PRL 101, 107603 (2008)
PHYSICAL REVIEW LETTERS
week ending
5 SEPTEMBER 2008
Onset of Ferrielectricity and the Hidden Nature of Nanoscale Polarization
in Ferroelectric Thin Films
Matias Nufiez1 and M. Buongiorno Nardelli1'2
1Center for High Performance Simulation and Department Physics, North Carolina State University,
Raleigh, North Carolina 27695, USA
2CCS-CSM, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
(Received 13 March 2008; published 5 September 2008)
Using calculations from first principles and the concept of layer polarization, we have elucidated the
nanoscale organization and local polarization in ferroelectric thin films between metallic contacts. The
profile of the local polarization for different film thicknesses unveils a peculiar spatial pattern of atomic
layers with uncompensated dipoles in what was originally thought to be a ferroelectric domain. This
effectively ferrielectric behavior is induced by the dominant roles of the interfaces at such reduced
dimensionality and can be interpreted using a simple classical model where the latter are explicitly taken
into account.
DOI: 10.1103/PhysRevLett.101.107603
Since ferroelectricity is a macroscopic collective prop-
erty of bulk materials, its existence in ultrathin nanoscale
films is a matter of debate and a subject of intense scientific
scrutiny [1,2]. In a seminal theoretical paper, Junquera
et al. [3] have suggested that the appearance of ferroelec-
tricity in thin films of BaTiO3 with SrRuO3 contacts should
be limited to thicknesses of more than six unit cells. More
recently this picture has been broadened, and a variety of
studies have shown that thin oxide films can indeed main-
tain some ferroelectricity at thicknesses even smaller than
six unit cells [4-7].
The size limit of ferroelectricity in ultrathin films can be
understood using a simple electrostatics argument: as the
thickness of the oxide film is reduced, the intensity of the
depolarization field (DF) is made stronger [3], thus increas-
ing the electrostatic energy of the system. In a ferroelectric
crystal this energy contribution can be minimized in two
ways: either by breaking the polarization pattern in 180
stripe domains to reduce the magnitude of the surface
dipole density or by a reduction of the ionic polarization
while the system remains in a monodomain state [7]. The
final polarization pattern depends on the individual mate-
rial and/or structure, and understanding which system
modification will occur under what conditions is still a
matter of debate [7].
At small dimensions, the spatial confinement and the
interface details become extremely relevant since they
determine the spatial localization of the electrons and
thus influence directly the ferroelectric characteristics
and the electronic properties of the system [8]. Therefore,
to clarify the behavior of ferroelectric thin films in the
nanometer regime it is crucial to obtain a precise descrip-
tion not only of the geometry and electronic properties of
the film but first and foremost of the polarization profile
inside the oxide.
In order to obtain a complete description of ferroelec-
tricity at the nanoscale we have exploited the notion of
PACS numbers: 77.80.Dj, 31.15.es, 77.55.+f, 77.90.+k
layer polarization (LP). This idea, based on modern theory
of polarization [9,10] and the concept of maximally local-
ized Wannier functions [11], was recently introduced to
describe the layer-by-layer modulation of polarization in
ferroelectric superlattices [12-14].
We have applied this method to a model metal-
ferroelectric system (BaTiO3/Pt) and obtained a detailed
spatial profile of the polarization in the oxide region in the
direction of growth that accounts not only for the ionic
displacements but also for the spatial rearrangement of the
electron density. It is important to note that using more
standard methods to evaluate macroscopic polarization,
this information would have remained hidden by the aver-
aging procedure, or would have produced misleading
results.
In this Letter we show that the ferroelectric structures
associated with small length scales are more complex than
previously thought, mainly due to the redistribution of the
electrons under the constraints imposed by the interfaces.
In particular, the oxide develops a ferrielectric pattern of
an unbalanced dipole structure that is particularly evident
in Fig. 1(a), where we show how positive ionic displace-
ments (rumplings) on all the atomic layers of a thin BaTiO3
film correspond actually to layer dipoles of opposite signs.
This is a consequence of the interplay between the orien-
tation and magnitude of the dipoles with the DF, their
mutual interaction and the nature of the interfaces. A
simple analytic model of a ferroelectric thin film where
these effects are explicitly taken into account can capture
all these features and it will be discussed in detail at the
end.
We have simulated thin films of BaTiO3 between Pt
metal contacts in a (001) stack, where the oxide is termi-
nated with a BaO plane at both interfaces [15] and the
system is simulated under short-circuit boundary condi-
tions. The different supercells can be labeled as
Pt/(BaO-TiO2)m-BaO/Pt with m =1, 2,4, 6. We used
2008 The American Physical Society
0031-9007/08/101(10)/107603(4)
107603-1
