Fine tuning epitaxial strain in ferroelectrics: PbxSr1-xTiO3 on DyScO3
ABSTRACT Epitaxial strain can be efficiently used to modify the properties of ferroelectric thin films. From the experimental viewpoint, the challenge is to fine-tune the magnitude of the strain. We illustrate here how, by using a suitable combination of composition and substrate, the magnitude of the epitaxial strain can be controlled in a continuous manner. The phase diagram of PbxSr1-xTiO3 films grown epitaxially on (110)-DyScO3 is calculated using a Devonshire-Landau approach. A boundary between in-plane and out-of-plane oriented ferroelectric phases is predicted to take place at x~0.8. A series of PbxSr1-xTiO3 epitaxial films grown by molecular beam epitaxy shows good agreement with the proposed phase diagram.
arXiv:1011.4458v1 [cond-mat.mtrl-sci] 19 Nov 2010
Fine tuning epitaxial strain in ferroelectrics: PbxSr1−xTiO3on DyScO3
G. Rispens,1, a)J.A. Heuver,1and B. Noheda1
Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen,
(Dated: 22 November 2010)
Epitaxial strain can be efficiently used to modify the properties of ferroelectric thin films. From the experi-
mental viewpoint, the challenge is to fine-tune the magnitude of the strain. We illustrate here how, by using a
suitable combination of composition and substrate, the magnitude of the epitaxial strain can be controlled in
a continuous manner. The phase diagram of PbxSr1−xTiO3films grown epitaxially on (110)-DyScO3is cal-
culated using a Devonshire-Landau approach. A boundary between an in-plane and an out-of-plane oriented
ferroelectric phases is predicted to take place at x ≈ 0.8. A series of PbxSr1−xTiO3epitaxial films grown by
Molecular Beam Epitaxy show good agreement with the proposed phase diagram.
PACS numbers: 77.55.Px, 77.80.bg, 77.80.bn
Keywords: ferroelectrics, strain, thin films, phase diagram, phase boundaries
Modifying the properties of crystalline thin films using
the epitaxial strain induced by the substrate as an ad-
justable parameter is known as strain engineering or
strain tuning1. This has captured the interest of several
condensed matter communities because ordering temper-
atures can be increased, physical responses can be en-
hanced and even new functionalities can be added to thin
films utilizing epitaxial strain2–5.
Ferroelectric materials are especially suitable for such
strain studies due to their strong coupling between strain
and electrical polarization. However, despite some very
impressive experimental results6–11, the realization of
strain engineering in ferroelectrics lags behind the pre-
dictions and it is difficult to fully employ the wealth of
interesting possibilities suggested by the theorists12–18.
The limited number of suitable substrate materials is
an important factor in this. Two substrates that have
a good lattice match with many functional perovskites
are SrTiO3 and DyScO3, but there is more than a
percent difference between their (pseudo)cubic lattice
parameters19(see Figure 1a). This difference is too large
if one aims to establish an experimental temperature-
strain (T-u) phase diagram. Moreover, a too large mis-
match will induce various relaxation mechanisms that
will prevent elastic strain accommodation.20,21.
importantly, only if the strain can be tuned continu-
ously, we will be able to access the novel phases18or
novel properties22,23that are theoretically predicted, and
which exist only for a narrow region of strain values.
In this letter we combine the epitaxial strain imposed
by the substrate with compositional variations of the film
in order to change the magnitude of the strain in a con-
tinuous manner. For that we use Sr-substituted PbTiO3
thin films grown on DyScO3substrates. Various reasons
led us to choose these materials. The lattice parame-
ters of PbxSr1−xTiO3, as well as the Curie temperatures,
Ansermet 24, CH-1211 Gen` eve 4, Switzerland
DPMC, University of Geneva, Quai Ernest
00.2 0.40.6 0.81
Nomura & Sawada
Somiya et al.
Xing et al.
Pb Sr TiO
FIG. 1. a) Comparison of the lattice parameter of SrTiO3and
DyScO3 substrates and PbxSr1−xTiO3 thin films. b) Transi-
tion temperature of PbxSr1−xTiO3 versus the Pb content x.
The solid line is calculated from LD theory. The data points
are taken from various literature sources24–26.
TC, vary linearly between the two end members of the
solid solution24–26(see figure 1b). Moreover, above room
temperature, the bulk solid solution does not show other
phases than the well-known paraelectric cubic and fer-
roelectric tetragonal phase of PbTiO326. In this way we
can use a phenomenological Landau-Devonshire (LD) ap-
proach to calculate the phase diagram of PbxSr1−xTiO3
epitaxial thin films on (110)-DyScO3.
was chosen because the strain state of PbxSr1−xTiO3
films epitaxially grown on (110)-DyScO3can be changed
from (slightly) compressive to tensile by varying the Sr-
content. This is in agreement with other reports show-
ing that the polarization of epitaxial PbTiO3 films on
(110)-DyScO3is predominantly out-of-plane27, whereas
the polarization of epitaxial SrTiO3films on DyScO3is
in the plane of the film7,8,28.
FIG. 2. Phase diagram versus composition for PbxSr1−xTiO3
strained on DyScO3 as calculated using LD theory. The top
axis defines the ’iso-strain’ lines in the composition versus
The phase diagram of PbxSr1−xTiO3on (110)-DyScO3
(110) was calculated including the epitaxial strain in the
LD free energy expansion, as described by Pertsev et
al.18. The composition-dependent Landau coefficients of
PbxSr1−xTiO3have been constructed as a linear combi-
nation of the well-known Landau coefficients of the end
members, PbTiO3and SrTiO3, similar to refs.29–31. The
Landau coefficients of the end members are those of refs.
32 and 31, respectively.33
For the temperature dependent coefficient a1= α1(T−
TC), the composition dependence of TC and α1 are
treated separately. The misfit strain depends on both
composition and temperature, because of differences in
thermal expansion between film and substrate. As the
thermal expansion for PbTiO3 and SrTiO3 are almost
equal34, the thermal expansion of PbxSr1−xTiO3 is as-
sumed to be that of PbTiO3.
sion of DyScO3 does significantly differ from that of
PbxSr1−xTiO319. The small anisotropy of 0.05% in the
lattice parameters of the (110) DyScO3plane (3.945˚ A vs
3.947˚ A at room temperature) was neglected, and the av-
The thermal expan-
erage of the a and b lattice parameters was used as the
in-plane lattice parameter in the calculations. This is
justified by the results in ref.35showing that Landau sim-
ulations on single domain PbTiO3and Pb0.35Sr0.65TiO3
films give no qualitative difference in the phase diagram
after including a substrate anisotropy as small as that of
DyScO335. Since the oxygen rotations present in SrTiO3
below 105K are not included in the calculations, our re-
sults are not expected to be valid for x < 0.531. Finally,
the LD approach used here considers uniform polariza-
tion throughout the film, thus possible domain formation
and polarization gradients are not taken into account in
this approximation. The resulting free energy expansion
was minimized with respect to the Cartesian components
of the polarization (along the axes of the perovskite unit
cell) to obtain a phase diagram as a function of Pb con-
The calculated phase diagram of PbxSr1−xTiO3 on
DyScO3is shown in figure . The misfit strain goes from
a very small compressive strain for pure PbTiO3 to a
tensile strain that increases with increasing Sr content.
The different strain values stabilize polarizations along
different directions. For large x, PbxSr1−xTiO3 is pre-
dicted to be a c-phase ferroelectric, with the electrical
polarization, P, perpendicular to the film plane, similar
to that of PbTiO3. At lower x an aa-phase, with P ?
?110?, should be stabilized. In between these two, an
intermediate r-phase is expected, in which the polariza-
tion points somewhere in between ?001? and ?110?. The
addition of Sr gives rise to the decrease in Tc.
To test our predictions, a series of PbxSr1−xTiO3thin
films with a thickness of 50 monolayers ( 20nm) were
grown on (110)-DyScO3using Molecular Beam Epitaxy
(MBE). The films were grown at a substrate temperature
of 650oC, with an adsorption controlled growth mecha-
nism as described for PbTiO336–38. Sr substitution is
obtained by providing a constant flux of atomic Sr for a
certain amount of time, tSr, at each monolayer. Figure 3
shows the out-of-plane lattice parameter c, obtained from
XRD 2θ-ω scans, versus the Pb content, x. At large x,
a lattice parameter larger than the pseudo-cubic lattice
parameters of DyScO3 (c= 3.945˚ A) is observed in the
films. For fully strained films and neglecting the small
difference between the two in-plane lattice parameters of
the substrate, this leads to a tetragonal structure similar
to that of bulk PbTiO3. The polarization is expected to
be along the symmetry axis, so this corresponds to a c-
ferroelectric phase18, with P?. At x≈ 0.83, there is a
discontinuous decrease in the out-of-plane lattice param-
eter to a value smaller than that of DyScO3, leading to
a structure with larger in-plane lattice parameters. Here
the polarization is expected to lie in the plane of the film.
The experimental observations are in good agreement
with the proposed phase diagram.
boundary between the in-plane and out-of-plane polar-
ization is well reproduced experimentally. Temperature-
dependent measurements indicate that the Curie temper-
atures of the strained films are also in agreement with the
In particular, the
44 4546 474849
42 43 44 454647
FIG. 3. Out-of-plane XRD results for PbxSr1−xTiO3 films grown on DyScO3. The middle graph shows the evolution of the c
lattice parameter with x. There is a clear transition with decreasing x from a unit cell with a long out-of-plane lattice parameter
to a unit cell with long in-plane lattice parameters.
calculated ones39. However, the assumption of uniform
polarization throughout the film is most likely not valid,
since domains are expected to form27,28, most likely mod-
ifying the phase diagram. Reciprocal space maps in our
films reveal, indeed, the presence of domains39. Next we
plan to look into the mechanisms of domain formation as
well as to grow similar films with bottom and top elec-
trodes in order to investigate the ferroelectric properties
across the phase diagram.
In summary we have shown that the misfit strain in
ferroelectric thin films can be fine-tuned by using a suit-
able combination of composition and substrate.
strategy was applied to epitaxial PbxSr1−xTiO3films on
(110)-DyScO3. The calculated phase diagram as a func-
tion of composition (which implies changes in epitaxial
strain) predicts a phase landscape similar to that in the
phase diagram of PbTiO3 as a function of strain18(in-
plane, out-of-plane and intermediate polar phases). In
the present case, continuous tuning across the phase di-
agram can be achieved. The structural evolution of a
series of PbxSr1−xTiO3epitaxial films is consistent with
a change in the polarization direction, in good agreement
with the proposed phase diagram.
We are grateful to Sergey Artyukhin for useful dis-
cussions. This work is part of the research programme
of the Foundation for Fundamental Research on Matter
(FOM), which is part of the Netherlands Organisation
for Scientific Research (NWO).
Annual Review of Materials Research 37, 589 (2007).
Journal of Magnetism and Magnetic Materials 93, 562 (1991).
3J.-P. Locquet, J. Perret, J. Fompeyrine, E. Machler, J. W. Seo,
and G. Van Tendeloo, Nature 394, 453 (1998).
4S. C. Jain, M. Willander, J. Narayan, and R. Van Overstraeten,
Journal of Applied Physics 87, 965.
5R. Ramesh and N. A. Spaldin, Nature materials 6, 21 (2007).
6H. B´ ea, B. Dup´ e, S. Fusil, R. Mattana, E. Jacquet, B. Warot-
Fonrose, F. Wilhelm, A. Rogalev, S. Petit, V. Cros, A. Anane,
F. Petroff, K. Bouzehouane, G. Geneste, B. Dkhil, S. Lisenkov,
I. Ponomareva, L. Bellaiche, M. Bibes,
Physical Review Letters 102, 217603 (2009).
and A. Barth´ el´ emy,
7M. D. Biegalski, Y. Jia, D. G. Schlom, S. Trolier-McKinstry,
S. K. Streiffer, V. Sherman, R. Uecker,
Applied Physics Letters 88, 192907 (2006).
8J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li,
S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagant-
sev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer,
J. Levy, and D. G. Schlom, Nature 430, 758 (2004).
9M. P. Warusawithana, C. Cen, C. R. Sleasman, J. C. Woicik,
Y. Li, L. F. Kourkoutis, J. A. Klug, H. Li, P. Ryan, L.-P. Wang,
M. Bedzyk, D. A. Muller, L.-Q. Chen, J. Levy, and D. G. Schlom,
Science 324, 367 (2009).
10R. J. Zeches, M. D. Rossell, J. X. Zhang, A. J. Hatt, Q. He, C. H.
Yang, A. Kumar, C. H. Wang, A. Melville, C. Adamo, G. Sheng,
Y. H. Chu, J. F. Ihlefeld, R. Erni, C. Ederer, V. Gopalan,
L. Q. Chen, D. G. Schlom, N. A. Spaldin, L. W. Martin, and
R. Ramesh, Science 326, 977 (2009).
11J. H. Lee, L. Fang, E. Vlahos, X. Ke, Y. W. Jung, L. F. Kourk-
outis, J.-W. Kim, P. J. Ryan, T. Heeg, M. Roeckerath, V. Goian,
M. Bernhagen, R. Uecker, P. C. Hammel, K. M. Rabe, S. Kamba,
J. Schubert, J. W. Freeland, D. A. Muller, C. J. Fennie, P. Schif-
fer, V. Gopalan, E. Johnston-Halperin,
Nature 466, 954 (2010).
Physical Review Letters 104, 037601 (2010).
Physical Review B 72, 144101 (2005).
Physical Review Letters 95, 257601 (2005).
15C. Fennie and K. Rabe, Physical Review Letters 97, 267602 (2006).
16V. G. Koukhar, N. A. Pertsev, and R. Waser, Physical Review
B 64, 214103 (2001).
Physical Review Letters 84, 3722 (2000).
18N. A. Pertsev, A. G. Zembilgotov,
Physical Review Letters 80, 1988 (1998).
D. G. Schlom,C. D. Brandle,
Journal of Materials Research 20, 952 (2005).
Journal of Applied Physics 76, 466 (1994).
21A. H. G. Vlooswijk, B. Noheda, G. Catalan, A. Janssens, B. Bar-
cones, G. Rijnders, D. H. A. Blank, S. Venkatesan, B. Kooi, and
J. T. M. de Hosson, Applied Physics Letters 91, 112901 (2007).
22J. Wojdel, Physical Review Letters 105, 037208 (2010).
23D. Damjanovic, Applied Physics Letters 97, 062906 (2010).
24S. Nomura and S. Sawada, Journal of the Physical Society of
Japan 10, 108 (1955).
25Y. Somiya, A. S. Bhalla, and L. E. Cross, International Journal
of Inorganic Materials 3, 709 (2001).
26X. R. Xing,J. Chen,J. X. Deng,
and P. Reiche,
and D. G. Schlom,
and A. K. Tagantsev,
and A. J. Ven Graitis,
Journal of Alloys and Compounds 360, 286 (2003).
Physical Review Letters 96, 127602 (2006).
28M. D. Biegalski, E. Vlahos, G. Sheng, Y. L. Li, M. Bern-
hagen, P. Reiche, R. Uecker, S. K. Streiffer, L. Q. Chen,
V. Gopalan,D. G. Schlom,
Physical Review B 79, 224117 (2009).
29Z. Ban and S. Alpay, Journal of Applied Physics 91, 9288 (2002).
30M. Dawber, N. Stucki, C. Lichtensteiger, S. Gariglio, P. Ghosez,
and J. M. Triscone, Advanced Materials 19, 4153 (2007).
31V. Shirokov,Y. Yuzyuk,B. Dkhil,
Physical Review B 79, 1 (2009).
32M. J. Haun, E. Furman, S. J. Jang, H. A. McKinstry, and L. E.
Cross, Journal of Applied Physics 62, 3331 (1987).
33All values are given in SI units (T = K, a1 = J m C−2, aij = J
m5C−4, aijk= J m9C−6, Qij = m4C−2, sij = m3J−1). For
PbTiO3: a1= 3.8×105(T-752), a11= -7.3×107, a12 = 7.5×108,
a111= 2.6×108, a112= 6.1×108, a123= -3.7×109, Q11= 0.089,
Q12= -0.026, Q44= 0.0675, s11= 3.7×10−12, s12= -2.5×10−12,
and V. Lemanov,
s44= 9.0×10−12. For SrTiO3: a1= 7.06×105(T-35.5) (this is an
approximation only valid above 100K40), a11= 1.04×108, a12=
0.746×108, a111 = 0, a112 = 0, a123 =0, Q11 = 0.0496, Q12 =
-0.0131, Q44= 0.019, s11= 3.52×10−12, s12= -0.85×10−12, s44
34A. M. H. K. H. Hellwege, ed., Landolt-Bornstein, Vol. III/16a
(Springer-Verlag, Berlin Heidelberg New York, 1981).
35A. G. Zembilgotov, N. A. Pertsev, U. Bottger, and R. Waser,
Applied Physics Letters 86, 052903 (2005).
Journal of Crystal Growth 174, 473 (1997).
37C. D. Theis, J. Yeh, D. G. Schlom, M. E. Hawley, and G. W.
Brown, Thin Solid Films 325, 107 (1998).
38G. Rispens and B. Noheda, Integrated Ferroelectrics 92, 30 (2007).
39G. Rispens, N. O., J. Heuver,
40K. A. Rabe, T. J.-M., and C. H. Ahn, eds., Physics of Ferro-
electrics, A modern perspective (Springer Verlag, Berlin, 2007).
and B. Noheda, In preparation