Static Dielectric Response Research Articles

Static dielectric response and screening in solid state physics: Why dimensionality matters in dielectrics

Textbooks often present the phenomenon of screening within the Thomas–Fermi model for three-dimensional free electron gases, but obtaining the dielectric response function and screening potential for dielectric systems of reduced dimensionality is also of pedagogical interest. In this work, we introduce a simple approach to investigate static screening in dielectric systems in the presence of an impurity charge for different dimensionalities. This approach is applicable to semiconductors and insulators alike. We demonstrate that, in 3D systems, the macroscopic dielectric function in reciprocal space is a constant, while in 2D and 1D systems, it strongly depends on the momentum transferred to the electrons in the dielectric. Through the proposed dielectric screening model, one can also determine binding energies in a hydrogenic model that can be used to describe excitations in real semiconductor systems.

Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response.

We demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation-dissipation method for water and acetonitrile. We examine this method's trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.

Critical analysis of the response function in low-dimensional materials

The presence of sharp peaks in the real part of the static dielectric response function are usually accepted as indication of charge or spin instabilities in a material. However, there are misconceptions that Fermi surface (FS) nesting guarantees a peak in the response function like in one-dimensional systems, and, in addition, response function matrix elements between empty and occupied states are usually considered of secondary importance and typically set to unity like in the free electron gas case. In this work, we explicitly show, through model systems and real materials, within the framework of density functional theory, that predictions about the peaks in the response function, using FS nesting and constant matrix elements yields erroneous conclusions. We find that the inclusion of the matrix elements completely alters the structure of the response function. In all the cases studied other than the one-dimensional case we find that the inclusion of matrix elements washes out the structure found with constant matrix elements. Our conclusion is that it is imperative to calculate the full response function, with matrix elements, when making predictions about instabilities in novel materials.

Broadband and Microwave Dielectric Studies on Ba5Nb4O15 Ceramics Supplemented with Its Nanoparticles for Cryogenic Electronic Applications

Ba5Nb4O15 (BNO) nanopowders were prepared by sol–gel process. The effect of BNO nanopowders (x = 1 wt.%, 2 wt.%, and 3 wt.%) on micron-sized BNO polycrystalline powders were studied systematically. Transmission electron microscope (TEM) images of BNO nanoparticles revealed spherical and cylindrical shapes with average particle sizes of 45 nm and 60 nm, respectively. Further, the dielectric response of BNO ceramics with x wt.% of nanosized particles (x = 1–3) measured in the temperature range of 80°C to 200°C showed relaxation behaviour and is described by using Havriliak–Negami equation. The best microwave dielectric properties of er and Q × f0 values of 39.2 GHz and 59,000 GHz, at 6.52 GHz are obtained for the x = 3 wt.% sample, sintered at 1100°C, and is attributed to maximum density, large and uniform microstructure. The acquired static dielectric response of BNO ceramics with x wt.% of nanosized particles (x = 1–3) are suitable for cryogenic electronic and dielectric resonator applications.

Effective dielectric constant of the polydomain ferroelectric plate

ABSTRACTThe static dielectric response to an external electric field is calculated for a ferroelectric plate with a plane-parallel domain structure. The case of the free not fixed by defects domain boundaries was investigated. It is assumed that domain boundaries under external field will bend in the surface region so as to fully compensate an external field by the field of bound charges at the bent boundary. It is shown that the effective dielectric constant of such a plate depends not only on dielectric properties of the single-domain ferroelectric, but also on the geometrical characteristics of the system.

Monoclinic Cc-phase stabilization in magnetically diluted lead free Na1/2Bi1/2TiO3—Evolution of spin glass like behavior with enhanced ferroelectric and dielectric properties

The effect of magnetic cation substitution on the phase stabilization, ferroelectric, dielectric and magnetic properties of a lead free Na0.5Bi0.5TiO3 (NBT) system prepared by O2 atmosphere solid state sintering were studied extensively. Cobalt (Co) was chosen as the magnetic cation to substitute at the Ti-site of NBT with optimized 2.5 mol%. Rietveld analysis of x-ray diffraction data favours the monoclinic Cc phase stabilization strongly rather than the parent R3c phase. FE-SEM micrograph supports the single phase characteristics without phase segregation at the grain boundaries. The stabilized Cc space group was explained based on the collective local distortion effects due to spin–orbit stabilization at Co3+ and Co2+ functional centres. The phonon mode changes as observed in the TiO6 octahedral modes also support the Cc phase stabilization. The major Co3+-ion presence was revealed from corresponding crystal field transitions observed through solid state diffuse reflectance spectroscopy. The enhanced spontaneous polarization (Ps) from ≅38 μC cm−2 to 45 μC cm−2 could be due to the easy rotation of polarization vector along the in Cc phase. An increase in static dielectric response (ϵ) from ϵ ≅ 42 to 60 along with enhanced diffusivity from γ ≅ 1.53 to 1.75 was observed. Magneto-thermal irreversibility and their magnetic field dependent ZFC/FC curves suggest the possibility of a spin glass like behaviour below 50 K. The monoclinic Cc phase stabilization as confirmed from structural studies was well correlated with the observed ferroic properties in magnetically diluted NBT.

Dielectric and phase behavior of dipolar spheroids.

The Stockmayer fluid, composed of dipolar spheres, has a well-known isotropic-ferroelectric phase transition at high dipole densities. However, there has been little investigation of the ferroelectric transition in nearly spherical fluids at dipole densities corresponding to those found in many polar solvents and in guest-host organic electro-optic materials. In this work, we examine the transition to ordered phases of low-aspect-ratio spheroids under both unperturbed and poled conditions, characterizing both the static dielectric response and thermodynamic properties of spheroidal systems. Spontaneous ferroelectric ordering was confined to a small region of aspect ratios about unity, indicating that subtle changes in sterics can have substantial influence on the behavior of coarse-grained liquid models. Our results demonstrate the importance of molecular shape in obtaining even qualitatively correct dielectric responses and provide an explanation for the success of the Onsager model as a phenomenological representation for the dielectric behavior of polar organic liquids.

Structural, vibrational, and dielectric properties of Ruddlesden-PopperBa2ZrO4from first principles

Using first-principles computational techniques, we have investigated the structural, vibrational, and dielectric properties of a Ruddlesden-Popper-type layered oxide ${\mathrm{Ba}}_{2}{\mathrm{ZrO}}_{4}$ subjected to a wide range of biaxial strains emulating epitaxial thin-film environment. Under compressive strains, this compound experiences an incommensurate distortion characterized by planar displacements of individual perovskite slabs away from their high symmetry positions. On the other hand, under increasing epitaxial tension, the original centrosymmetric structure becomes unstable---first, with respect to antiferrodistortive oxygen cage rotations and then also with respect to in-plane polar distortions. Both the incommensurate-to-commensurate and the nonpolar-to-polar phase transformations are accompanied by anomalies of the static dielectric response, however, only in the latter case a divergence of the in-plane dielectric constant is observed. Remarkably, even after the transition into the ferroelectric state (with polarization of up to 0.12 ${\mathrm{C}/\mathrm{m}}^{2}$ at 3.5% tension) dielectric permittivity of ${\mathrm{Ba}}_{2}{\mathrm{ZrO}}_{4}$ remains unusually high, which is explained by an emergence of a Goldstone-like excitation in the system manifested through an in-plane libration of the polarization vector. Since ${\mathrm{Ba}}_{2}{\mathrm{ZrO}}_{4}$ displays a yet poorly understood tendency to absorb small molecules, such as water and ${\mathrm{CO}}_{2}$, acquiring better insights into the physical underpinnings of its behavior can produce more efficient functional materials for applications in advanced technologies for carbon sequestration.

Enhancement of electron mobility in asymmetric coupled quantum well structures

We study the low temperature multisubband electron mobility in a structurally asymmetric GaAs/AlxGa1-xAs delta doped double quantum well. We calculate the subband energy levels and wave functions through selfconsistent solution of the coupled Schrodinger equation and Poisson's equation. We consider ionized impurity scattering, interface roughness scattering, and alloy disorder scattering to calculate the electron mobility. The screening of the scattering potentials is obtained by using static dielectric response function formalism within the random phase approximation. We analyze, for the first time, the effect of asymmetric structure parameters on the enhancement of multisubband electron mobility through intersubband interactions. We show that the asymmetric variation of well width, doping concentration, and spacer width considerably influences the interplay of scattering mechanisms on mobility. Our results of asymmetry induced enhancement of electron mobility can be utilized for low temperature device applications.

Multisubband electron mobility in asymmetric GaAs/AlGaAs quantum well structures

The effect of structural asymmetry on multisubband electron mobility is studied by considering a barrier delta doped GaAs/AlxGa1−x As quantum well structure. The subband wave functions and energy levels are obtained by adopting selfconsistent solution of the coupled Schrodinger and Poisson’s equations. We consider scatterings due to ionized impurities, interface roughness and alloy disorder. The screening of the scattering potentials is obtained by adopting static dielectric response function formalism. We show that the interplay of different scattering mechanisms on low temperature electron mobility yields interesting results through intersubband interaction. Further, we show that asymmetry in structure parameters, such as, doping concentrations and spacer widths, influence in enhancing the mobility considerably.

Static dielectric response and polar phonons of Ba(Mn1/3Nb2/3)O3 and Ba(Ni1/3Nb2/3)O3 complex perovskites

Abstract The electronic structure, static dielectric response, and zone-center lattice dynamics of 1:2 ordered complex perovskites Ba(Mn 1/3 Nb 2/3 )O 3 and Ba(Ni 1/3 Nb 2/3 )O 3 are investigated using density functional theory within generalized gradient approximation (GGA) and GGA + U methods. Our results indicate that Ba(Mn 1/3 Nb 2/3 )O 3 is a typical Mott–Hubbard insulator, while the band gap of Ba(Ni 1/3 Nb 2/3 )O 3 shows a mixture of charge-transfer and Mott–Hubbard type. The calculated dielectric constants are in excellent agreement with experiments. The IR phonon frequencies and oscillator strengths for these two compounds are also analyzed in detail with the purpose of relating to their electronic structures and dielectric properties.

Field-induced percolation of polar nanoregions in relaxor ferroelectrics.

A first-principles-based effective Hamiltonian is used to investigate low-temperature properties of Ba(Zr,Ti)O(3) relaxor ferroelectrics under an increasing dc electric field. This system progressively develops an electric polarization that is highly nonlinear with the dc field. This development leads to a maximum of the static dielectric response at a critical field, E(th), and involves four different field regimes. Each of these regimes is associated with its own behavior of polar nanoregions, such as shrinking, flipping, and elongation of dipoles or change in morphology. The clusters propagating inside the whole sample, with dipoles being parallel to the field direction, begin to form at precisely the E(th) critical field. Such a result, and further analysis we perform, therefore, reveal that field-induced percolation of polar nanoregions is the driving mechanism for the transition from the relaxor to ferroelectric state.

Electronic structure and static dielectric response of Ba(Mn1/3Nb2/3)O3 from first principles

The electronic structure and dielectric properties of Ba(Mn1/3Nb2/3)O3 have been studied in the framework of the GGA(PBE)+U implementation of density functional theory. We show that Ba(Mn1/3Nb2/3)O3 is a typical Mott–Hubbard insulator which is characterized by the Mn 3d(eg)–Nb 4d(t2g) band gap. Excellent agreement between calculated and measured dielectric constants can be obtained only when taking suitable on-site Coulomb interaction parameters in both Mn 3d and Nd 4d electronic orbitals.

Self-consistent treatment of the local dielectric permittivity and electrostatic potential in solution for polarizable macromolecular force fields.

A self-consistent method is presented for the calculation of the local dielectric permittivity and electrostatic potential generated by a solute of arbitrary shape and charge distribution in a polar and polarizable liquid. The structure and dynamics behavior of the liquid at the solute/liquid interface determine the spatial variations of the density and the dielectric response. Emphasis here is on the treatment of the interface. The method is an extension of conventional methods used in continuum protein electrostatics, and can be used to estimate changes in the static dielectric response of the liquid as it adapts to charge redistribution within the solute. This is most relevant in the context of polarizable force fields, during electron structure optimization in quantum chemical calculations, or upon charge transfer. The method is computationally efficient and well suited for code parallelization, and can be used for on-the-fly calculations of the local permittivity in dynamics simulations of systems with large and heterogeneous charge distributions, such as proteins, nucleic acids, and polyelectrolytes. Numerical calculation of the system free energy is discussed for the general case of a liquid with field-dependent dielectric response.

First-principles study of phonons and intrinsic dielectric response of Ba(Ni1/3Ta2/3)O3

Electronic structure, lattice dynamics, and static dielectric response of 1:2 ordered Ba(Ni1/3Ta2/3)O3 are studied using the density functional theory. We find that, at intermediate value of on-site Coulomb interaction, the nature of the band gap is a mixture of Mott–Hubbard and charge-transfer type. After an analysis of electronic structure, zone-center optical phonon frequencies and their contributions dielectric response are evaluated. The computed dielectric constant and optical phonon frequencies are found to be in excellent agreement with experiments. Contributions of the dominant IR-active phonons to intrinsic static dielectric response are also analyzed in detail.

Magnetic and Static Nonlinear Dielectric Response in Doped CdCr2S4

The influence of cation substitution on the magnetic and static nonlinear dielectric response in the doped magnetic relaxor ferroelectrics CdCr2S4 is investigated within the framework of the spherical random-bond-random-field model (SRBRF) and the site-dilution Heisenberg model by adding an appropriate coupling term between the magnetic and ferroelectric subsystems. A-site substitution of the Cd by Fe in Cd1-xFexCr2S4 is found to reduce significantly the magnetization, which well agrees with the experimental results. Furthermore, the doping Fe ions play a crucial role in the spin-pair correlation and the nonlinear dielectric properties.

Single-file water as a one-dimensional Ising model

We show that single-file water in nanopores can be viewed as a one-dimensional (1D) Ising model, and we investigate, on the basis of this, the static dielectric response of a chain of hydrogen-bonded water molecules to an external field. To achieve this, we use a recently developed dipole lattice model that accurately captures the free energetics of nanopore water. In this model, the total energy of the system can be expressed as the sum of the effective interactions of chain ends and orientational defects. Neglecting these interactions, we essentially obtain the 1D Ising model, which allows us to derive analytical expressions for the free energy as a function of the total dipole moment and for the dielectric susceptibility. Our expressions, which agree very well with simulation results, provide the basis for the interpretation of future dielectric spectroscopy experiments on water-filled nanopore membranes.

Effects of Zr and Ti doping on the dielectric response of [formula omitted]: A comparative first-principles study

Zr doping in ceria (CeO 2) results in enhanced static dielectric response compared to pure ceria. On the other hand, Ti doping in ceria keeps its dielectric constant unchanged. We use first-principles density functional theory calculations based on pseudopotentials and a plane wave basis to determine electronic properties and dielectric response of Zr/Ti-doped and oxygen-vacancy-introduced ceria. Softening of phonon modes is responsible for the enhancement in dielectric response of Zr-doped ceria compared to that of pure ceria. The ceria–zirconia mixed oxides should have potential use as high- k materials in the semiconductor industry.

Static dielectric properties of polarizable ion models: Molecular dynamics study of molten AgI and NaI

The fluctuation-dissipation theorem for the static dielectric response function of systems of ions with inducible point dipoles is derived. It is shown that the static longitudinal dielectric function is determined by spatial correlations of both charge and dipole-moment density fluctuations. Moreover, it is deduced that the long-wavelength behavior of the charge structure factor for polarizable ion systems is different from that for systems of rigid ions. Molecular dynamics simulation results of rigid and polarizable ion models for molten AgI and NaI are reported.

The magnetic effect on static nonlinear dielectric response in magnetic relaxor ferroelectrics

The nonlinear dielectric response for the external field plays a very important role in providing useful information on relaxor ferroelectrics. Based on the spherical random-bond-random-field model and the Heisenberg model, considering the coupling interaction between the relaxor ferroelectricity and magnetism, we calculated the third-order static nonlinear dielectric susceptibility χ3 as well as the scaled nonlinear susceptibility a3=χ3/χ14 of magnetic relaxor ferroelectrics. We find that in contrast to the electric field, the external magnetic field remains relaxor state being a glass state. As the temperature passes through the magnetic phase temperature Tc, χ3, similar to linear dielectric susceptibility χ1, deviates its original low temperature behavior and shows a sharp increase. Furthermore, the position of the peak of χ3 and a3 are greatly affected by Tc and h. The temperature of maximum χ3 and a3 shift to higher temperature region with increasing Tc and h, indicating that freezing temperature Tf of magnetic relaxor ferroelectrics might be controlled by magnetism through magnetoelectric coupling.