LETTERS
A strong ferroelectric ferromagnet created by means
of spin–lattice coupling
June Hyuk Lee
1,2
, Lei Fang
3
*, Eftihia Vlahos
2
*, Xianglin Ke
4
*, Young Woo Jung
3
, Lena Fitting Kourkoutis
5
,
Jong-Woo Kim
6
, Philip J. Ryan
6
, Tassilo Heeg
1
, Martin Roeckerath
7
, Veronica Goian
8
, Margitta Bernhagen
9
,
Reinhard Uecker
9
, P. Chris Hammel
3
, Karin M. Rabe
10
, Stanislav Kamba
8
, Ju ¨rgen Schubert
7
, John W. Freeland
6
,
David A. Muller
5,11
, Craig J. Fennie
5
, Peter Schiffer
4
, Venkatraman Gopalan
2
, Ezekiel Johnston-Halperin
3
& Darrell G. Schlom
1
Ferroelectric ferromagnets are exceedingly rare, fundamentally
interesting multiferroic materials that could give rise to new
technologies in which the low power and high speed of field-effect
electronics are combined with the permanence and routability of
voltage-controlled ferromagnetism
1,2
. Furthermore, the properties of
the few compounds that simultaneously exhibit these phenomena
1–5
are insignificant in comparison with those of useful ferroelectrics or
ferromagnets: their spontaneous polarizations or magnetizations are
smaller by a factor of 1,000 or more. The same holds for magnetic- or
electric-field-induced multiferroics
6–8
. Owing to the weak properties
of single-phase multiferroics, composite and multilayer approaches
involving strain-coupled piezoelectric and magnetostrictive com-
ponents are the closest to application today
1,2
. Recently, however,
a new route to ferroelectric ferromagnets was proposed
9
by which
magnetically ordered insulators that are neither ferroelectric nor
ferromagnetic are transformed into ferroelectric ferromagnets
using a single control parameter, strain. The system targeted,
EuTiO
3
, was predicted to exhibit strong ferromagnetism (spontan-
eous magnetization, 7 Bohr magnetons per Eu) and strong ferro-
electricity (spontaneous polarization, 10 mC cm
22
) simultaneously
under large biaxial compressive strain
9
. These values are orders of
magnitude higher than those of any known ferroelectric ferromag-
net and rival the best materials that are solely ferroelectric or fer-
romagnetic. Hindered by the absence of an appropriate substrate to
provide the desired compression we turned to tensile strain. Here we
show both experimentally and theoretically the emergence of a
multiferroic state under biaxial tension with the unexpected benefit
that even lower strains are required, thereby allowing thicker high-
quality crystalline films. This realization of a strong ferromagnetic
ferroelectric points the way to high-temperature manifestations of
this spin–lattice coupling mechanism
10
. Our work demonstrates
that a single experimental parameter, strain, simultaneously con-
trols multiple order parameters and is a viable alternative tuning
parameter to composition
11
for creating multiferroics.
Using epitaxy and the mis-fit strain imposed by an underlying sub-
strate, it is possible to strain dielectric thin films to per cent levels—far
beyond where they would crack in bulk. Such strains are used to
enhance the mobility of transistors
12
and increase superconducting
13
,
ferromagnetic
14,15
and ferroelectric
16
transition temperatures. In fact, it
has been shown experimentally and theoretically that such strains can
even stabilize systems in novel non-bulk phases, for example SrTiO
3
in
ferroelectric phases
17,18
.
Recently a route to achieving simultaneously strong ferromagnetism
and ferroelectricity in a single phase has been proposed
9
. This tech-
nique makes use of a generic mechanism in which the electron spin
couples to the lattice:
v
2
~v
2
0
{l S
i
.S
j
ð1Þ
Here v is the frequency of an infrared-active phonon (lattice) mode,
v
0
is the bare phonon frequency, l is the macroscopic spin–phonon
coupling constant and ÆS
i
N S
j
æ is the nearest-neighbour spin–spin cor-
relation function. Such spin–lattice coupling normally leads to mag-
netocapacitance
19
, but in theory
9
this term, in conjunction with strain,
could tune multiple ferroic order parameters simultaneously, resulting
in the emergence of new ground states
9
. A simple model that captures
the essential physics of this tuning behaviour can be written as a first-
order transition induced by a biquadratic coupling of lattice and mag-
netic order parameters:
F (M,P)~
A
P
P
2
2
z
A
M
M
2
2
z
B
P
P
4
4
z
B
M
M
4
4
{jl’jM
2
P
2
F (L,P)~
A
P
P
2
2
z
A
L
L
2
2
z
B
P
P
4
4
z
B
L
L
4
4
zjl’jL
2
P
2
Here F is the Landau free energy, P, M and L are the ferroelectric,
ferromagnetic and antiferromagnetic order parameters, respectively,
and A
P
, B
P
, A
M
, B
M
, A
L
and B
L
are expansion coefficients. The sign and
strength of the biquadratic coupling coefficient, l9, which is positive
for antiferromagnetic order and negative for ferromagnetic order,
originates in the spin–lattice coupling and is fundamental to the tuning
behaviour. Such biquadratic magnetoelectric coupling, as well its
change of sign under magnetic bias, was recently confirmed for
unstrained bulk EuTiO
3
and was found to be large
20
. The above model
led to the prediction
9
that (001) EuTiO
3
would transform from its
paraelectric and antiferromagnetic unstrained ground state
19
to a
simultaneously ferromagnetic and ferroelectric ground state for com-
pressive strains exceeding 1.2%.
Owing to the lack of appropriate substrates and the high strains
involved for those that do exist (for example, a commensurate EuTiO
3
1
Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853-1501, USA.
2
Department of Materials Science and Engineering, Pennsylvania State
University, University Park, Pennsylvania 16802-5005, USA.
3
Department of Physics, Ohio State University, Columbus, Ohio 43210-1117, USA.
4
Department of Physics and Materials
Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
5
School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853,
USA.
6
Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA.
7
Institute of Bio and Nanosystems, JARA-Fundamentals of Future Information
Technologies, Research Centre Ju ¨lich, D-52425 Ju ¨lich, Germany.
8
Institute of Physics ASCR, Na Slovance 2, 182 21 Prague 8, Czech Republic.
9
Leibniz Institute for Crystal Growth,
Max-Born-Straße 2, D-12489 Berlin, Germany.
10
Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA.
11
Kavli Institute at Cornell for
Nanoscale Science, Ithaca, New York 14853, USA.
*These authors contributed equally to this work.
Vol 466 | 19 August 2010 | doi:10.1038/nature09331
954
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