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DOE OSTI2025

The influence of cooling rates on strain phase diagrams and domain structures of ferroelectric thin films: A case study of PbTiO 3

Strain engineering has been established as an effective approach to control phase equilibria, domain configurations, and functional properties of ferroelectric thin films. Temperature-strain phase diagrams have been used as powerful tools for providing insights into strain engineering. However, almost all existing phase diagrams established using the phase-field approach assume quenching conditions without considering actual cooling rates during the post-deposition annealing process of ferroelectric thin films. Within this work, we systematically investigate the influence of cooling rates on domain structures and the strain-phase diagram of ferroelectric thin films using phase-field simulations, taking PbTiO 3 thin films as a model system. We found that both the position of phase boundaries in the strain phase diagrams and the domain morphology are significantly influenced by the cooling rates. It is revealed that while the paraelectric-ferroelectric phase boundary remains invariant, the phase boundaries between single-phase and multi-phase regions tend to shift toward the corresponding multi-phase region as the cool rate reduces. Slow cooling generally leads to more ordered domain structures with increased domain size. Using the obtained equilibrium domain structures, we calculated effective thermal conductivities and found significant variations that can be tuned by the cooling rates. In conclusion, this work reveals an underexplored yet critical impact of cooling rates on phase equilibria and domain structures in ferroelectric thin films, which may inspire further fine-tuning of domains and domain walls in low-dimensional ferroelectrics for multifunctional applications.

Domain structures↗

DOE OSTI2016

Phase transitions, domain structure, and pseudosymmetry in La- and Ti-doped BiFeO{sub 3}

The phase transitions and domain structure of the promising PbO-free solid solution series, (0.95-x)BiFeO{sub 3}-xLaFeO{sub 3}-0.05La{sub 2/3}TiO{sub 3}, were investigated. X ray diffraction (XRD) revealed a transition from a ferroelectric R3c to a PbZrO{sub 3}-like (Pbam) antiferroelectric (AFE) structure at x = 0.15 followed by a transition to a paraelectric (PE, Pnma) phase at x > 0.30. The ferroelastic/ferroelectric twin domain width decreased to 10–20 nm with increasing x as the AFE phase boundary was approached but coherent antiphase tilted domains were an order of magnitude greater. This domain structure suggested the local symmetry (20 nm) is lower than the average structure (R3c, a{sup −}a{sup −}a{sup −}) of the tilted regions. The PE phase (x = 0.35) exhibited a dominant a{sup −}a{sup −}c{sup +} tilt system with Pnma symmetry but diffuse reflections at ∼1/4(ooe) positions suggest that short range antipolar order is residual in the PE phase. The complex domain structure and phase assemblage of this system challenge the conventional interpretation of phase transitions based on macroscopic symmetry. Instead, it supports the notion that frustration driven by chemical distributions at the nanometric level influences the local or pseudo-symmetry as well as the domain structure, with XRD giving only the average macroscopic structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Toward Decoding the Relationship between Domain Structure and Functionality in Ferroelectrics via Hidden Latent Variables

Polarization switching mechanisms in ferroelectric materials are fundamentally linked to local domain structure and the presence of the structural defects, which both can act as nucleation and pinning centers and create local electrostatic and mechanical depolarization fields affecting wall dynamics. However, the general correlative mechanisms between domain structure and polarization dynamics are only weakly explored, precluding insight into the associated physical mechanisms. In this work, the correlation between local domain structures and switching behavior in ferroelectric materials is explored using convolutional encoder–decoder networks, enabling image to spectral (im2spec) and spectral to image (spec2im) translations via encoding of latent variables. The latter reflect the assumption that the relationship between domain structure and polarization switching is parsimonious, i.e., is based upon a small number of local mechanisms. The analysis of latent variables distributions and their real-space representations provides insight into the predictability of the local switching behavior and hence associated physical mechanisms. We further pose that the regions where these correlative relationships are violated, i.e., predictability of the polarization dynamics from domain structure is reduced, represent the obvious target for detailed studies, e.g., in the context of automated experiments. This approach provides a workflow to establish the presence of correlation between local spectral responses and local structure and can be universally applied to spectral imaging techniques such as piezoresponse force microscopy (PFM), scanning tunneling microscopy (STM) and spectroscopy, and electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM).

36 MATERIALS SCIENCE↗

DOE OSTI2018

Specific Features of the Domain Structure of BaTiO{sub 3} Crystals during Thermal Heating and Cooling

This paper presents the results of the study of the domain structure of barium titanate crystals in a wide temperature range including the Curie point (T{sub C}) using the polarization-optical method in the reflected light and the force microscopy of the piezoelectric response. It is shown that a new a–c domain structure forms during cyclic heating of the crystal above T{sub C} and subsequent cooling to the ferroelectric phase. The role of uncompensated charges appeared on the crystal surface during the phase transition and their influence on the formation of the domain structure during cooling are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Simulations of super-structure domain walls in two dimensional assemblies of magnetic nanoparticles

We simulate the formation of domain walls in two-dimensional assemblies of magnetic nanoparticles. Particle parameters are chosen to match recent electron holography and Lorentz microscopy studies of almost monodisperse cobalt nanoparticles assembled into regular, elongated lattices. As the particles are small enough to consist of a single magnetic domain each, their magnetic interactions can be described by a spin model in which each particle is assigned a macroscopic “superspin.” Thus, the magnetic behaviour of these lattices may be compared to magnetic crystals with nanoparticle superspins taking the role of the atomic spins. The coupling is, however, different. The superspins interact only by dipolar interactions as exchange coupling between individual nanoparticles may be neglected due to interparticle spacing. We observe that it is energetically favorable to introduce domain walls oriented along the long dimension of nanoparticle assemblies rather than along the short dimension. This is unlike what is typically observed in continuous magnetic materials, where the exchange interaction introduces an energetic cost proportional to the area of the domain walls. Structural disorder, which will always be present in realistic assemblies, pins longitudinal domain walls when the external field is reversed, and makes a gradual reversal of the magnetization by migration of longitudinal domain walls possible, in agreement with previous experimental results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Domain structures and magnetization reversal in Co/Pd and CoFeB/Pd multilayers

Domain structures and magnetization reversal of (Co/Pd) and (CoFeB/Pd) multilayers with 7 and 14 repeats were investigated. The Co-based multilayers show much larger coercivities, a better squareness, and a sharper magnetization switching than CoFeB-based multilayers. From magnetic force microscopy observations, both structures show strong reduction in domains size as the number of repeats increases but the magnetic domains for Co-based multilayers are more than one order of magnitude larger than for CoFeB-based multilayers. By imaging domains at different times, breaks in the (CoFeB/Pd) multilayer stripes were observed within only few hours, while no change could be seen for (Co/Pd) multilayers. Although CoFeB single layers are suitable for magnetoresistive devices due to their large spin polarization and low damping constants, their lamination with Pd suffers mainly from thermal instability.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Mapping domain structures near a grain boundary in a lead zirconate titanate ferroelectric film using X-ray nanodiffraction

The effect of an electric field on local domain structure near a 24° tilt grain boundary in a 200 nm-thick Pb(Zr 0.2 Ti 0.8 )O 3 bi-crystal ferroelectric film was probed using synchrotron nanodiffraction. The bi-crystal film was grown epitaxially on SrRuO 3 -coated (001) SrTiO 3 24° tilt bi-crystal substrates. From the nanodiffraction data, real-space maps of the ferroelectric domain structure around the grain boundary prior to and during application of a 200 kV cm −1 electric field were reconstructed. In the vicinity of the tilt grain boundary, the distributions of densities of c -type tetragonal domains with the c axis aligned with the film normal were calculated on the basis of diffracted intensity ratios of c - and a -type domains and reference powder diffraction data. Diffracted intensity was averaged along the grain boundary, and it was shown that the density of c -type tetragonal domains dropped to ∼50% of that of the bulk of the film over a range ±150 nm from the grain boundary. This work complements previous results acquired by band excitation piezoresponse force microscopy, suggesting that reduced nonlinear piezoelectric response around grain boundaries may be related to the change in domain structure, as well as to the possibility of increased pinning of domain wall motion. The implications of the results and analysis in terms of understanding the role of grain boundaries in affecting the nonlinear piezoelectric and dielectric responses of ferroelectric materials are discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Linking Domain Structure Evolution at a Grain Boundary to Piezoelectric Response via Nano‐Diffraction

Electric-field-induced domain structure switching in a 1 𝜇⁢m -thick Pb 0.99 (Zr 0.45 Ti 0.55 ) 0.98 Nb 0.02 O 3 (Nb-doped PZT) bicrystal film was characterized in situ via nano-focused synchrotron diffraction. The epitaxial film was deposited on a (100) SrTiO 3 bicrystal substrate. The changes in domain structure were mapped within a 5 𝜇⁢m × 5 𝜇⁢m area at and around an in-plane tilt-type (23.6°) grain boundary with 50 nm spatial resolution. Rocking curves collected at each point of the mapped area provided the ability to reconstruct spatially-varying three-dimensional (3D) reciprocal space maps around the grain boundary. The 3D reciprocal space maps reveal how different tilted 𝑎 -type domain variants interact with the grain boundary as a function of increasing electric field. Initially, a subset of 𝑎 -type domain variants with their polarization vectors largely orthogonal to the grain boundary were found in greater abundance within 570 nm of the grain boundary, possibly due to X-ray beam-induced local increases in the electrical conductivity, but after the coercive field was exceeded, reconfiguration of the ferroelastic domains was observed. The spatially-varying reciprocal space maps also facilitated evaluation of the strain field across the mapped area, along with 𝑑 33,𝑓 . Significant spatial heterogeneity of strain and 𝑑 33,𝑓 are observed, especially at the coercive field, which was attributed to maintaining deformation compatibility and correlated ferroelastic switching.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Oxyanion Induced Variations in Domain Structure for Amorphous Cobalt Oxide Oxygen Evolving Catalysts, Resolved by X-ray Pair Distribution Function Analysis

Amorphous thin film oxygen evolving catalysts, OECs, of first-row transition metals show promise to serve as self-assembling photoanode materials in solar-driven, photoelectrochemical `artificial leaf' devices. This report demonstrates the ability to use high-energy X-ray scattering and atomic pair distribution function analysis, PDF, to resolve structure in amorphous metal oxide catalyst films. The analysis is applied here to resolve domain structure differences induced by oxyanion substitution during the electrochemical assembly of amorphous cobalt oxide catalyst films, Co-OEC. PDF patterns for Co-OEC films formed using phosphate, Pi, methylphosphate, MPi, and borate, Bi, electrolyte buffers show that the resulting domains vary in size following the sequence Pi < MPi < Bi. The increases in domain size for CoMPi and CoBi were found to be correlated with increases in the contributions from bilayer and trilayer stacked domains having structures intermediate between those of the LiCoOO and CoO(OH) mineral forms. The lattice structures and offset stacking of adjacent layers in the partially stacked CoMPi and CoBi domains were best matched to those in the LiCoOO layered structure. The results demonstrate the ability of PDF analysis to elucidate features of domain size, structure, defect content and mesoscale organization for amorphous metal oxide catalysts that are not readily accessed by other X-ray techniques. Finally, PDF structure analysis is shown to provide a way to characterize domain structures in different forms of amorphous oxide catalysts, and hence provide an opportunity to investigate correlations between domain structure and catalytic activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Influence of crystallographic orientation and applied magnetic field on domain structure in duplex stainless steel studied using magnetic force microscopy

Highlights: • Ferrite phase in a duplex stainless steel consists of stripe type domains. • Domain contrast decreases with deviation of plane normal from <100>. • Domain width increases with deviation of plane normal from <100>. • Domain alignment with applied field observed along <100> directions. • Grain boundary stray field is a function of misorientation between grains. - Abstract: The paper investigates the local micro-magnetization behavior in duplex stainless steel (DSS) using magnetic force microscopy (MFM). DSS has equal amount of austenite phase in ferrite matrix. The MFM imaging clearly differentiates ferrite phase (ferromagnetic) from the austenite phase (paramagnetic) due to the maze type magnetic domains present in the ferrite phase. The magneto crystalline anisotropic effect on the domain structure is discussed with the support of electron backscatter diffraction (EBSD) measurements. The MFM phase contrast and domain width are correlated with the orientation of surface normal with respect to the easy axis of magnetization (<100>). The influence of external magnetic field (±127 kA/m) application on the domain structure is studied as a function of the grain orientation and the leakage field at the grain boundaries is analyzed based on the mis-orientation between the grains.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Experimental observation of the interaction of propagating spin waves with Néel domain walls in a Landau domain structure

The interaction of propagating dipolar spin waves with magnetic domain walls is investigated in square-shaped microstructures patterned from the Heusler compound Co{sub 2}Mn{sub 0.6}Fe{sub 0.4}Si. Using magnetic force microscopy, the reversible preparation of a Landau state with four magnetic domains separated by Néel domain walls is confirmed. A local spin-wave excitation using a microstructured antenna is realized in one of the domains. It is shown by Brillouin light scattering microscopy that the domain structure in the remanence state has a strong influence on the spin-wave excitation and propagation. The domain walls strongly reflect the spin waves and can be used as spin-wave reflectors. A comparison with micromagnetic simulations shows that the strong reflection is due to the long-range dipolar interaction which has important implications for the use of these spin waves for exerting an all-magnonic spin-transfer torque.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Formation of the domain structure in CLN under the pyroelectric field induced by pulse infrared laser heating

The evolution of the self-assembled quasi-regular micro- and nanodomain structures after pulse infrared laser irradiation in congruent lithium niobate crystal was studied by in situ optical observation. Several scenarios of domain kinetics represented covering of the irradiated zone by nets of the separated domain chains and rays have been revealed. The time dependence of the total domain length was analyzed in terms of modified Kolmogorov-Avrami theory. The domain structure evolution was attributed to the action of pyroelectric field appeared during cooling. The time dependence of the spatial distribution of the pyroelectric field during pulse laser heating and subsequent cooling was calculated by finite element method. The results of computer simulation allowed us to explain the experimental results and can be used for creation of tailored domain structures thus opening the new abilities of the submicron-scale domain engineering in ferroelectrics.

36 MATERIALS SCIENCE↗

DOE OSTI2019

A Method for Analyzing the Domain Structure in Magnetic Powder Microparticles

A method for analyzing the domain structure in magnetic powder microparticles based on the Mössbauer effect is proposed. This method has been experimentally verified for gadolinium ferrite-garnet (Gd{sub 3}Fe{sub 5}O{sub 12}) powder particles 40 ± 5 μm in diameter in the vicinity of the magnetic compensation point T{sub cm} = 286 K. It is shown that ferrite particles are single-domain near T{sub cm} and pass to the multidomain state while moving away from T{sub cm}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Tunable thermal conductivity via domain structure engineering in ferroelectric thin films: A phase-field simulation

Effective thermal conductivity as a function of domain structure is studied by solving the heat conduction equation using a spectral iterative perturbation algorithm in materials with inhomogeneous thermal conductivity distribution. Using this proposed algorithm, the experimentally measured effective thermal conductivities of domain-engineered {001} p- BiFeO 3 thin films are quantitatively reproduced. In conjunction with two other testing examples, this proposed algorithm is proven to be an efficient tool for interpreting the relationship between the effective thermal conductivity and micro-/domain-structures. By combining this algorithm with the phase-field model of ferroelectric thin films, the effective thermal conductivity for PbZr 1-x Ti x O 3 films under different composition, thickness, strain, and working conditions is predicted. It is shown that the chemical composition, misfit strain, film thickness, film orientation, and a Piezoresponse Force Microscopy tip can be used to engineer the domain structures and tune the effective thermal conductivity. Furthermore, we expect our findings will stimulate future theoretical, experimental and engineering efforts on developing devices based on the tunable effective thermal conductivity in ferroelectric nanostructures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2018

Strain effects on domain structures in ferroelectric thin films from phase‐field simulations

Abstract Strain and applied external electric fields are known to influence domain evolution and associated ferroelectric responses in ferroelectric thin films. Here, phase‐field simulations are used to predict equilibrium domain structures and polarization‐field ( P ‐ E ) hysteresis loops of lead zirconate titanate (PZT) thin films under a series of mismatch strains, ranging from strongly tensile to strongly compressive. In particular, the evolution of domains and the P ‐ E curves under different applied strains reveal the mesoscale mechanism, the appearance of in‐plane polarization during domain switching, that is responsible for a relatively small coercive field and remnant polarization. A Landau energy distribution is analyzed to better understand the domain evolution under various strain conditions. The results provide guidance for choice of mismatched strains to yield the desired P ‐ E hysteresis loops and the domain structures.

Lin, Fang‐Yin↗

DOE OSTI2018

Conversion of spectral characteristics of laser radiation in periodic domain structures written by the electron-beam method in planar waveguides formed by Ti diffusion in Y-oriented LiNbO{sub 3}

Periodic domain structures for nonlinear conversion of spectral characteristics of laser radiation in the planar Ti : LiNbO{sub 3} waveguide have been formed by the method of electron-beam writing. Domain gratings with a spatial period of 6.50 μm formed in the Y-cut plate over a wide range of accelerating voltages have been visualised by the method of second harmonic generation microscopy (SHG-microscopy) in transmitting geometry and at waveguide excitation. It is found that the domain structure written at an accelerating voltage of 10 kV in a waveguide with an exponential refractive index profile and an effective thickness of 1.75 μm is characterised by high homogeneity. It is composed of continuous domain rows and provides near-quasi-phase-matching radiation conversion at a wavelength of 1053 nm into the second harmonic for the TE{sub 0} → TE{sub 1} waveguide process. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Influence of growth temperature of KTiOAsO{sub 4} single crystals on their physicochemical parameters and formation of domain structures

A potassium titanyl arsenate (KTiOAsO{sub 4}, KTA) crystal 50 × 80 × 60 mm in size has been grown by upgraded Czochralski method from flux (TGGS) with a decrease in temperature from 900 to 770 °C during pulling. It is shown that the spectroscopic properties of the parts of KTA crystals grown at 900 and 770 °C are close, whereas the electrical conductivity of the low-temperature (770 °C) KTA part turned out to be an order of magnitude lower than that of the high-temperature part. Visualisation of the domain structure by second-harmonic generation microscopy revealed a more efficient domain intergrowth (throughout the sample) in the low-temperature KTA, which is important for forming a regular domain structure (RDS) in a KTA-based nonlinear optical element. It is established that the quantum efficiency of parametric generation of light in the RDS formed in low-temperature KTA is several times higher than in the case of high-temperature KTA. The results obtained are important for optimising RDS parameters. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Hierarchical domain structures associated with oxygen octahedra tilting patterns in lead-free (Bi 1/2 Na 1/2 )TiO 3

Hierarchical domain structures associated with oxygen octahedra tilting patterns were observed in lead-free (Bi 1/2 Na 1/2 )TiO 3 ceramics using aberration-corrected high-resolution transmission electron microscopy (HRTEM). Three types of domains are induced by distinct mechanisms: the 'orientation-domain' is induced at micrometer scale formed by different tilting orientations of the oxygen octahedra, the 'meso-chemical-domain' occurs at a few tens of nanometer scale by chemical composition variation on the A-site in the ABO 3 perovskite structure, and the 'nano-cluster-region' runs across several unit-cells with apparent A-site cation segregation with oxygen vacancies clustering around Na cations. Based on HRTEM amplitude contrast imaging (ACI), the correlation between the oxygen octahedral tilting pattern and compositional non-stoichiometry was established. The role of the hierarchical domain structure associated with the tilting patterns of the oxygen octahedra on the ferroelectric behavior of (Bi 1/2 Na 1/2 )TiO 3 is also discussed.

36 MATERIALS SCIENCE↗