Design of a Mott Multiferroic from a Non-Magnetic Polar Metal

Abstract

We examine the electronic properties of newly discovered "ferroelectric"
metal LiOsO$_3$ combining density-functional and dynamical mean-field theories.
We show that the material is close to a Mott transition and that electronic
correlations can be tuned to engineer a Mott multiferroic state in 1/1
superlattice of LiOsO$_3$ and LiNbO$_3$. We use electronic structure
calculations to predict that the (LiOsO$_3$)$_1$/(LiNbO$_3$)$_1$ superlattice
is a type-I multiferroic material with a ferrolectric polarization of
41.2~$\mu$C cm$^{-2}$, Curie temperature of 927\,K, and N\'eel temperature of
671\,K. Our results support a route towards high-temperature multiferroics,
\emph{i.e.}, driving non-magnetic \emph{polar metals} into correlated
insulating magnetic states.

Full text

Design of a Mott Multiferroic from a Non-Magnetic Polar Metal
Danilo Puggioni,
1
Gianluca Giovannetti,
2
Massimo Capone,
2
and James M. Rondinelli
1
1
Department of Materials Science and Engineering, Northwestern University, IL 60208-3108, USA
2
CNR-IOM-Democritos National Simulation Centre and International School for Advanced Studies (SISSA), Trieste, Italy
We examine the electronic properties of newly discovered “ferroelectric” metal LiOsO
3
combining
density-functional and dynamical mean-field theories. We show that the material is close to a Mott
transition and that electronic correlations can be tuned to engineer a Mott multiferroic state in 1/1
superlattice of LiOsO
3
and LiNbO
3
. We use electronic structure calculations to predict that the
(LiOsO
3
)
1
/(LiNbO
3
)
1
superlattice is a type-I multiferroic material with a ferrolectric polarization of
41.2
µ
C cm
−2
, Curie temperature of 927 K, and N´eel temperature of 671 K. Our results support a
route towards high-temperature multiferroics, i.e., driving non-magnetic polar metals into correlated
insulating magnetic states.
PACS numbers: 75.85.+t, 71.45.Gm, 77.80.B−, 71.20.−b,
Introduction.—Multiferroics (MF) are a class of insu-
lating materials where two (or more) primary ferroic
order parameters, such as a ferroelectric polarization
and long-range magnetic order, coexist. Technologically,
they offer the possibility to control magnetic polariza-
tions with an electric field for reduced power consumption
[
1
,
2
]. Nonetheless, intrinsic room-temperature MF re-
main largely elusive. This fact may be understood by ex-
amining the microscopic origins for the ferroic order which
aids in classifying different phases: In Type-I MF, ferro-
electricity and magnetism arise from different chemical
species with ordering temperatures largely independent
of one another and weak magnetoelectric (ME) coupling
[
3
]. The ferroelectric ordering also typically appears at
temperatures higher than the magnetic order, and the
spontaneous polarization
P
is large since it is driven by
a second-order Jahn-Teller distortion, e.g., BiFeO
3
[
3
,
4
].
In Type-II MF, however, magnetic order induces ferro-
electricity, which indicates a strong ME coupling between
the two order parameters. Nonetheless,
P
is usually much
smaller, e.g., by a factor of 10
2
as in
R
-Mn
2
O
5
(
R
be-
ing rare earth) [
5
]. In a few MFs with high-transition
temperatures, i.e., BiFeO
3
[
6
] and Sr
1−x
Ba
x
MnO
3
[
7
–
9
],
magnetism is caused by Mott physics arising from strong
correlations. The interactions localize the spins at high
temperature, paving the way for magnetic ordering at
room temperature. Materials where this robust mag-
netism is coupled with ferroelectric distortions are ideal
candidates for a room-temperature MFs.
Herein, we propose a design strategy for novel Mott
MF phases. It relies on tuning the degree of correlation
of the recently discovered class of materials referred to
as ‘ferroelectric metals’ with LiOsO
3
as the prototypi-
cal member [
10
]. This material is the first undisputed
realization of the Anderson-Blount mechanism [
11
], and
challenges the expectation that conduction electrons in
metals would screen the electric field induced by polar
displacements [
10
,
12
,
13
]. Despite robust metallicity, this
material shares structural similarities with prototypical
insulating ferroelectric oxides, such as LiNbO
3
[
14
,
15
]: A
R
3
c
crystal structure with acentric cation displacements
and distorted OsO
6
octahedra [
16
,
17
] and comparable
lattice parameters [
10
,
14
]. While the polar displacements
in LiNbO
3
rely on cross-gap hybridization between
p
(O)
and
d
(Nb) states [
18
], in LiOsO
3
they are weakly coupled
to the states at the Fermi level (
EF
), which makes possi-
ble the coexistence of an acentric structure and metallicity
[
16
,
19
]. In LiOsO
3
the empty
d
-manifold of LiNbO
3
is
replaced by a non-magnetic 5
d3
ground state with a half-
filled
t2g
(
dxy
,
dxz
,
dyz
) configuration, which is responsible
for the metallic response [
16
]. However, the strength of
the electronic interactions is insufficient to drive a Mott
transition in the correlated
t2g
manifold as revealed by
low-temperature resistivity measurements; nonetheless, if
it would be possible to enhance the electronic correlations
in LiOsO
3
and achieve a metal-insulator transition, then a
previously unidentified multiferroic material should result.
The concept is that if an insulating state can be obtained
from a ‘ferroelectric metal’ through enhanced correlations,
it would then naturally lead to magnetic ordering of the
localized electron spins, coexisting polar displacements,
and potentially strong ME coupling.
In this work we explore the feasibility of this ap-
proach using a combination of first-principles density
functional theory (DFT) plus dynamical mean field the-
ory (DMFT) calculations [
20
]. We first show that the
electronic Coulomb interactions and Hund’s coupling in
LiOsO
3
make it an ideal candidate for realizing a Mott
MF due to the multi-orbital
t2g
physics. Next, we de-
scribe the design of a new multiferroic by control of the
electronic structure through atomic scale engineering of a
Mott metal-insulator transition (MIT) in an ultrashort
period (LiOsO
3
)
1
/(LiNbO
3
)
1
superlattice. The insulat-
ing and magnetic state is driven by an enhancement of
the electronic correlations in LiOsO
3
layers owing to the
kinetic energy reduction of the
t2g
orbitals from the su-
perlattice geometry. The ferroelectric properties mainly
originate from cooperative Li and O displacements. The
multiferroic phase emerges across the MIT, exhibiting
a net electric polarization (41.2
µ
C cm
−2
) and magneti-
arXiv:1503.01948v1 [cond-mat.mtrl-sci] 6 Mar 2015

2
zation [0.9
µB
per formula unit (f.u.)], with calculated
magnetic-ordering and ferroelectric temperatures of 671 K
and 927 K, respectively. Our results uncover a promising
alternative route to discovery of room-temperature mul-
tiferroics: One could search for correlated polar metals
near Mott transitions and drive the phases into insulating
states, rather than the often-pursed approach of inducing
polar displacements in robustly insulating magnets.
Calculation Details.—We perform first-principles DFT
calculations within local-density approximation (LDA)
+Hubbard
U
method as implemented in the Vienna Ab
initio Simulation Package (VASP) [
21
] with the projector
augmented wave (PAW) approach and a 600 eV plane
wave cutoff with a 5
×
7
×
7
k
-point mesh. We relax the
volume and atomic positions (forces
<
0.1 meV
˚
A
−1
) using
Gaussian smearing (20 meV width) for the Brillouin zone
(BZ) integrations. We perform LDA+DMFT calculations
including local Coulomb interactions parameterized by
the
U
and the Hund’s coupling
Jh
starting from Wannier
orbitals constructed from the LDA bands [
22
] using an
energy range spanned by the full
d
manifold. The impurity
model is solved using Exact Diagonalization (ED) with a
parallel Arnoldi algorithm [23,24].
Correlations in LiOsO
3
.—We first examine the effect
of the interactions on the metallic state of LiOsO
3
and
determine the critical values for a Mott transition
Uc
in
the paramagnetic and antiferromagnetic (AFM) phases
using LDA+DMFT. The criterion for a Mott-Hubbard
transition is frequently associated with the ratio between
the bandwidth (
W
) and the interaction strength
U
, so
that the Mott transition occurs for
Uc
of the order of
W
.
In a multiband Hubbard model with
M
orbitals,
Uc
is
enhanced by orbital fluctuations, i.e.,
Uc∼√MW
, [
25
]
and it is influenced by the Hund’s coupling
Jh
. Indeed, at
half-filling, Ucis reduced by an enhancement of Jh[26].
In the following, we show this is precisely the situation
in LiOsO
3
[
16
]. Due to the energy separation between
t2g
and
eg
orbitals in the spectral density of state of LiOsO
3
around the Fermi level, we resort to using a model for
the
t2g
levels only [
16
]. Owing to the symmetry breaking
in bulk LiOsO
3
, the orbitals in the
d
manifold are also
permitted to mix, which lifts the degeneracy of
t2g
orbitals
with two of states remaining degenerate.
Fig. 1 shows the orbital resolved quasiparticle weight
(Z) of the occupied orbitals as a function of
U
for two
different values of
Jh
for paramagnetic LiOsO
3
in the
experimental structure (see top panels). Z measures the
metallic character of the system, and it evolves from Z=1
for a non-interacting metal to Z=0 for a Mott insulator.
Upon increasing the value of
Jh
, the critical value of
U
required to reach the Mott state (Z=0) is shifted to larger
values of U[26].
In the correlated regime, we anticipate electron localiza-
tion will lead to long-range magnetic order of the localized
spins. Spin-polarized LDA+DMFT calculations, initial-
ized with a
G
-type AFM structure (every spin on an Os
(a)
(b)
m(μ )
Β
J /U=0.3 J /U=0.15 h
h
U(eV) U(eV)
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
Z
1
0.8
0.6
0.4
0.2
0
3
2.5
2
1.5
1
0.5
0
FIG. 1. (Color online) (a) Orbital resolved quasiparticle orbital
weight Z (filled symbols) for paramagnetic LiOsO
3
and (b)
local magnetization
m
(
µB
) (obtained from a spin-polarized
calculation) of the
t2g
orbitals in LiOsO
3
as function of
U
for
different ratios of
Jh/U
within the LDA+DMFT calculations.
Vertical arrows indicate the critical value of
U
required to
reach the insulating state in the G-type AFM structure.
cation is antiparallel to all its neighbors), reveal that the
local magnetic moment rapidly saturates to the atomic
value
S
= 3
/
2. A finite magnetization also develops at
intermediate
U
in the metallic state (Fig. 1, lower panels).
The MIT, marked by vertical arrows, occurs for a weaker
coupling in the AFM than in the paramagnetic state.
Design of a Mott Multiferroic.—The LDA+DMFT cal-
culations reveal that a simultaneous Mott and magnetic
state could be engineered in LiOsO
3
by reducing the
electronic kinetic energy. One avenue to control and
decrease the kinetic energy relies on heterostructuring
and interleaving two perovskites together to form a co-
herent superlattice, whereby an isostructural insulator
would restrict the electron hopping due to the reduction
in available channels [
27
–
29
]. Such geometries can be
achieved in practice using oxide molecular-beam epitaxy
or pulsed-laser deposition methods [30,31].
Owing to the chemical and structural compatibility of
LiOsO
3
with LiNbO
3
, with a lattice mismatch of 3.2%,
we devise an ultrashort period perovskite superlattice
of (LiOsO
3
)
1
/(LiNbO
3
)
1
as illustrated in panel (a) of
Fig. 2. The superlattice is constructed by beginning from
the
R
3
c
crystal structure of LiOsO
3
(LiNbO
3
) and im-
posing a layered order along the [110] direction in the
rhombohedral setting, which is equivalent to a 1/1 period
LiOsO
3
/LiNbO
3
grown along the pseudocubic (pc) [001]
direction [
32
]. The geometry in Fig. 2 is also different from
a superlattice constructed along the [101]
pc
direction (c.f.,
Ref.
33
), which is likely more challenging to realize ex-
perimentally. Following full relaxation of the superlattice,
we find the cation order results in a symmetry reduction
to the polar space group
P c
with out-of-phase OsO
6
and
NbO
6
octahedral rotations, i.e., the
a−b−b−
tilt pattern

3
(a)
-5 0 5
0
5
10
-5 0 5
-5 0 5
Energy (eV)
0
5
10 Nb
4d
Os
5d
O
2p
DOS (states/eV per f.u.)
(b) (c)
(d)
LiNbO
3
LiOsO
3
Li
2
NbOsO
6
LiO
OsO
2
LiO
LiO
NbO
2
FIG. 2. (Color online) (a) The superlattice exhibits the
a−b−b−
tilt pattern. Atom- and orbital-resolved DOS for
(b) LiOsO
3
, (c) LiNbO
3
and (d) LiOsO
3
/LiNbO
3
at the DFT-
LDA level. EFis given by the (broken) vertical line at 0eV.
given in Glazer notation [
34
]. The microscopic origin of
polar displacements are described in detail below.
Electronic Properties.—Fig. 2 shows the LDA electronic
density of states (DOS) for the LiOsO
3
/LiNbO
3
superlat-
tice (d), compared with LiOsO
3
(b) and LiNbO
3
(c) using
the LDA-optimized atomic structures. The results for
LiOsO
3
(Fig. 2b) highlight the metallic character of the
former, where the weight at the Fermi level (
EF
) mainly
comes from Os 5
d
states which show strong admixture
from the O 2
p
states. In contrast, LiNbO
3
is a band
insulator, with the O 2
p
states forming the valence band
and Nb
4d
states at the conduction band minimum, sepa-
rated by a gap of 3.28 eV (Fig. 2c). In the superlattice,
we find essentially no charge transfer between Os and Nb:
Each component (LiOsO
3
and LiNbO
3
) is isoelectronic
to its bulk configuration; the DOS can be described as a
direct superposition of the two components (Fig.2d). The
Os 5
d
states partially fill the gap in the electronic spec-
trum formed from the the two-dimensional NbO
2
planes.
There is some spectral weight transfer in the vicinity of
EF
among the Os orbitals, which are sensitive to the
electron correlation strength as shown in Fig. 1.
We now explore the effect of electronic correlations
by means of LSDA+
U
calculations at different values of
Ueff
=
U−Jh
. An accurate value of the Hubbard
U
is
FIG. 3. (Color online) Band gap
Eg
and averaged local mag-
netic moment for Os as a function of
Ueff
with and without
spin-orbit interaction (SOI).
unknown for perovskite osmates, but it is expected to be
comparable to that of NaOsO
3
[
35
] and double perovskite
Sr
2
CrOsO
6
[
36
] for which a correct description of the
electronic properties are obtained with
U
values of 1.0
and 2.0 eV, respectively. Note that the differences from
various implementations of the LDA+
U
scheme for bulk
LiOsO
3
were found to be minor [
16
], and are anticipated
to also be insignificant for the superlattice.
Fig. 3 shows the evolution in the band gap (
Eg
) and
magnetic moment of Os
3+
ions (
m
) as a function of the
strength of
Ueff
for LSDA including spin-orbit interaction
(SOI, broken lines). A gap opens at a critical
Ueff ∼
1 eV
(
Uc
), signaling a MIT into a magnetic insulating ground
state. As expected the LiOsO
3
/LiNbO
3
superlattice be-
comes insulating for smaller values of the interaction with
respect to bulk LiOsO
3
. The enhancement of electronic
correlations is also found for small values of
U
. In fact,
LiOsO
3
remains paramagnetic [
16
] while the superlattice
is weakly ferrimagnetic already below
Uc
, where it turns
into a G-type AFM insulator at Ueff ∼0.5 eV.
The reduction in
Uc
for the MIT in the superlattice
can be understood by analyzing the effect of the geo-
metrical confinement on the
t2g
band dispersions. (For
simplicity, we use the LDA electronic structures given
in Ref.
32
.) While the bandwidth of the
dxy
orbitals is
essentially the same as for bulk LiOsO
3
, the
dxz
and
dyz
bands in LiOsO
3
/LiNbO
3
are significantly narrowed as a
consequence of the reduced hopping along the superlattice
direction. This leads to a reduction of the kinetic energy
which enhances the electron-electron correlations, making
the superlattice a Mott insulator at moderate interaction
strengths. We note that when SOI are excluded in the
calculations (Fig. 3, solid lines), the MIT occurs at a fur-
ther reduced correlation strength (
Uc∼
0
.
5 eV), and the
magnetic moment only slightly increases. Such behaviors
are also observed in bulk LiOsO3[16].
Ferroelectric Polarization.—We now apply a group the-

4
FIG. 4. (Color online) Illustration of the polar zone-center
mode along the [101]-direction labeled by irrep Γ
−
2
. Anti-polar
displacements along the [010]-direction are omitted for clarity.
oretical analysis [
37
,
38
] of the LiOsO
3
/LiNbO
3
structure
to understand the inversion symmetry-breaking displace-
ments that produce the
P c
ground state. We use a fic-
titious
P
2
1/c
centrosymmetric phase (where polar dis-
placements are switched off) as the reference phase from
which the symmetry-adapted mode displacements are ob-
tained as different irreducible representations (irreps) of
the
P
2
1/c
space group operators [
39
]. We find the loss
of inversion symmetry mainly derives from cooperative
Li and O displacements in the (101) mirror plane of the
P c
phase. Moreover, we find anti-polar displacements
along the
b
-axis which result in no net polarization. All
polar displacements are described by a distortion vector
that corresponds to the irrep Γ
−
2
along the [101]-direction
of the
P c
structure (Fig. 4). These displacements are
consistent with the acentric Li and O ionic displacements
identified to be responsible for lifting inversion symme-
try in bulk LiOsO
3
[
10
,
13
] and across the ferroelectric
transition in LiNbO3[40].
We now compute the ferroelectric polarization in
LiOsO
3
/LiNbO
3
using the Berry’s phase approach [
41
]
within LSDA+
U
(
Uc
= 0
.
5 eV). The spontaneous elec-
tric polarization of the
P c
phase is 32.3
µ
C cm
−2
and
25.5
µ
C cm
−2
along the [100]-direction, i.e., along the
pseudo-cubic [001] superlattice repeat direction and [001]-
directions, respectively. (Note that the [101]-direction in
LiOsO
3
/LiNbO
3
corresponds to the polar [111]-direction
in LiNbO
3
.) Together this yields a net polarization along
the [101]-direction of 41.2
µ
C cm
−2
. These values are also
robust to SOI, with a change of less than 15% to value
of the total polarization. Following the recipe of Ref.
42
,
we use the energy difference between the high-symmetry
(
P
2
1/c
) and low-symmetry (
P c
) to obtain a ferroelectric
Curie temperature of 927 K for the superlattice. This
value is close to the extrapolated transition temperature
for LiNbO
3
(
>
1,400 K) [
43
], and far exceeds that of bulk
LiOsO
3
where inversion symmetry is lost near 140K [
10
].
Magnetic Ordering Temperature.—Our DMFT calcula-
tions indicate that when the superlattice material enters
in the Mott state the magnetic moment is
∼
3
µB
, corre-
sponding to a high-spin
S
= 3
/
2 state. We now estimate
the N´eel temperature for LiOsO
3
/LiNbO
3
by extracting
the exchange interaction constants from spin-polarized
DFT energies computed at
Uc
without SOI following
the approach in Ref.
44
. Assuming that the magnetism
arises by ordering such localized spins, we obtain intra-
and inter-plane Os–Os exchange magnetic couplings of
-5.6 meV and -0.2 meV respectively, where a negative in-
teraction indicate AFM exchange. From these values and
without Anderson’s renormalization [
45
], we estimate a
N´eel temperature of 671 K for the LiOsO
3
/LiNbO
3
super-
lattice, which makes the material a correlation-induced
room-temperature multiferroic.
Conclusions.—We used a LDA+DMFT approach to
study the electronic properties of the “ferroelectric” metal
LiOsO
3
. A detailed understanding of the electronic struc-
ture of LiOsO
3
shows that a reduction of the kinetic
energy can drive the system into a Mott insulating state.
We use this concept to propose a strategy to design mul-
tiferroic materials by constructing a superlattice with
the uncorrelated polar LiNbO
3
dielectric. On the basis
of LSDA+U calculations we show that the ultra-short
period LiOsO
3
/LiNbO
3
superlattice should be a type-I
room-temperature Mott multiferroic with a large 41.2
µ
C
cm−2electric polarization.
The large ferroelectric displacements from the LiNbO
3
layers facilitate the high ferroelectric ordering temperature
in the LiOsO
3
/LiNbO
3
heterostructure as observed from
the similarity in the Curie temperature of the superlattice
with that of LiNbO
3
. In this case LiOsO
3
/LiNbO
3
would
behave as a paramagnetic Mott ferroelectric at high tem-
peratures and transition into Mott multiferroic below the
N´eel temperature, which is predicted to be well-above
room temperature. Because the exchange interactions of
Os are mediated by the coordinating O ligands, which
are essential to and produce the ferroelectric distortion, a
strong ME coupling is anticipated as in Sr
1−x
Ba
x
MnO
3
[
7
–
9
]. We hope this work motivates the synthesis of new
artificial multiferroics, and the adds to the growing dis-
cussion of new applications where noncentrosymmetric
metals and ferroelectric materials may be united.
GG and MC acknowledge financial support by the Euro-
pean Research Council under FP7/ERC Starting Indepen-
dent Research Grant “SUPERBAD” (Grant Agreement
No. 240524). DP and JMR acknowledge the ARO under
Grant Nos. W911NF-12-1-0133 and W911NF-15-1-0017
for financial support and the HPCMP of the DOD for
computational resources.
[1] T. Kimura et al. , Nature (London) 426, 55 (2003).
[2] N. Hur et al. , Nature (London) 429, 392 (2004).

5
[3] J. Wang et al. , Science 299, 1719 (2003).
[4]
R. G. Pearson, Journal of Molecular Structure:
THEOCHEM 103, 25 (1983).
[5] S.-W. Cheong and M. Mostovoy, Nat. Mat. 6, 13 (2007).
[6]
Sanghyun Lee, M. T. Fernandez-Diaz, H. Kimura, Y. Noda,
D. T. Adroja, Seongsu Lee, Junghwan Park, V. Kiryukhin,
S.-W. Cheong, M. Mostovoy, and Je-Geun Park Phys. Rev.
B88, 060103(R) (2013)
[7]
H. Sakai, J. Fujioka, T. Fukuda, D. Okuyama, D.
Hashizume, F. Kagawa, H. Nakao, Y. Murakami, T. Arima,
A. Q. R. Baron, Y. Taguchi, and Y. Tokura, Phys. Rev.
Lett. 107, 137601 (2011)
[8]
G. Giovannetti, S. Kumar, C. Ortix, M. Capone, and J.
van den Brink, Phys. Rev. Lett. 109, 107601 (2012).
[9]
R. Nourafkan, G. Kotliar, and A.-M. S. Tremblay, Phys.
Rev. B 90, 220405(R) (2014)
[10]
Y. Shi, Y. Guo, X. Wang, A. J. Princep, D. Khalyavin, P.
Manuel, Y. Michiue, A. Sato, K. Tsuda, S. Yu, M. Arai,
Y. Shirako, M. Akaogi, N. Wang, K. Yamaura and A. T.
Boothroyd , Nat. Mat. 12, 1024 (2013).
[11]
P. W. Anderson and E. I. Blount, Phys. Rev. Lett.
14
,
217 (1965).
[12]
Q. Yao, H. Wu, K. Deng, and E. Kan, RSC Adv.
4
, 26843
(2014)
[13]
Sim Hyunsu and Kim Bog G., Phys. Rev. B
89
201107
(2014).
[14]
H. Boysen and F. Altorfer, Acta Crystallogr. B
50
, 405
(1994).
[15]
H.D. Megaw, Acta Crystallogr. Section A
24
, 583 (1968).
[16]
G. Giovannetti and M. Capone, Phys. Rev. B
90
, 195113
(2014)
[17]
H. Sim and B. G. Kim, Phys. Rev. B
89
, 201107(R)
(2014).
[18]
I. Inbar and R. E. Cohen, Phys. Rev. B
53
, 1193 (1996).
[19]
D. Puggioni and J. M. Rondinelli, Nat. Commun.
5
, 3432
(2014).
[20]
A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg,
Rev. Mod. Phys. 68, 13 (1996).
[21]
G. Kresse and J. Furthmuller, Phys. Rev. B
54
, 11 169
(1996); Comput. Mater. Sci. 6, 15 (1996).
[22]
A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Van-
derbilt and N. Marzari, Comput. Phys. Commun.
178
, 685
(2008).
[23]
M. Capone, L. de’ Medici, and A. Georges, Phys. Rev. B
76, 245116 (2007).
[24]
R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK
Users’ Guide (SIAM, Philadelphia, 1997).
[25]
O. Gunnarsson, E. Koch, and R. Martin, Phys. Rev B
54
R11026 (1996)
[26]
A. Georges, L. de’ Medici, J. Mravlje, Annual Reviews of
Condensed Matter Physics 4, 137-178 (2013).
[27]
B. Gray, H.N. Lee Ho, J. Liu, J. Chakhalian, and J.W.
Freeland, Appl. Phys. Lett. 97 013105 (2010).
[28]
S. Middey, D. Meyers, M. Kareev, E. J. Moon, B. A. Gray,
X. Liu, J. W. Freeland, and J. Chakhalian, Appl. Phys.
Lett. 101 261602 (2012).
[29]
S. Middey, P. Rivero, D. Meyers, M. Kareev, X. Liu, Y.
Cao, J.W. Freeland, S. Barraza-Lopez, and J. Chakhalian,
Sci. Rep 46819 (2014).
[30]
D. G. Schlom, L.-Q. Chen, X. Pan, A. Schmehl, and M.A.
Zurbuchen, J. Amer. Ceram. Soc. 91 2429 (2008).
[31]
Blok J. L., Wan X., Koster, G., Blank D. H. A. and
Rijnders G., Appl. Phys. Lett. 99 151917 (2011).
[32]
See Supplemental Material at [URL will be inserted by
publisher] for discussion of the superlattice construction,
equilibrium atomic positions using the LDA and LSDA+
U
with
U
= 0
.
5 eV, and additional electronic structures. Note
for simplicity, we assume
α
=
β
=
γ
= 90
◦
which slightly
shifts the results by few percent, but the constraint is
anticipated to be appropriate for coherent epitaxial growth.
[33] H. J. Xiang, Phys. Rev. B 90, 094108 (2014).
[34] A. M. Glazer, Acta Cryst. A 31, 756 (1975)
[35]
Y. G. Shi, Y. F. Guo, S. Yu, M. Arai, A. A. Belik, A. Sato,
K. Yamaura, E. Takayama-Muromachi, H. F. Tian, H. X.
Yang, J. Q. Li, T. Varga, J. F. Mitchell, and S. Okamoto,
Phys. Rev. B 80, 161104(R) (2009).
[36]
O. Nganba Meetei, Onur Erten, Mohit Randeria, Nandini
Trivedi, and Patrick Woodward, Phys. Rev. Lett.
110
,
087203 (2013).
[37]
D. Orobengoa, C. Capillas, M. I. Aroyo, and J. M. Perez-
Mato, Journal of Applied Crystallography
42
, 820 (2009).
[38]
J. M. Perez-Mato, D. Orobengoa, and M. I. Aroyo, Acta
Crys. A 66, 558 (2010).
[39]
The ferroelectric transition in LiOsO
3
and LiNbO
3
is
R¯
3c→R
3
c
. Using the same method described in the main
paper for the construction of the superlattice but starting
from the
R¯
3c
crystal structure of LiOsO
3
(LiNbO
3
) the
atomic relaxation of the ‘idealized’ superlattice gives the
centrosymmetric
P
21
/c
phase. This structure is used as
the reference for both the mode decomposition and in the
calculation of the ferroelectric Curie temperature.
[40]
N. A. Benedek, and C. J. Fennie, The Journal of Physical
Chemistry C 117 13339 (2013)
[41]
R.D. King-Smith and D. Vanderbilt, Phys. Rev. B
47
,
1651 (1993); D. Vanderbilt and R. D. Smith, Phys. Rev. B
48, 4442 (1993).
[42] Jacek C. Wojdel and Jorge ´
I˜niguez, arXiv:1312.0960.
[43]
G. A. Smolenskii, N. N. Krainik, N. P. Khuchua, V. V.
Zhdanova, and I. E. Mylnikova, phys. stat. sol. (b)
13
, 309
(1966).
[44]
N. Lampis, C. Franchini, G. Satta, A. Geddo-Lehmann,
and S. Massidda, Phys. Rev. B 69, 064412 (2004).
[45] P. W. Anderson, Phys. Rev. 115, 2 (1959)

6
Design of a Mott Multiferroic from a Non-Magnetic Polar Metal
Supplementary Materials
[1]
H. T. Stokes and D. M. Hatch, ”FINDSYM: Program for
Identifying the Space Group Symmetry of a Crystal.” J.
Appl. Cryst.
38
, 237-238 (2005), ISOTROPY Software
Suite, http://iso.byu.edu.

7
TABLE I. Calculated crystallographic parameters for R3cLiOsO3using LDA functional.
LiOsO3a=b= 4.9399 ˚
A, c= 13.3019 ˚
A
R3c α =β= 90◦,γ= 120◦
Atom Wyck. Site x y z
Li 6a0 0 0.61117
Os 6b0 0 0.32084
O 18b-0.00388 0.36259 0.06825
TABLE II. Calculated crystallographic parameters for R3cLiNbO3using LDA functional.
LiNbO3a=b= 5.1052 ˚
A, c= 13.7472 ˚
A
R3c α =β= 90◦,γ= 120◦
Atom Wyck. Site x y z
Li 6a0 0 0.61517
Nb 6b0 0 0.33169
O 18b-0.01367 0.35987 0.06330
TABLE III. Calculated crystallographic parameters for P c Li2NbOsO6using the LDA functional.
LiOsO3/LiNbO3a= 7.35270 ˚
A, b= 5.02739 ˚
A, c= 5.36541 ˚
A
P c α =γ= 90◦,β= 95.109◦
Atom Wyck. Site x y z
Li1 2a0.27896 0.25751 0.45909
Li2 2a0.78342 0.74972 -0.07013
Nb 2a-0.00633 0.25287 0.00169
Os 2a0.49713 0.75123 0.53150
O1 2a0.23965 0.12376 0.02510
O2 2a0.73578 0.60514 0.54599
O3 2a-0.09599 0.05685 0.71217
O4 2a0.41768 0.54538 0.23192
O5 2a0.04578 0.58866 0.85929
O6 2a0.54412 0.04168 0.32305
TABLE IV. Calculated crystallographic parameters for P c Li2NbOsO6without monoclinic angle using the LDA functional.
LiOsO3/LiNbO3a= 7.35884 ˚
A, b= 5.03159 ˚
A, c= 5.36989 ˚
A
P c α =β=γ= 90◦
Atom Wyck. Site x y z
Li1 2a0.27310 0.26765 0.47516
Li2 2a0.78081 0.75357 -0.05429
Nb 2a-0.00421 0.25110 0.00188
Os 2a0.49815 0.75234 0.52637
O1 2a0.24071 0.12246 0.01238
O2 2a0.73609 0.60651 0.54411
O3 2a-0.09326 0.05556 0.71992
O4 2a0.41773 0.53696 0.24015
O5 2a0.04603 0.58671 0.85024
O6 2a0.54504 0.03169 0.30376

8
TABLE V. Calculated crystallographic parameters for
P c
Li
2
NbOsO
6
without monoclinic angle using the LSDA+
U
with
U=Uc=0.5 eV.
LiOsO3/LiNbO3a= 7.35714 ˚
A, b= 5.03042 ˚
A, c= 5.36865 ˚
A
P c α =β=γ= 90◦
Atom Wyck. Site x y z
Li1 2a0.27431 0.26460 0.47149
Li2 2a0.77680 0.75646 -0.05271
Nb 2a-0.00460 0.25150 0.00212
Os 2a0.49708 0.75063 0.52604
O1 2a0.24114 0.12241 0.01487
O2 2a0.73596 0.60719 0.54175
O3 2a-0.09280 0.05536 0.72002
O4 2a0.41875 0.54274 0.23604
O5 2a0.04702 0.58598 0.84961
O6 2a0.54653 0.03942 0.31046
0
1
2
dxy
dxz+dyz
-2 -1 0 1 2 3
Energy (eV)
0
1
2
DOS (states/ev per f.u.)
LiOsO3
Li2NbOsO6
(a)
(b)
FIG. 5. (Color online) Resolved 5
d
t
2g
states of Os for (a) LiOsO
3
and (b) Li
2
NbOsO
6
within LDA. The bandwidth of the
dxy
orbitals for bulk LiOsO
3
and Li
2
NbOsO
6
are the same while in the superlattice the
dxz
and
dyz
orbitals have a reduced
bandwidth.

9
LiNbO3 hexagonal
setting (R3C)
LiNbO3
rhombohedral
setting
1 0 0
0 1 -1
0 1 1
Substitute Nb layer
with Os layer
Use
FINDSYM Pc symmetry
without
monoclinic
angle
(a) (b) (c)
(d) (e) (f)
giovedì 26 febbraio 15
FIG. 6. (Color online) Superlattice construction: (a) Starting from the
R
3
c
crystal structure of LiNbO
3
in the hexagonal setting
with 30 atoms, (b) we transform to the rhombohedral setting with 10 atoms. (c) Next we double the cell with the transformation
matrix and (d) substitute a NbO
2
layer with OsO
2
layer. (e) We identify the new space group
P c
with FINDSYM [
1
] and finally
(f) we set the monoclinic angle to 90◦.