponding to
Ro, Rq=0, and Rq=π,π,0, respectively. Correspond ing in-plane projections of
the Bi-O and V-O layers are given in panels (d) ,(e) for Ro, panels (f), (g)
for Rq=0, and panels (h), (i) for Rq=π,π,0. In successive order, the
polarization is $\bm{0}$, $\bm{0.435\mathbf{i}+0.237\mathbf{j}}$ $Cm^{-2}$,
and $\bm{0.354\mathbf{i}+0.354\mathbf{j}}$ $Cm^{-2}$.

###  III.2 Energy barriers and polarization

Figure 3: Energy barrier and ferroelectric moment $|$ (a)  Total polarization
P, (b)  total energy profile Etot as a function of the polar distortion
characterized by $\lambda$ (ie. $\lambda=0$ denotes the ferroelectric phase
and $\lambda=1$ is the midpoint). The energy barrier is obtained via the
nudged elastic band method and polarization is calculated through both the
modern theory of polarization and Born effective charge analysis of fully
distorted structure

In order to achieve a precise understanding of the ferroelectricity, we
employed the modern theory of polarization to study the ferroelectric moment
of BaBiCuVO6 in more detail. The modern theory of polarization has
theoretically reproduced the precise magnitude of the ferroelectric moment in
many systemsKing-Smith and Vanderbilt (1993); Resta (1994). In our system,
spontaneous breaking of $C_{4v}$ symmetry inherently provides disparate paths
between symmetry equivalent minima, and we explore the paths defined by the
Rq=π,π,0 structure rotated by Cπ and Cπ/2, respectively. To begin with, the
path defined by Cπ is computed using the modern theory of polarization
yielding 0.65 $Cm^{-2}$ (see Figure 3a). This value is in the vicinity of the
polarization of BiFeO3Neaton  _et al._ (2005), which is 0.8 $Cm^{-2}$.
Additionally, the corresponding energy barrier is calculated to be 277 meV per
transition metal ion (see Figure 3b). Alternatively, the path defined by Cπ/2
results in half of the energy barrier, and this could lead to enhanced
switching speedsXu  _et al._ (2015). These energy barriers for BaBiCuVO6 are
reasonable in the sense that BiFeO3 has a theoretical energy barrier of 427
$meVperf.u.$ (ie. within Generalized gradient approximation + U) yet the
ferroelectric moment is experimentally switchableRavindran  _et al._ (2006).

The differences in total polarization between the Berry-phase approach and
Born effective charge analysis reflects the presence of anomalous dynamical
chargesGhosez  _et al._ (1998) in BaBiCuVO6. In other words, it highlights the
covalent character of the atomic bonds and, in turn, of the electronic
structure of BaBiCuVO6, which is also seen in BaTiO3Ghosez  _et al._ (1998).
Additionally, the born effective charges of active ions in the Ro structure
exhibit a striking deviation from nominal charges, which clearly demonstrates
a highly covalent character. More specifically, using the Born effective
charges from the Ro structure yields a polarization of 0.81 $Cm^{-2}$, while
using the Born effective charges from the Rq=π,π,0 structure yields 0.54
$Cm^{-2}$. The average of those two values is similar to the value from the
modern theory of polarization, 0.65 $Cm^{-2}$. These observations are a clear
demonstration of the importance of hybridization effects.

###  III.3 Electronic structure and magnitude of band gap

Figure 4: $|$ Electronic structure  Atomic resolved density of states of
BaBiCuVO6 in the Rq=π,π,0 structure for (a)  UV = 0 and UCu = 5 ; (b)  UV = 0
and UCu = 0 eV  ; (c)  projection onto copper d-orbitals; Fermi energy is set
to be 0; (d)  The variance of band gap depending on UV and UCu.

Here we explore the basic electronic structure of BaBiCuVO6, which follows the
simple rules outlined in the introduction. More specifically, V nominally
donates its sole $d$-electron to Cu, analogous to what was observed for Ti in
La2NiTiO6Chen  _et al._ (2013). We begin by illustrating this via density
functional theory (DFT)+U calculations, where we use a Hubbard $U$ of 5 eV on
the copper site, consistent with previous studies Önsten  _et al._ (2007), and
we conservatively use $U=$0 on the V site. The effect of the on-site Hubbard
$U$ will be explored in detail below. The standard fully localized limit
double countingAnisimov  _et al._ (1993); Czyżyk and Sawatzky (1994) is used,
and no on-site exchange is employed given that we are using a spin-dependent
density functionalPark  _et al._ (2015). The resulting density of states (DOS)
for the ground state antiferromagnetic spin ordering yields a band gap of 1.1
$eV$ (see Figure 4a). The atom resolved DOS for V exhibits a strong peak above
the gap indicating a complete nominal charge transfer, which is corroborated
by zero magnetic moment on the V atom. However, there is a substantial orbital
occupation of $\approx$ 4 electrons for the V $d$-orbitals due to strong
hybridization with the oxygen, as illustrated by the substantial DOS
projection of V towards the bottom of the oxygen bands. Below we demonstrate
that this results in the band gap being very insensitive to the value of $U$
on the V site. Cu has a magnetic moment of 0.5 $\mu_{B}$, which is
substantially reduced from the nominal value of 1 $\mu_{B}$. Projecting the
DOS onto the Cu-3d states reveals states above the gap, which are driven by
the on-site Coulomb repulsion $U$ (see Figure 4a, 4b). This scenario is
analogous to the cuprates, where there is a substantial crystal field that
breaks $E_{g}$ symmetry and results in an effective single band Hubbard model
which yields an antiferromagnetic Mott insulator. This is clearly illustrated
by the orbitally resolved DOS presented in Figure 4c, where $d_{xy}$ character
is seen both above and below the gap while $d_{z^{2}}$ is nearly completely
filled.

The precise value of the on-site Coulomb repulsion $U$ is still an open
problem, and the DFT+U method is crude in the sense that it is a Hartree
approximation to the dynamical mean field theory(DMFT) impurity problem within
the DFT+DMFT formalism. Both of these issues warrant a careful exploration of
how the results are affected by changes in $U$. Therefore, we compute the band
gap of the system as a function of $U$ for vanadium and copper, exploring
essentially all feasible values (ie. 0 - 6$eV$, 0 - 10 $eV$ for vanadium and
copper, respectively; See Figure 4d). The $U$ of vanadium has very little
effect due to the large hybridization with the oxygen. Neglecting exchange,
the orbital dependent term within DFT+U that is added to the Kohn-Sham
potential has the form $U(1/2-n_{i})$Anisimov  _et al._ (1997), such that
orbitals near half filling will not be substantially perturbed unless $U$ is
sufficiently large relative to the hybridization. Alternatively, the $U$ on Cu
is essential for driving the Mott physics and is necessary to open a gap (see
Figure 4a, 4b). Increasing the value of $U$ increases the gap, as expected,
though the magnitude of the increase is relatively small due to the strong
hybridization of Cu and oxygen, and eventually the band gap largely saturates
due to the upper band edge being dominated by V. Even for a relatively large
value of $U=$ 6 $eV$, the band gap remains relatively small at 1.35 $eV$. This
scenario should be contrasted to La2TiNiO6, where the gap depended strongly on
the $U$ value for TiChen  _et al._ (2013) due to a relatively smaller
electronegativity difference for Ti-Ni and less Ti-O hybridization.

###  III.4 Generalization to other compounds

Table 1: The summary of planar Ferroelectric Mott $|$ The electronic gap, energy barrier, (layer-resolved) polarization, and AA′ size difference based on Shannon radiiShannon (1976) for AA′BB′O6 compounds. The energy barrier is normalized per transition metal. Total polarization is computed by modern theory of polarization. The asterisk indicates that $U$ was increased to 6.5 $eV$ and 8.0 $eV$ on Ni and Cu, respectively, in order to ensure a gap was maintained over the entire distortion path, which is a necessary condition for the modern theory of polarization. This change has a negligible effect on the other observables.  AA′BB′O6 | BaBiCuVO6 | PbLaCuVO6 | BaBiNiVO6 | BaLaCuVO6
---|---|---|---|---
Gap (eV) | 1.08 | 1.00 | 1.05 | 0.86
Energy barrier (meV) | 287 | 226 | 269 | 214
Polarization ($Cm^{-2}$) | 0.65 | 0.52∗ | 0.68∗ | 0.41∗
A/A′size mismatch ($\AA$) | 0.25 | 0.13 | 0.25 | 0.26
Unit Cell Volume ($\AA^{3}$) | 240.47 | 229.72 | 237.41 | 239.38
A-O ($Cm^{-2}$) | 0.04 | 0.12 | 0.03 | 0.03
A′-O ($Cm^{-2}$) | 0.28 | 0.10 | 0.28 | 0.08
B-O ($Cm^{-2}$) | 0.00 | 0.00 | 0.03 | 0.00
B′-O ($Cm^{-2}$) | 0.19 | 0.23 | 0.22 | 0.16

While we have illustrated our design principles in the context of BaBiCuVO6,
these rules can obviously be used to generate numerous other compounds with
similar properties. To illustrate this point, we have successfully realized
three additional candidates in addition to BaBiCuVO6: PbLaCuVO6, BaBiNiVO6,
and BaLaCuVO6 (see Table 1). We first consider the case of PbLaCuVO6, where we
have decreased the A/A′ mismatch while retaining one lone-pair cation and kept
everything else identical. As expectedTakagi  _et al._ (2010a), the smaller
A/A′ mismatch results in a smaller polarization within the lone-pair cation
layer, though a nontrivial polarization does form in the La-O layer.
Nonetheless, the net effect is an overall decrease in polarization and a large
decrease in the energy barrier, which could be beneficial for ease of
electrical switching. Due to the relatively small changes in the Cu-O2 planes,
the band gap changes very little. Another interesting possibility is to retain
the Ba/Bi cations and instead exchange Ni in place of Cu. In this case, Ni
will result in a 2+ state, which is susceptible to Mott physics, similar to
NiO and the scenario outlined in La2TiNiO6Chen  _et al._ (2013). We find a
similar barrier and polarization to BaBiCuVO6, which is consistent with the
only change being associated with the ion exhibiting Mott physics.
Additionally, the band gaps are relatively similar, assuming a reasonable
value of $U=$5$eV$ for NiPark  _et al._ (2012). The final scenario we explore
corresponds to the removal of lone-pair cations, which is the case of
BaLaCuVO6. Here the only nontrivial polarization in the A/A′ layers is
associated with La-O, which is analogous to the large size mismatch as in the
KNbO3-LiNbO3 systemBilc and Singh (2006). The band gap is slightly reduced
relative to BaBiCuVO6 due to diminished tilting in the Cu-O2 layer.

##  IV Discussion

Our proposed class of planar ferroelectric Mott insulators optimally matches
the criteria for use as a photo-ferroelectricButler  _et al._ (2014); Shockley
and Queisser (1961): band gap of $\approx 1eV$, strong ferroelectric
polarization and covalent character, and a large phase space of chemical
elements such that properties can be tuned. The low band gap is essential to
absorb a significant portion of the solar spectrum. The sizable polarization
and strong covalent character are necessary to obtain a substantial shift
currentYoung and Rappe (2012); Young  _et al._ (2012), which is believed to be
indicative of the photocurrent and hence the power conversion efficiency
(PCE). Our current work has identified four compounds which satisfy our design
rules, and there are many more compounds which could be included to form a
substantial phase space of possibilities. Additionally, the fact that our
systems are antiferromagnet Mott insulators could further enhance the
potential of these materials in two waysManousakis (2010). First, multiple
charge carriers through impact ionization suggest the possibility of exceeding
the Shockley-Queisser efficiency limitShockley and Queisser (1961). Second,
high drift voltage and large diffusion length could be helpful despite a low
mobility due to strong correlations. Antiferromagnetic Mott insulators have
demonstrated the possibility of enhancing ultrafast separation of photo doped
carriers before recombinationEckstein and Werner (2014). Only careful
experiments will be able to definitively determine the applicability of Mott
insulators in this context due to the complexity of strongly correlated
electron systems.

Another potential area of application exists in the context of non-volatile
memory. The photovoltaic output of BiFeO3 was employed as a read-out signal,
switching between 0.11 $V$ and -0.23 $V$ for up to 108 cyclesGuo  _et al._
(2013). In terms of non-volatile memory devices, an in-plane ferroelectric
polarization has several benefitsYao  _et al._ (2005). First, in-plane
ferroelectrics should be much less sensitive to explicitly broken symmetry
induced by a substrate, leading to a more symmetric voltage and current bi-
state. Second, in-plane ferroelectrics may be straightforwardly exploited via
the growth of large area thin-films generating a large voltage, which would be
difficult to achieve in a thick film out-of-plane ferroelectric. An open
circuit voltage of 8 volts is achieved with a small incident intensity of 1
$mWcm^{-2}$ for a thin film device of Pb0.97La0.03(Zr0.52Ti0.48O3. Thus our
proposed class of materials could be multifunctional in the sense that the
ferroelectric order is coupled to optical and electronic transport channels.
This could lead to optically addressed ferroelectric memory with non-
destructive read outWu  _et al._ (2011). It is also worth noting that a large
planar ferroelectric moment could assist the formation of charged domain
walls, which have their own potential device applicationsOh  _et al._ (2015).

It is worthwhile to compare our systems with the recent resurgence of
organometallic halides in the context of photovoltaic, which has also resolved
the aforementioned deficiencies of ferroelectric oxide photovoltaicButler  _et
al._ (2014). In the organometallic halides, variation in hysteresis of the
current-voltage profile under different scanning conditions implies
ferroelectric behavior and exceptionally long carrier diffusion lengths,
leading to the hypothesis of “ferroelectric highways”. Recent ab-initio
calculations confirm a large polarization and strong covariance in
photovoltaicly promising hybrid lead halide perovskitesFrost  _et al._ (2014);
Zheng  _et al._ (2015), which is consistent with the general view of shift
current theoryYoung and Rappe (2012). Nonetheless, their instability against
water due to weak halide bonding and environmental issues associated with lead
are still very serious problemsGreen  _et al._ (2014), and resolving these
deficiencies could be formidable. Therefore, the approach outlined in this
paper could be a very valuable path to explore in parallel with the recent
trends in organometallics.

###### Acknowledgements.

We would like to thank D. Vanderbilt and K. Rabe for valuable discussions. The
authors acknowledge funding from the FAME, one of six centers of STARnet, a
Semiconductor Research Corporation program sponsored by MARCO and DARPA. The
research used resources of the National Energy Research Scientific Computing
Center, a DOE Office of Science User Facility supported by the Office of
Science of the U. S. Department of Energy under Contract No. DE-AC02-05CH11231

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