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At least 361 records · Page 20

Strongly anisotropic electronic and magnetic structures in oxide dichlorides RuOCl 2 and OsOCl 2

The van der Waals oxide dichlorides MOX 2 (M=V, Ta, Nb, Ru, and Os; X=halogen element), with different electronic densities, are attracting considerable attention. Ferroelectricity, spin-singlet formation, and orbital-selective Peierls phases were reported in this family with d 1 or d 2 electronic configurations, all believed to be caused by the strongly anisotropic electronic orbital degree of freedom. Here, using density functional theory and density matrix renormalization group methods, we investigate the electronic and magnetic properties of RuOCl 2 and OsOCl 2 with d 4 electronic configurations. Different from a previous study using VOI 2 with d 1 configuration, these systems with 4d4 or 5d4 do not exhibit a ferroelectric instability along the a axis. Due to the fully occupied dxy orbital in RuOCl 2 and OsOCl 2 , the Peierls instability distortion disappears along the b axis, leading to an undistorted Immm phase (No. 71). Furthermore, we observe strongly anisotropic electronic and magnetic structures along the a axis. For this reason, the materials of our focus can be regarded as “effective one-dimensional” systems even when they apparently have a dominant two-dimensional lattice geometry. The large crystal-field splitting energy (between dxz/yz and dxy orbitals) and large hopping between nearest-neighbor Ru and Os atoms suppresses the J = 0 singlet state in MOCl 2 (M=Ru or Os) with electronic density n = 4, resulting in a spin-1 system. Moreover, we find staggered antiferromagnetic order with π wave vector along the M-O chain direction (a axis) while the magnetic coupling along the b axis is weak. Based on Wannier functions from first-principles calculations, we calculated the relevant hopping amplitudes and crystal-field splitting energies of the t 2g orbitals for the Os atoms to construct a multiorbital Hubbard model for the M-O chains. Staggered AFM with ↑|-|↓-↑|-|↓ spin structure dominates in our density matrix renormalization group calculations, in agreement with density functional theory calculations. Our results for RuOCl 2 and OsOCl 2 provide guidance to experimentalists and theorists working on this interesting family of oxide dichlorides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Iron telluride ladder compounds: Predicting the structural and magnetic properties of BaFe 2 Te 3

Since the discovery of pressure-induced superconductivity in the two-leg ladder system BaFe 2 X 3 (X=S, Se), with the 3d iron electronic density n=6, quasi-one-dimensional iron-based ladders have attracted considerable attention. In this work, we use density-functional theory to predict that the novel n=6 iron ladder BaFe 2 Se 3 could be stable with a similar crystal structure as BaFe 2 Se 3 . Furthermore, our results also indicate that BaFe2Te3 will display a complex 2×2 block-type magnetic order. Due to the magnetic striction effects of this block order, BaFe2Te3 should be a magnetic noncollinear ferrielectric system with a net polarization 0.31μC/cm2. In summary, the similar electronic density and magnetic ground state of Te- and Se-based ladders indicates both should display similar properties. In particular, the physical and structural similarity with BaFe 2 Se 3 suggests that BaFe 2 Se 3 could become superconducting under high pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Optical transient grating pumped X-ray diffraction microscopy for studying mesoscale structural dynamics

Abstract A fundamental understanding of materials’ structural dynamics, with fine spatial and temporal control, underpins future developments in electronic and quantum materials. Here, we introduce an optical transient grating pump and focused X-ray diffraction probe technique (TGXD) to examine the structural evolution of materials excited by modulated light with a precisely controlled spatial profile. This method adds spatial resolution and direct structural sensitivity to the established utility of a sinusoidal transient-grating excitation. We demonstrate TGXD using two thin-film samples: epitaxial BiFeO 3 , which exhibits a photoinduced strain (structural grating) with an amplitude proportional to the optical fluence, and FeRh, which undergoes a magnetostructural phase transformation. In BiFeO 3 , structural relaxation is location independent, and the strain persists on the order of microseconds, consistent with the optical excitation of long-lived charge carriers. The strain profile of the structural grating in FeRh, in comparison, deviates from the sinusoidal excitation and exhibits both higher-order spatial frequencies and a location-dependent relaxation. The focused X-ray probe provides spatial resolution within the engineered optical excitation profile, resolving the spatiotemporal flow of heat through FeRh locally heated above the phase transition temperature. TGXD successfully characterizes mesoscopic energy transport in functional materials without relying on a specific transport model.

36 MATERIALS SCIENCE↗

Synthesis and Properties of Bulk Mg 3 WN 4 in a Wurtzite-Derived Structure

Experimental synthesis of theoretically predicted materials with controlled elemental coordination environments can lead to the realization of useful properties, such as facile ion transport or ferroelectric switching. Among such materials are ternary nitrides in the Mg−W−N composition space, where several stable and metastable compounds have been predicted and synthesized recently in bulk and film forms. Here, we report for the first time on the bulk synthesis of Mg 3 WN 4 in a wurtzite-derived crystal structure via a solid-state metathesis reaction. In situ synchrotron powder X-ray diffraction shows how the ion exchange proceeds from Li 6 WN 4 + MgCl 2 precursors to Mg 3 WN 4 + LiCl products, with the reaction starting slowly near 380 °C and completing by 600 °C, including the presence of a competing disordered rocksalt-derived phase (Mg,W)N above 440 °C. The follow-up ex situ powder synthesis at 400 °C for 0.5 h with 10% excess MgCl 2 reveals the cation-ordered nature of the wurtzite-derived Mg 3 WN 4 structure with polar symmetry confirmed by second-harmonic generation measurements. Optical absorption spectra, chemical composition analysis, and electron microscopy imaging suggest that bulk Mg 3 WN 4 obtained via metathesis reaction is prone to defect formation. Overall, this study shows that selective ex situ synthesis of the phase-pure ternary nitrides, informed by in situ measurements, is possible by carefully controlling the thermal budget of the reaction and paves the way toward property characterization of the Mg 3 WN 4 wurtzite-derived material.

36 MATERIALS SCIENCE↗

Sn-modified BaTiO 3 thin film with enhanced polarization

Hybrid molecular beam epitaxy (MBE) growth of Sn-modified BaTiO 3 films was realized with varying domain structures and crystal symmetries across the entire composition space. Macroscopic and microscopic structures and the crystal symmetry of these thin films were determined using a combination of optical second harmonic generation (SHG) polarimetry and scanning transmission electron microscopy (STEM). SHG polarimetry revealed a variation in the global crystal symmetry of the films from tetragonal (P4mm) to cubic (PM3¯m) across the composition range, x = 0 to 1 in BaTi 1–x Sn x O 3 (BTSO). STEM imaging shows that the long-range polar order observed when the Sn content is low (x = 0.09) transformed to a short-range polar order as the Sn content increased (x = 0.48). Consistent with atomic displacement measurements from STEM, the largest polarization was obtained at the lowest Sn content of x = 0.09 in Sn-modified BaTiO 3 as determined by SHG. Furthermore, these results agree with recent bulk ceramic reports and further identify this material system as a potential replacement for Pb-containing relaxor-based thin film devices.

36 MATERIALS SCIENCE↗

The influence of the 6s 2 configuration of Bi 3+ on the structures of A′BiNb 2 O 7 (A′ = Rb, Na, Li) layered perovskite oxides

Solid state compounds which exhibit non-centrosymmetric crystal structures are of great interest due to the physical properties they can exhibit. Here, the ‘hybrid improper’ mechanism – in which two non-polar distortion modes couple to, and stabilize, a further polar distortion mode, yielding an acentric crystal structure – offers opportunities to prepare a range of novel non-centrosymmetric solids, but examples of compounds exhibiting acentric crystal structures stabilized by this mechanism are still relatively rare. Here we describe a series of bismuth-containing layered perovskite oxide phases, RbBiNb 2 O 7 , LiBiNb 2 O 7 and NaBiNb 2 O 7 , which have structural frameworks compatible with hybrid-improper ferroelectricity, but also contain Bi 3+ cations which are often observed to stabilize acentric crystal structures due to their 6s 2 electronic configurations. Neutron powder diffraction analysis reveals that RbBiNb 2 O 7 and LiBiNb 2 O 7 adopt polar crystal structures (space groups I2cm and B2cm respectively), compatible with stabilization by a trilinear coupling of non-polar and polar modes. The Bi 3+ cations present are observed to enhance the magnitude of the polar distortions of these phases, but are not the primary driver for the acentric structure, as evidenced by the observation that replacing the Bi 3+ cations with Nd 3+ cations does not change the structural symmetry of the compounds. In contrast the non-centrosymmetric, but non-polar structure of NaBiNb 2 O 7 (space group P2 1 2 1 2 1 ) differs significantly from the centrosymmetric structure of NaNdNb 2 O 7 , which is attributed to a second-order Jahn-Teller distortion associated with the presence of the Bi3+ cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhancing Chiroptoelectronic Activity in Chiral 2D Perovskites via Chiral–Achiral Cation Mixing

Rational design of chiral two-dimensional hybrid organic–inorganic perovskites is crucial to achieve chiroptoelecronic, spintronic, and ferroelectric applications. Here, in this study, an efficient way to manipulate the chiroptoelectronic activity of 2D lead iodide perovskites is reported by forming mixed chiral (R- or S-methylbenzylammonium (R-MBA + or S-MBA + )) and achiral (n-butylammonium (nBA + )) cations in the organic layer. The strongest and flipped circular dichroism signals are observed in (R/S-MBA 0.5 nBA 0.5 ) 2 PbI 4 films compared to (R/S-MBA) 2 PbI 4 . Moreover, the (R/S-MBA 0.5 nBA 0.5 ) 2 PbI 4 films exhibit pseudo-symmetric, unchanged circularly polarized photoluminescence peak as temperature increases. First-principles calculations reveal that mixed chiral–achiral cations enhance the asymmetric hydrogen-bonding interaction between the organic and inorganic layers, causing more structural distortion, thus, larger spin-polarized band-splitting than pure chiral cations. Temperature-dependent powder X-ray diffraction and pair distribution function structure studies show the compressed intralayer lattice with enlarged interlayer spacing and increased local ordering. Overall, this work demonstrates a new method to tune chiral and chiroptoelectronic properties and reveals their atomic scale structural origins.

2D perovskites↗

GdWN 3 is a nitride perovskite

Nitride perovskites ABN3 are an emerging and highly underexplored class of materials that are of interest due to their intriguing calculated ferroelectric, optoelectronic, and other functional properties. Incorporating novel A-site cations is one strategy to tune and expand such properties; for example, Gd 3+ is compelling due to its large magnetic moment, potentially leading to multiferroic behavior. However, the theoretically predicted ground state of GdWN 3 was a non-perovskite monoclinic structure. Here, we experimentally show that GdWN 3-y crystallizes in a perovskite structure. High-throughput combinatorial sputtering with activated nitrogen is employed to synthesize thin films of Gd 2-x W x N 3-y O y with oxygen content y < 0.05. Ex situ annealing crystallizes a polycrystalline perovskite phase in a narrow composition window near x = 1. LeBail fits of synchrotron grazing incidence wide angle x-ray scattering data are consistent with a perovskite ground-state structure. Refined density functional theory calculations that included antiferromagnetic configurations confirm that the ground-state structure of GdWN 3 is a distorted Pnma perovskite with antiferromagnetic ordering, in contrast to prior predictions. Initial property measurements find that GdWN 3-y is paramagnetic down to T = 2 K with antiferromagnetic correlations and that the absorption onset depends on cation stoichiometry. This work provides an important path toward both the rapid expansion of the emerging family of nitride perovskites and understanding their potential multiferroic properties.

14 SOLAR ENERGY↗

Dielectrics Under Extreme Electric Fields: In Situ Studies on Nanoscale Mechanisms (Final Technical Report)

The lack of materials that can function reliably under extreme electric fields is a critical roadblock to achieving higher energy efficiency and extended service lifetime of devices in electricity generation, transmission, and consumption. Materials typically fail at two or three orders of magnitude below their theoretical dielectric breakdown strength. Identifying the origins of premature dielectric breakdown using state-of-the-art characterization tools will, therefore, enable the design and discovery of transformational materials capable of approaching their intrinsic limits. The vast improvement in the resolution power of imaging tools, combined with the recently developed in situ electric biasing technique, has made high resolution observations of dielectric breakdown as it happens possible. The overall goal of the project is to directly image the dynamic processes of defect formation, accumulation, and interaction with preexisting defects (e.g., dislocations, domain walls, and grain boundaries in crystalline dielectric films) under electric fields up to 1,000 MV/m with a temporal resolution better than 5 microseconds. Using the newly acquired, custom-made Hysitron PI95 transmission electron microscopy (TEM) specimen holder, in situ TEM observations of breakdown at the sub nanometer resolution will be made on representative dielectric compounds with progressive complexities: the linear dielectric SiO 2 , CuO, and TiO 2 , the ferroelectric BaTiO 3 nanocrystals and nanocubes. Through direct observation of the breakdown event at high spatial and temporal resolutions, the nanoscale mechanisms for the failure of dielectrics under intense electric fields will be identified. The results of the project will be applied to the design and processing of new dielectric materials with higher efficiency, improved reliability, and a prolonged lifetime. Such new dielectrics are urgently needed for modernizing energy infrastructures.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evidence for a single-layer van der Waals multiferroic

Here we searched for signatures of type-II multiferroic order in ultrathin van der Waals materials, to determine if such a state, comprising coexisting electrical polarization and spin order with strong magnetoelectric effects, could persist down to a single-atomic layer. We reported the first observation of such a state in triangular lattice material NiI 2 . This system has a layered structure and built-in magnetic frustration that promotes a complex magnetic ground state with proper-screw spin helices. The spin helix pattern breaks inversion symmetry and induces electrical polarization via magnetoelectric coupling. We use circular dichroic Raman measurements to directly probe the magneto-chiral ground state and its electromagnon modes originating from dynamic magnetoelectric coupling. Using birefringence and second-harmonic generation measurements, we detect a highly anisotropic electronic state simultaneously breaking three-fold rotational and inversion symmetry. The evolution of the optical signatures as a function of temperature and layer number surprisingly revealed a multiferroic state that persists down to the ultrathin limit of monolayer NiI 2 . These observations establish NiI 2 and transition metal dihalides as a new platform for studying emergent multiferroic phenomena, chiral magnetic textures and ferroelectricity in the 2D limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA Tech Briefs, January 2008

Topics covered include: Induction Charge Detector with Multiple Sensing Stages; Generic Helicopter-Based Testbed for Surface Terrain Imaging Sensors; Robot Electronics Architecture; Optimized Geometry for Superconducting Sensing Coils; Sensing a Changing Chemical Mixture Using an Electronic Nose; Inertial Orientation Trackers with Drift Compensation; Microstrip Yagi Antenna with Dual Aperture-Coupled Feed; Patterned Ferroelectric Films for Tunable Microwave Devices; Micron-Accurate Laser Fresnel-Diffraction Ranging System; Efficient G(sup 4)FET-Based Logic Circuits; Web-Enabled Optoelectronic Particle-Fallout Monitor; SiO2/TiO2 Composite for Removing Hg from Combustion Exhaust; Lightweight Tanks for Storing Liquefied Natural Gas; Hybrid Wound Filaments for Greater Resistance to Impacts; Making High-Tensile-Strength Amalgam Components; Bonding by Hydroxide-Catalyzed Hydration and Dehydration; Balanced Flow Meters without Moving Parts; Deflection-Compensating Beam for Use inside a Cylinder; Four-Point-Latching Microactuator; Curved Piezoelectric Actuators for Stretching Optical Fibers; Tunable Optical Assembly with Vibration Dampening; Passive Porous Treatment for Reducing Flap Side-Edge Noise; Cylindrical Piezoelectric Fiber Composite Actuators; Patterning of Indium Tin Oxide Films; Gimballed Shoulders for Friction Stir Welding; Improved Thermal Modulator for Gas Chromatography; Nuclear-Spin Gyroscope Based on an Atomic Co-Magnetometer; Utilizing Ion-Mobility Data to Estimate Molecular Masses; Optical Displacement Sensor for Sub-Hertz Applications; Polarization/Spatial Combining of Laser-Diode Pump Beams; Spatial Combining of Laser-Diode Beams for Pumping an NPRO; Algorithm Optimally Orders Forward-Chaining Inference Rules; Project Integration Architecture; High Power Amplifier and Power Supply; Estimating Mixing Heights Using Microwave Temperature Profiler; and Multiple-Cone Sunshade for a Spaceborne Telescope.

Source record↗

Structure and phase transitions in niobium and tantalum derived nanoscale transition metal perovskites, Ba(Ti,MV)O3, M=Nb,Ta

The prospect of creating ferroelectric or high permittivity nanomaterials provides motivation for investigating complex transition metal oxides of the form Ba(Ti, MV)O3, where M = Nb or Ta. Solid state processing typically produces mixtures of crystalline phases, rarely beyond minimally doped Nb/Ta. Using a modified sol-gel method, we prepared single phase nanocrystals of Ba(Ti, M)O3. Compositional and elemental analysis puts the empirical formulas close to BaTi0.5Nb0.5O3−δ and BaTi0.5Ta0.5O3−δ. For both materials, a reversible temperature dependent phase transition (non-centrosymmetric to symmetric) is observed in the Raman spectrum in the region 533–583 K (260–310 °C); for Ba(Ti, Nb)O3, the onset is at 543 K (270 °C); and for Ba(Ti, Ta)O3, the onset is at 533 K (260 °C), which are comparable with 390–393 K (117–120 °C) for bulk BaTiO3. The crystal structure was resolved by examination of the powder x-ray diffraction and atomic pair distribution function (PDF) analysis of synchrotron total scattering data. It was postulated whether the structure adopted at the nanoscale was single or double perovskite. Double perovskites (A2B′B″O6) are characterized by the type and extent of cation ordering, which gives rise to higher symmetry crystal structures. PDF analysis was used to examine all likely candidate structures and to look for evidence of higher symmetry. The feasible phase space that evolves includes the ordered double perovskite structure Ba2(Ti, MV)O6 (M = Nb, Ta) Fm-3m, a disordered cubic structure, as a suitable high temperature analog, Ba(Ti, MV)O3Pm-3m, and an orthorhombic Ba(Ti, MV)O3Amm2, a room temperature structure that presents an unusually high level of lattice displacement, possibly due to octahedral tilting, and indication of a highly polarized crystal.

Chemistry↗

Light-driven transitions in quantum paraelectrics

Motivated by recent experiments on pump-induced polar ordering in the quantum paraelectric SrTiO 3 , we study a driven phonon system close to a second-order phase transition. Analyzing its classical dynamics, we find that sufficiently strong driving leads to transitions into polar phases whose structures, determined by the light polarization, are not all accessible in equilibrium. In addition, for certain intensity profiles, we demonstrate the possibility of two-step transitions as a function of fluence. For even stronger field intensities, the possibility of period-doubling and chaotic behavior is demonstrated. Finally we develop a generalized formalism that allows us to consider quantum corrections to the classical dynamics in a systematic fashion. Furthermore, we predict a shift in the critical pump fluence due to quantum fluctuations with a characteristic dependence on the fluence increase rate that should be observable in experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Structural characterization of highly alloyed (Al,Gd)N thin films

Highly alloyed (Al,Gd)N is of potential interest in a variety of applications, including neutron detection and in devices such as non-volatile memory. Gd has been shown to have very low equilibrium solubility in AlN at room temperature; however, non-equilibrium deposition techniques such as sputtering are able to deposit thin films, which incorporate large amounts of Gd. Here, we characterize a highly-alloyed (Al,Gd)N combinatorial thin film grown by RF sputtering on a GaN substrate, looking for any evidence of chemical or phase segregation or structural disorder in the films. Compositions with between 13% and 32% Gd (on a cation basis) were studied. No evidence was found for chemical or phase segregation in any studied composition. Higher degrees of Gd incorporation led to greater structural disorder in the film and a tendency toward amorphization; however, electron diffraction shows that the film does not become fully amorphous at any of the studied compositions, instead retaining textured local order even at 32% Gd. Electron energy loss spectra suggest that the material retains a locally wurtzite-like tetrahedral bonding environment at all studied compositions.

36 MATERIALS SCIENCE↗

Effective Landau-type model of a Hf x Zr 1 - x O 2 -graphene nanostructure

Here, to describe the charge-polarization coupling in the nanostructure formed by a thin Hf x Zr 1-x O 2 film with a single-layer graphene as a top electrode, we develop the “effective” Landau-Ginzburg-Devonshire model. This approach is based on the parametrization of the Landau expansion coefficients for the polar (FE) and antipolar (AFE) orderings in thin Hf 1-x Zr x O 2 films from a limited number of polarization-field curves and hysteresis loops. The Landau expansion coefficients are nonlinearly dependent on the film thickness h and Zr/[Hf+Zr] ratio x, in contrast to h-independent and linearly x-dependent expansion coefficients of a classical Landau energy. We explain the dependence of the Landau expansion coefficients by the strong nonmonotonic dependence of the Hf 1-x Zr x O 2 film polar properties on the film thickness, grain size and surface energy. The proposed Landau free energy with five “effective” expansion coefficients, which are interpolation functions of x and h, describes the continuous transformation of polarization dependences on applied electric field and hysteresis loop shapes induced by the changes of x and h in the range 0 < x < 1 and 5 nm < h < 35 nm. Using the effective free energy, we demonstrated that the polarization of Hf 1-x Zr x O 2 film influences strongly on the graphene conductivity, and the full correlation between the distribution of polarization and charge carriers in graphene is revealed. In accordance with our modeling, the polarization of the (5 – 25) nm thick Hf 1-x Zr x O 2 films, which are in the ferroelectric-like or antiferroelectric-like states for the chemical compositions 0.35 ≤ x ≤ 0.95, determine the concentration of carriers in graphene and can control its field dependence. The result can be promising for creation of next generation Si-compatible nonvolatile memories and graphene-ferroelectric FETs, because the working voltages applied to the Hf 1-x Zr x O 2 film (which acts as a gate) can be relatively low (less than 2 V). These low voltages are sufficient to induce the pronounced hysteresis of ferroelectric polarization in the Hf 1-x Zr x O 2 gate, which, due to the strong electric coupling, induces the hysteresis of the graphene charge.

36 MATERIALS SCIENCE↗

Large off-diagonal magnetoelectricity in a triangular Co2+-based collinear antiferromagnet

Abstract Magnetic toroidicity is an uncommon type of magnetic structure in solid-state materials. Here, we experimentally demonstrate that collinear spins in a material with R -3 lattice symmetry can host a significant magnetic toroidicity, even parallel to the ordered spins. Taking advantage of a single crystal sample of CoTe 6 O 13 with an R -3 space group and a Co 2+ triangular sublattice, temperature-dependent magnetic, thermodynamic, and neutron diffraction results reveal A-type antiferromagnetic order below 19.5 K, with magnetic point group -3′ and k = (0,0,0). Our symmetry analysis suggests that the missing mirror symmetry in the lattice could lead to the local spin canting for a toroidal moment along the c axis. Experimentally, we observe a large off-diagonal magnetoelectric coefficient of 41.2 ps/m that evidences the magnetic toroidicity. In addition, the paramagnetic state exhibits a large effective moment per Co 2+ , indicating that the magnetic moment in CoTe 6 O 13 has a significant orbital contribution. CoTe 6 O 13 embodies an excellent opportunity for the study of next-generation functional magnetoelectric materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ferro-ionic states and domains morphology in Hf x Zr 1–x O 2 nanoparticles

Unique polar properties of nanoscale hafnia-zirconia oxides (Hf x Zr 1–x O 2 ) are of great interest for condensed matter physics, nanophysics, and advanced applications. These properties are connected (at least partially) to the ionic–electronic and electrochemical phenomena at the surface, interfaces, and/or internal grain boundaries. Here, we calculated the phase diagrams, dielectric permittivity, spontaneous polar, and antipolar ordering, as well as the domain structure morphology in Hf x Zr 1–x O 2 nanoparticles covered by ionic–electronic charge originating from surface electrochemical adsorption. We revealed that the ferro-ionic coupling supports the polar long-range order in nanoscale Hf x Zr 1–x O 2 , induces, and/or enlarges the stability region of the labyrinthine domains toward smaller sizes and smaller environmental dielectric constant at low concentrations of the surface ions. The ferro-ionic coupling causes the transition to the single-domain ferro-ionic state at high concentrations of the surface ions. We predict that the labyrinthine domain states, being multiple-degenerated, may significantly affect the emergence of the negative differential capacitance state in the nanograined/nanocrystalline Hf x Zr 1–x O 2 films.

36 MATERIALS SCIENCE↗