The three-dimensional arrangement and orientation of domain walls in ferroelectric K0.9Na0.1NbO3/(110)NdScO3 epitaxial thin films were investigated at different temperatures both experimentally by means of piezoresponse force microscopy and three-dimensional x-ray diffraction and theoretically by three-dimensional phase-field simulations. At room temperature, a well-ordered herringbone-like domain pattern appears in which there is a periodic arrangement of a1a2/MC monoclinic phases. Four different types of domain walls are observed, which can be characterized by out-of-plane tilt angles of ±45° and in-plane twist angles of ±21°. For the orthorhombic high-temperature phase, a periodic a1/a2 stripe domain pattern with exclusive in-plane polarization is formed. Here, two different types of domain walls are observed, both of them having a fixed out-of-plane domain wall angle of 90° but distinguished by different in-plane twist angles of ±45°. The experimental results are fully consistent with three-dimensional phase-field simulations using anisotropic misfit strains. The qualitative agreement between the experiment and the theory applies, in particular, to the wide phase transition range between about 180 °C and 260 °C. In this temperature range, a complex interplay of coexisting monoclinic a1a2/MC and orthorhombic a1/a2 phases takes place.
REFERENCES
1.
A. K.
Tagantsev
, L. E.
Cross
, and J.
Fousek
, Domains in Ferroic Crystals and Thin Films
(Springer
, 2010
), ISBN: 978-1-4419-1417-0.2.
Topological Structures in Ferroic Materials
, Springer Series in Materials Science, edited by J.
Seidel
(Springer
, 2016
), ISBN: 978-3-319-25301-5.3.
G.
Catalan
, J.
Seidel
, R.
Ramesh
, and J. F.
Scott
, “Domain wall nanoelectronics
,” Rev. Mod. Phys.
84
, 119
–156
(2020
). 4.
L. J.
McGilly
, P.
Yudin
, L.
Feigl
, A. K.
Tagantsev
, and N.
Setter
, “Controlling domain wall motion in ferroelectric thin films
,” Nat. Nanotechnol.
10
, 145
–150
(2015
). 5.
L. J.
McGilly
, L.
Feigl
, T.
Sluka
, P.
Yudin
, A. K.
Tagantsev
, and N.
Setter
, “Velocity control of 180° domain walls in ferroelectric thin films by electrode modification
,” Nano Lett.
16
, 68
–73
(2016
). 6.
C.
Kittel
, “Theory of the structure of ferromagnetic domains in films and small particles
,” Phys. Rev.
70
, 965
–971
(1946
). 7.
A. S.
Everhardt
, S.
Matzen
, N.
Domingo
, G.
Catalan
, and B.
Noheda
, “Ferroelectric domain structures in low-strain BaTiO3
,” Adv. Electron. Mater.
2
, 1500214
(2016
). 8.
B.
Meyer
and D.
Vanderbilt
, “Ab initio study of ferroelectric domain walls in PbTiO3
,” Phys. Rev. B
65
, 104111
(2002
). 9.
A. A.
Bokov
and Z. G.
Ye
, “Domain structure in the monoclinic Pm phase of Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystals
,” J. Appl. Phys.
95
, 6347
–6359
(2004
). 10.
D.
Braun
, M.
Schmidbauer
, M.
Hanke
, A.
Kwasniewski
, and J.
Schwarzkopf
, “Tunable ferroelectric domain wall alignment in strained monoclinic KxNa1−xNbO3 epitaxial films
,” Appl. Phys. Lett.
110
, 232903
(2017
). 11.
Z.
Chen
, Z.
Luo
, C.
Huang
, Y.
Qi
, P.
Yang
, L.
You
, C.
Hu
, T.
Wu
, J.
Wang
, C.
Gao
, T.
Sritharan
, and L.
Chen
, “Low-symmetry monoclinic phases and polarization rotation path mediated by epitaxial strain in multiferroic BiFeO3 thin films
,” Adv. Funct. Mater.
21
, 133
–138
(2011
). 12.
C.
Hu
, X.
Meng
, M.-H.
Zhang
, H.
Tian
, J. E.
Daniels
, P.
Tan
, F.
Huang
, L.
Li
, K.
Wang
, J.-F.
Li
, Q.
Lu
, W.
Cao
, and Z.
Zhou
, “Ultra-large electric field-induced strain in potassium sodium niobate crystals
,” Sci. Adv.
6
, eaay5979
(2020
). 13.
J.
Koruza
, H.
Liu
, M.
Höfling
, M.-H.
Zhang
, and P.
Veber
, “(K,Na)NbO3-based piezoelectric single crystals: Growth methods, properties, and applications
,” J. Mater. Res.
35
, 990
–1016
(2020
). 14.
Y.
Saito
, H.
Takao
, T.
Tani
, T.
Nonoyama
, K.
Takatori
, T.
Homma
, T.
Nagaya
, and M.
Nakamura
, “Lead-free piezoceramics
,” Nature
432
, 84
–87
(2004
). 15.
P. K.
Panda
and B.
Sahoo
, “PZT to lead free piezo ceramics: A review
,” Ferroelectrics
474
, 128
–143
(2015
). 16.
N. A.
Pertsev
, A. G.
Zembilgotov
, and A. K.
Tagantsev
, “Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films
,” Phys. Rev. Lett.
80
, 1988
–1991
(1998
). 17.
G.
Bai
and W.
Ma
, “Phenomenological analysis of phase transitions in epitaxial perovskite ferroelectric thin films
,” Phys. B Condens. Matter
405
, 1901
–1907
(2010
). 18.
M.-J.
Zhou
, J.-J.
Wang
, L.-Q.
Chen
, and C.-W.
Nan
, “Strain, temperature, and electric-field effects on the phase transition and piezoelectric responses of K0.5Na0.5NbO3 thin films
,” J. Appl. Phys.
123
, 154106
(2018
). 19.
J.
Luo
, W.
Sun
, Z.
Zhou
, H.-Y.
Lee
, K.
Wang
, F.
Zhu
, Y.
Bai
, Z. J.
Wang
, and J.-F.
Li
, “Monoclinic (K,Na)NbO3 ferroelectric phase in epitaxial films
,” Adv. Electron. Mater.
3
, 1700226
(2017
). 20.
J.
Luo
, W.
Sun
, Z.
Zhou
, Y.
Bai
, Z. J.
Wang
, G.
Tian
, D.
Chen
, X.
Gao
, F.
Zhu
, and J.-F.
Li
, “Domain evolution and piezoelectric response across thermotropic phase boundary in (K,Na)NbO3-based epitaxial thin films
,” ACS Appl. Mater. Interfaces
9
, 13315
–13322
(2017
). 21.
J.
Schwarzkopf
, D.
Braun
, M.
Hanke
, R.
Uecker
, and M.
Schmidbauer
, “Strain engineering of ferroelectric domains in KxNa1−xNbO3 epitaxial layers
,” Front. Mater.
4
, 26
(2017
). 22.
V. G.
Koukhar
, N. A.
Pertsev
, and R.
Waser
, “Thermodynamic theory of epitaxial ferroelectric thin films with dense domain structures
,” Phys. Rev. B
64
, 214103
(2001
). 23.
F.
Xue
, Y.
Ji
, and L.-Q.
Chen
, “Theory of strain phase separation and strain spinodal: Applications to ferroelastic and ferroelectric systems
,” Acta Mater.
133
, 147
–159
(2017
). 24.
B.
Wang
, H.-N.
Chen
, J.-J.
Wang
, and L.-Q.
Chen
, “Ferroelectric domain structures and temperature-misfit strain phase diagrams of K1−xNaxNbO3 thin films: A phase-field study
,” Appl. Phys. Lett.
115
, 092902
(2019
). 25.
L.
Bogula
, L.
von Helden
, C.
Richter
, M.
Hanke
, J.
Schwarzkopf
, and M.
Schmidbauer
, “Ferroelectric phase transitions in multi-domain K0.9Na0.1NbO3 strained thin films
,” Nano Futures
4
, 035005
(2020
). 26.
M.
Schmidbauer
, D.
Braun
, T.
Markurt
, M.
Hanke
, and J.
Schwarzkopf
, “Strain engineering of monoclinic domains in K0.9Na0.1NbO3 epitaxial layers: A pathway to enhanced piezoelectric properties
,” Nanotechnology
28
, 24LT02
(2017
). 27.
L.-Q.
Chen
, “Phase-field method of phase transitions/domain structures in ferroelectric thin films: A review
,” J. Am. Ceram. Soc.
91
, 1835
–1844
(2008
). 28.
J.-J.
Wang
, B.
Wang
, and L.-Q.
Chen
, “Understanding, predicting, and designing ferroelectric domain structures and switching guided by the phase-field method
,” Annu. Rev. Mater. Res.
49
, 127
–152
(2019
). 29.
Y. L.
Li
, S. Y.
Hu
, Z. K.
Liu
, and L. Q.
Chen
, “Effect of electrical boundary conditions on ferroelectric domain structures in thin films
,” Appl. Phys. Lett.
81
, 427
–429
(2002
). 30.
Y. L.
Li
, S. Y.
Hu
, Z. K.
Liu
, and L. Q.
Chen
, “Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films
,” Acta Mater.
50
, 395
–411
(2002
). 31.
L.
Liang
, Y. L.
Li
, L.-Q.
Chen
, Y.
Hu
, and G.-H.
Lu
, “A thermodynamic free energy function for potassium niobate
,” Appl. Phys. Lett.
94
, 072904
(2009
). 32.
H.
Pohlmann
, J.-J.
Wang
, B.
Wang
, and L.-Q.
Chen
, “A thermodynamic potential and the temperature-composition phase diagram for single-crystalline K1−xNax NbO3 (0≤ x≤ 0.5)
,” Appl. Phys. Lett.
110
, 102906
(2017
). 33.
B.
Wang
, L.
Bogula
, A.
Ladera
, J.-J.
Wang
, and L.-Q.
Chen
, “Phase stability and three-dimensional structures of polydomains in orthorhombic ferroelectric thin films under anisotropic misfit strains,” (unpublished).34.
C.
Hirschle
, J.
Schreuer
, S.
Ganschow
, and L.
Peters
, “Thermoelastic anisotropy in NdScO3 and NdGaO3 perovskites
,” Mater. Chem. Phys.
254
, 123528
(2020
). 35.
H. D.
Megaw
, “The thermal expansion of interatomic bonds, illustrated by experimental evidence from certain niobates
,” Acta Crystallogr. A
24
, 589
–604
(1968
). 36.
I. T.
Weber
, A.
Rousseau
, M.
Guilloux-Viry
, V.
Bouquet
, and A.
Perrin
, “Microstructure comparison between KNbO3 thin films grown by polymeric precursors and PLD methods
,” Solid State Sci.
7
, 1317
–1323
(2005
). 37.
J.
Sellmann
, J.
Schwarzkopf
, A.
Kwasniewski
, M.
Schmidbauer
, D.
Braun
, and A.
Duk
, “Strained ferroelectric NaNbO3 thin films: Impact of pulsed laser deposition growth conditions on structural properties
,” Thin Solid Films
570
, 107
–113
(2014
). 38.
T.-H.
Lee
, D.-H.
Kim
, B.-Y.
Kim
, H.-Y.
Choi
, J.-H.
Oh
, C.-Y.
Kang
, and S.
Nahm
, “Structural and electrical properties of KNbO3 thin film grown on a Pt/Ti/SiO2/Si substrate using the RF magnetron sputtering method
,” Acta Mater.
112
, 53
–58
(2016
). 39.
J.
Schwarzkopf
, M.
Schmidbauer
, T.
Remmele
, A.
Duk
, A.
Kwasniewski
, S.
Bin Anooz
, A.
Devi
, and R.
Fornari
, “Strain induced phase transitions in NaNbO3 epitaxial thin films grown by metal-organic chemical vapor deposition
,” J. Appl. Crystallogr.
45
, 1015
–1023
(2012
). 40.
J.
Als-Nielsen
and D.
McMorrow
, Elements of Modern X-ray Physics
(Wiley
, 2011
).41.
A. S.
Disa
, F. J.
Walker
, and C. H.
Ahn
, “High-resolution crystal truncation rod scattering: Application to ultrathin layers and buried interfaces
,” Adv. Mater. Interfaces
7
, 1901772
(2020
). 42.
M.
Schmidbauer
, P.
Schäfer
, S.
Besedin
, D.
Grigoriev
, R.
Köhler
, and M.
Hanke
, “A novel multi-detection technique for 3D reciprocal space mapping in grazing incidence x-ray diffraction
,” J. Synchrotron Radiat.
15
, 549
–557
(2008
). 43.
Z. L.
Luo
, H.
Huang
, H.
Zhou
, Z. H.
Chen
, Y.
Yang
, L.
Wu
, C.
Zhu
, H.
Wang
, M.
Yang
, S.
Hu
, H.
Wen
, X.
Zhang
, Z.
Zhang
, L.
Chen
, D. D.
Fong
, and C.
Gao
, “Probing the domain structure of BiFeO3 epitaxial films with three-dimensional reciprocal space mapping
,” Appl. Phys. Lett.
104
, 182901
(2014
). 44.
D.
Braun
, M.
Schmidbauer
, M.
Hanke
, and J.
Schwarzkopf
, “Hierarchy and scaling behaviour of multi-rank domain patterns in ferroelectric K0.9Na0.1NbO3 strained films
,” Nanotechnology
29
, 015701
(2018
). 45.
See https://www.anton-paar.com for detailed technical specifications.
46.
R.
Xu
, S.
Liu
, I.
Grinberg
, J.
Karthik
, A. R.
Damodaran
, A. M.
Rappe
, and L. W.
Martin
, “Ferroelectric polarization reversal via successive ferroelastic transitions
,” Nat. Mater.
14
, 79
–86
(2015
). 47.
W. L.
Li
, T. D.
Zhang
, Y. F.
Hou
, Y.
Zhao
, D.
Xu
, W. P.
Cao
, and W. D.
Fei
, “Giant piezoelectric properties of BZT–0.5BCT thin films induced by nanodomain structure
,” RSC Adv.
4
, 56933
(2014
). © 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
