[en] The observation of unexpected polarization textures such as vortices, skyrmions, and merons in various oxide heterostructures has challenged the widely accepted picture of ferroelectric domain walls as being Ising-like. Bloch components in the 180° domain walls of PbTiO3 have recently been reported in PbTiO3/SrTiO3 superlattices and linked to domain wall chirality. While this opens exciting perspectives, the ubiquity of this Bloch component remains to be further explored. In this work, we present a comprehensive investigation of domain walls in PbTiO3/SrTiO3 superlattices, involving a combination of first- and second-principles calculations, phase-field simulations, diffuse scattering calculations, and synchrotron-based diffuse x-ray scattering. Our theoretical calculations highlight that the previously predicted Bloch polarization in the 180° domain walls in PbTiO3/SrTiO3 superlattices might be more sensitive to the boundary conditions than initially thought and is not always expected to appear. Employing diffuse scattering calculations for larger systems, we develop a method to probe the complex structure of domain walls in these superlattices via diffuse x-ray scattering measurements. Through this approach, we investigate depolarization-driven ferroelectric polarization rotation at the domain walls. Our experimental findings, consistent with our theoretical predictions for realistic domain periods, do not reveal any signatures of a Bloch component in the centers of the 180° domain walls of PbTiO3/SrTiO3 superlattices, suggesting that the precise nature of domain walls in the ultrathin PbTiO3 layers is more intricate than previously thought and deserves further attention.
Disciplines :
Physics
Author, co-author :
Zatterin, Edoardo; ESRF - The European Synchrotron, Grenoble, France
Ondrejkovic, Petr; Institute of Physics of the Czech Academy of Sciences, Praha 8, Czech Republic
Bastogne, Louis ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM)
Lichtensteiger, Céline ; Department of Quantum Matter Physics, University of Geneva, Geneva, Switzerland
Tovaglieri, Ludovica ; Department of Quantum Matter Physics, University of Geneva, Geneva, Switzerland
Chaney, Daniel A. ; ESRF - The European Synchrotron, Grenoble, France
Sasani, Alireza ; Université de Liège - ULiège > Département de physique > Physique théorique des matériaux
Schülli, Tobias; ESRF - The European Synchrotron, Grenoble, France
Bosak, Alexei; ESRF - The European Synchrotron, Grenoble, France
Leake, Steven ; ESRF - The European Synchrotron, Grenoble, France
Zubko, Pavlo ; Department of Physics and Astronomy, University College London, London, United Kingdom ; London Centre for Nanotechnology, London, United Kingdom
Ghosez, Philippe ; Université de Liège - ULiège > Département de physique > Physique théorique des matériaux
Hlinka, Jirka ; Institute of Physics of the Czech Academy of Sciences, Praha 8, Czech Republic
Triscone, Jean-Marc; Department of Quantum Matter Physics, University of Geneva, Geneva, Switzerland
Hadjimichael, Marios ; Department of Quantum Matter Physics, University of Geneva, Geneva, Switzerland ; Department of Physics, University of Warwick, Coventry, United Kingdom
SNF - Schweizerischer Nationalfonds zur Förderung der wissenschaftlichen Forschung EU - European Union MSMT - Ministerstvo školství, mládeže a tělovýchovy České republiky F.R.S.-FNRS - Fonds de la Recherche Scientifique UKRI - UK Research and Innovation ESRF - European Synchrotron Radiation Facility FWB - Fédération Wallonie-Bruxelles
Funding text :
The authors thank Evgenios Stylianidis for help with sample fabrication, Pavel M\u00E1rton for help with treating second-principles data, Ji\u0159\u00ED Kulda for his generous support with the mp _ tools software package, and Jorge \u00CD\u00F1iguez-Gonz\u00E1lez and Fernando G\u00F3mez-Ortiz for fruitful discussions. This work was supported by the Swiss National Science Foundation (SNSF) Scientific Exchanges Scheme [Grant No. IZSEZ0_212990 (M.H.)], by Division II of the SNSF [Project No. 200021_200636 (C.L., L.\u2009T., J.-M.T., M.H.)], and the European Union\u2019s Horizon 2020 research and innovation program [Grant Agreement No. 766726\u2014TSAR (P.O., L.\u2009B., A.\u2009S., P.\u2009Z., P.\u2009G., J.H.)]. P.\u2009O. and J.\u2009H. acknowledge the assistance provided by the Operational Programme Johannes Amos Comenius of the Ministry of Education, Youth and Sport of the Czech Republic, within the frame of project Ferroic Multifunctionalities (FerrMion) [Project No. CZ.02.01.01/00/22_008/0004591], co-funded by the European Union. P.\u2009G. acknowledges support from F.R.S.-FNRS Belgium (Grant No. T.0107.20, PROMOSPAN). M.\u2009H. acknowledges support from UK Research and Innovation (UKRI). We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities and the ID01 and ID28 beamline staff for support during the synchrotron experiments. For simulations, we acknowledge access to the CECI supercomputer facilities funded by the F.R.S.-FNRS Belgium (Grant No. 2.5020.1) and to the Tier-1 supercomputer of the F\u00E9d\u00E9ration Wallonie-Bruxelles funded by the Walloon Region of Belgium (Grant No. 1117545).
G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, Domain wall nanoelectronics, Rev. Mod. Phys. 84, 119 (2012). RMPHAT 0034-6861 10.1103/RevModPhys.84.119
I. I. Naumov, L. Bellaiche, and H. Fu, Unusual phase transitions in ferroelectric nanodisks and nanorods, Nature (London) 432, 737 (2004). NATUAS 0028-0836 10.1038/nature03107
P. Aguado-Puente and J. Junquera, Ferromagneticlike closure domains in ferroelectric ultrathin films: First-principles simulations, Phys. Rev. Lett. 100, 177601 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.177601
C. T. Nelson, Spontaneous vortex nanodomain arrays at ferroelectric heterointerfaces, Nano Lett. 11, 828 (2011). NALEFD 1530-6984 10.1021/nl1041808
C.-L. Jia, K. W. Urban, M. Alexe, D. Hesse, and I. Vrejoiu, Direct observation of continuous electric dipole rotation in flux-closure domains in ferroelectric (Equation presented), Science 331, 1420 (2011). SCIEAS 0036-8075 10.1126/science.1200605
Y. L. Tang, Observation of a periodic array of flux-closure quadrants in strained ferroelectric (Equation presented) films, Science 348, 547 (2015). SCIEAS 0036-8075 10.1126/science.1259869
A. K. Yadav, Observation of polar vortices in oxide superlattices, Nature (London) 530, 198 (2016). NATUAS 0028-0836 10.1038/nature16463
S. Das, Observation of room-temperature polar skyrmions, Nature (London) 568, 368 (2019). NATUAS 0028-0836 10.1038/s41586-019-1092-8
Y. J. Wang, Polar meron lattice in strained oxide ferroelectrics, Nat. Mater. 19, 881 (2020). NMAACR 1476-1122 10.1038/s41563-020-0694-8
D. Lee, R. K. Behera, P. Wu, H. Xu, Y. L. Li, S. B. Sinnott, S. R. Phillpot, L. Q. Chen, and V. Gopalan, Mixed Bloch-Néel-Ising character of 180° ferroelectric domain walls, Phys. Rev. B 80, 060102(R) (2009). PRBMDO 1098-0121 10.1103/PhysRevB.80.060102
P. Marton, I. Rychetsky, and J. Hlinka, Domain walls of ferroelectric (Equation presented) within the Ginzburg-Landau-Devonshire phenomenological model, Phys. Rev. B 81, 144125 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.81.144125
J. C. Wojdeł and J. Íñiguez, Ferroelectric transitions at ferroelectric domain walls found from first principles, Phys. Rev. Lett. 112, 247603 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.247603
S. Cherifi-Hertel, H. Bulou, R. Hertel, G. Taupier, K. D. Dorkenoo, C. Andreas, J. Guyonnet, I. Gaponenko, K. Gallo, and P. Paruch, Non-Ising and chiral ferroelectric domain walls revealed by nonlinear optical microscopy, Nat. Commun. 8, 15768 (2017). NCAOBW 2041-1723 10.1038/ncomms15768
C. Weymann, S. Cherifi-Hertel, C. Lichtensteiger, I. Gaponenko, K. D. Dorkenoo, A. B. Naden, and P. Paruch, Non-Ising domain walls in (Equation presented)-phase ferroelectric lead titanate thin films, Phys. Rev. B 106, L241404 (2022). PRBMDO 2469-9950 10.1103/PhysRevB.106.L241404
Y.-J. Wang, Y.-L. Zhu, and X.-L. Ma, Chiral phase transition at 180° domain walls in ferroelectric (Equation presented) driven by epitaxial compressive strains, J. Appl. Phys. 122, 134104 (2017). JAPIAU 0021-8979 10.1063/1.5006607
F. Gómez-Ortiz, P. García-Fernández, J. M. López, and J. Junquera, Melting of crystals of polarization vortices and chiral phase transitions in oxide superlattices, Phys. Rev. B 105, L220103 (2022). PRBMDO 2469-9950 10.1103/PhysRevB.105.L220103
R. Wahl, D. Vogtenhuber, and G. Kresse, (Equation presented) and (Equation presented) revisited using the projector augmented wave method: Performance of hybrid and semilocal functionals, Phys. Rev. B 78, 104116 (2008). PRBMDO 1098-0121 10.1103/PhysRevB.78.104116
J. C. Wojdeł, P. Hermet, M. P. Ljungberg, P. Ghosez, and J. Íñiguez, First-principles model potentials for lattice-dynamical studies: General methodology and example of application to ferroic perovskite oxides, J. Phys. Condens. Matter 25, 305401 (2013). JCOMEL 0953-8984 10.1088/0953-8984/25/30/305401
B. Meyer and D. Vanderbilt, Ab initio study of ferroelectric domain walls in (Equation presented), Phys. Rev. B 65, 104111 (2002). PRBMDO 0163-1829 10.1103/PhysRevB.65.104111
P. Aguado-Puente and J. Junquera, Structural and energetic properties of domains in (Equation presented) superlattices from first principles, Phys. Rev. B 85, 184105 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.184105
B. C. Frazer, H. R. Danner, and R. Pepinsky, Single-crystal neutron analysis of tetragonal (Equation presented), Phys. Rev. 100, 745 (1955). PHRVAO 0031-899X 10.1103/PhysRev.100.745
G. H. Kwei, A. C. Lawson, S. J. L. Billinge, and S. W. Cheong, Structures of the ferroelectric phases of barium titanate, J. Phys. Chem. 97, 2368 (1993). JPCHAX 0022-3654 10.1021/j100112a043
G. Shirane, R. Pepinsky, and B. C. Frazer, X-ray and neutron diffraction study of ferroelectric (Equation presented), Acta Crystallogr. 9, 131 (1956). ACCRA9 0365-110X 10.1107/S0365110X56000309
F. Gómez-Ortiz, H. Aramberri, J. M. López, P. García-Fernández, J. Íñiguez, and J. Junquera, Kittel law and domain formation mechanism in (Equation presented) superlattices, Phys. Rev. B 107, 174102 (2023). PRBMDO 2469-9950 10.1103/PhysRevB.107.174102
J. S. Baker and D. R. Bowler, Polar morphologies from first Principles: (Equation presented) films on (Equation presented) substrates and the (Equation presented) surface reconstruction, Adv. Theory Simulations 3, 2000154 (2020). 10.1002/adts.202000154
J. Wu, J. Yang, L. Ma, L. Zhang, and S. Liu, Modular development of deep potential for complex solid solutions, Phys. Rev. B 107, 144102 (2023). PRBMDO 2469-9950 10.1103/PhysRevB.107.144102
C. Escorihuela Sayalero, Second-principles methods for large-scale simulations of realistic functional oxides, Ph.d. Thesis, University of Luxembourg, 2019.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevX.14.041052 for the extraction of the superlattice equilibrium domain period from second-principles calculations, schematics of the expected diffraction patterns for different types of domain walls, the comparison of diffuse scattering from superlattices with different layer thicknesses, a discussion on the asymmetry of the scattering near the (Equation presented) substrate peak, a comparison of the 1054 and 101 superlattice peaks, and a discussion of the high-resolution measurements at low and high temperatures.
G. Catalan, A. Lubk, A. H. G. Vlooswijk, E. Snoeck, C. Magen, A. Janssens, G. Rispens, G. Rijnders, D. H. A. Blank, and B. Noheda, Flexoelectric rotation of polarization in ferroelectric thin films, Nat. Mater. 10, 963 (2011). NMAACR 1476-1122 10.1038/nmat3141
F. H. Gong, Atomic mapping of periodic dipole waves in ferroelectric oxide, Sci. Adv. 7, eabg5503 (2021). SACDAF 2375-2548 10.1126/sciadv.abg5503
S. K. Streiffer, J. A. Eastman, D. D. Fong, C. Thompson, A. Munkholm, M. V. Ramana Murty, O. Auciello, G. R. Bai, and G. B. Stephenson, Observation of nanoscale 180° stripe domains in ferroelectric (Equation presented) thin films, Phys. Rev. Lett. 89, 067601 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.067601
D. D. Fong, G. B. Stephenson, S. K. Streiffer, J. A. Eastman, O. Auciello, P. H. Fuoss, and C. Thompson, Ferroelectricity in ultrathin perovskite films, Science 304, 1650 (2004). SCIEAS 0036-8075 10.1126/science.1098252
C. Thompson, D. D. Fong, R. V. Wang, F. Jiang, S. K. Streiffer, K. Latifi, J. A. Eastman, P. H. Fuoss, and G. B. Stephenson, Imaging and alignment of nanoscale 180° stripe domains in ferroelectric thin films, Appl. Phys. Lett. 93, 182901 (2008). APPLAB 0003-6951 10.1063/1.3013512
C. Lichtensteiger, S. Fernandez-Pena, C. Weymann, P. Zubko, and J. M. Triscone, Tuning of the depolarization field and nanodomain structure in ferroelectric thin films, Nano Lett. 14, 4205 (2014). NALEFD 1530-6984 10.1021/nl404734z
M. Hadjimichael, E. Zatterin, S. Fernandez-Peña, S. J. Leake, and P. Zubko, Domain wall orientations in ferroelectric superlattices probed with synchrotron x-ray diffraction, Phys. Rev. Lett. 120, 037602 (2018). PRLTAO 0031-9007 10.1103/PhysRevLett.120.037602
M. Seul and D. Andelman, Domain shapes and patterns: The phenomenology of modulated phases, Science 267, 476 (1995). SCIEAS 0036-8075 10.1126/science.267.5197.476
P. Zubko, N. Jecklin, A. Torres-Pardo, P. Aguado-Puente, A. Gloter, C. Lichtensteiger, J. Junquera, O. Stéphan, and J.-M. M. Triscone, Electrostatic coupling and local structural distortions at interfaces in ferroelectric/paraelectric superlattices, Nano Lett. 12, 2846 (2012). NALEFD 1530-6984 10.1021/nl3003717
S. L. Zhang, G. Van Der Laan, and T. Hesjedal, Direct experimental determination of the topological winding number of skyrmions in (Equation presented), Nat. Commun. 8, 14619 (2017). NCAOBW 2041-1723 10.1038/ncomms14619
J. Y. Chauleau, W. Legrand, N. Reyren, D. Maccariello, S. Collin, H. Popescu, K. Bouzehouane, V. Cros, N. Jaouen, and A. Fert, Chirality in magnetic multilayers probed by the symmetry and the amplitude of dichroism in x-ray resonant magnetic scattering, Phys. Rev. Lett. 120, 037202 (2018). PRLTAO 0031-9007 10.1103/PhysRevLett.120.037202
S. L. Zhang, G. van der Laan, W. W. Wang, A. A. Haghighirad, and T. Hesjedal, Direct observation of twisted surface skyrmions in bulk crystals, Phys. Rev. Lett. 120, 227202 (2018). PRLTAO 0031-9007 10.1103/PhysRevLett.120.227202
S. Zhang, G. Van Der Laan, J. Müller, L. Heinen, M. Garst, A. Bauer, H. Berger, C. Pfleiderer, and T. Hesjedal, Reciprocal space tomography of 3D skyrmion lattice order in a chiral magnet, Proc. Natl. Acad. Sci. U.S.A. 115, 6386 (2018). PNASA6 0027-8424 10.1073/pnas.1803367115
W. Li, Anatomy of skyrmionic textures in magnetic multilayers, Adv. Mater. 31, 1807683 (2019). ADVMEW 0935-9648 10.1002/adma.201807683
E. Bousquet, M. Dawber, N. Stucki, C. Lichtensteiger, P. Hermet, S. Gariglio, J.-M. Triscone, and P. Ghosez, Improper ferroelectricity in perovskite oxide artificial superlattices, Nature (London) 452, 732 (2008). NATUAS 0028-0836 10.1038/nature06817
J. Bang, N. Strkalj, M. Sarott, M. Trassin, and T. Weber, Probing hidden order in ferroelectric oxide thin films with single-crystal diffuse x-ray scattering, Acta Crystallogr. Sect. A 78, e577 (2022). ACACEQ 0108-7673 10.1107/S2053273322091884
K. Huang, X-ray reflexions from dilute solid solutions, Proc. R. Soc. A. 190, 102 (1947). 10.1098/rspa.1947.0064
P. H. Dederichs, The theory of diffuse x-ray scattering and its application to the study of point defects and their clusters, J. Phys. F 3, 471 (1973). JPFMAT 0305-4608 10.1088/0305-4608/3/2/010
B. J. Campbell, S. K. Sinha, R. Osborn, S. Rosenkranz, J. F. Mitchell, D. N. Argyriou, L. Vasiliu-Doloc, O. H. Seeck, and J. W. Lynn, Polaronic orbital polarization in a layered colossal magnetoresistive manganite, Phys. Rev. B 67, 020409(R) (2003). PRBMDO 0163-1829 10.1103/PhysRevB.67.020409
J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, Nanosecond dynamics of ferroelectric/dielectric superlattices, Phys. Rev. Lett. 107, 055501 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.055501
M. R. McCarter, Structural chirality of polar skyrmions probed by resonant elastic x-ray scattering, Phys. Rev. Lett. 129, 247601 (2022). PRLTAO 0031-9007 10.1103/PhysRevLett.129.247601
Y.-T. Shao, Emergent chirality in a polar meron to skyrmion phase transition, Nat. Commun. 14, 1355 (2023). NCAOBW 2041-1723 10.1038/s41467-023-36950-x
D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.085117
M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G. M. Rignanese, The PSEUDODOJO: Training and grading a 85 element optimized norm-conserving pseudopotential table, Comput. Phys. Commun. 226, 39 (2018). CPHCBZ 0010-4655 10.1016/j.cpc.2018.01.012
X. Gonze, The ABINIT project: Impact, environment and recent developments, Comput. Phys. Commun. 248, 107042 (2020). CPHCBZ 0010-4655 10.1016/j.cpc.2019.107042
P. Marton and J. Hlinka, Simulation of domain patterns in (Equation presented), Phase Transitions 79, 467 (2006). PHTRDP 0141-1594 10.1080/01411590600892351
J. Hlinka and P. Márton, Phenomenological model of a 90° domain wall in (Equation presented)-type ferroelectrics, Phys. Rev. B 74, 104104 (2006). PRBMDO 1098-0121 10.1103/PhysRevB.74.104104
P. Ondrejkovic, P. Marton, V. Stepkova, and J. Hlinka, Fundamental properties of ferroelectric domain walls from Ginzburg-Landau models, in Domain Walls: From Fundamental Properties to Nanotechnology, edited by D. Meier, J. Seidel, M. Gregg, and R. Ramesh (Oxford University Press, New York, 2020), pp. 76-108.
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). PRBMDO 0163-1829 10.1103/PhysRevB.64.214103
M. Hadjimichael, Metal-ferroelectric supercrystals with periodically curved metallic layers, Nat. Mater. 20, 495 (2021). NMAACR 1476-1122 10.1038/s41563-020-00864-6
G. Sheng, Y. L. Li, J. X. Zhang, S. Choudhury, Q. X. Jia, V. Gopalan, D. G. Schlom, Z. K. Liu, and L. Q. Chen, A modified Landau-Devonshire thermodynamic potential for strontium titanate, Appl. Phys. Lett. 96, 232902 (2010). APPLAB 0003-6951 10.1063/1.3442915
J. Hlinka and E. Klotins, Application of elastostatic Green function tensor technique to electrostriction in cubic, hexagonal and orthorhombic crystals, J. Phys. Condens. Matter 15, 5755 (2003). JCOMEL 0953-8984 10.1088/0953-8984/15/33/309
J. Kulda, mp _ tools: Neutron and x-ray diffuse scattering from distorted lattices, https://mptools.fr.
A. Girard, T. Nguyen-Thanh, S. M. Souliou, M. Stekiel, W. Morgenroth, L. Paolasini, A. Minelli, D. Gambetti, B. Winkler, and A. Bosak, A new diffractometer for diffuse scattering studies on the ID28 beamline at the ESRF, J. Synchrotron Radiat. 26, 272 (2019). JSYRES 0909-0495 10.1107/S1600577518016132
S. J. Leake, The nanodiffraction beamline ID01/ESRF: A microscope for imaging strain and structure, J. Synchrotron Radiat. 26, 571 (2019). JSYRES 0909-0495 10.1107/S160057751900078X
10.26037/yareta:rt7uwof32jhdxbs54h7qhx4q5a
C. Lichtensteiger, E. Zatterin, M. Hadjimichael, and S. Leake, Probing phase transitions in ferroelectric domain walls with x-ray diffraction, European Synchrotron Radiation Facility, 2024, 10.15151/ESRF-ES-550197419.
C. Lichtensteiger, E. Zatterin, Ludovica Tovaglieri, M. Hadjimichael, and S. Leake, Probing phase transitions in ferroelectric domain walls with x-ray diffraction, European Synchrotron Radiation Facility, 2025, 10.15151/ESRF-ES-649493071.