Uniaxial Field Research Articles

Elastic dielectric composites: Theory and application to particle-filled ideal dielectrics

A microscopic field theory is developed with the aim of describing, explaining, and predicting the macroscopic response of elastic dielectric composites with two-phase particulate (periodic or random) microstructures under arbitrarily large deformations and electric fields. The central idea rests on the construction — via an iterated homogenization technique in finite electroelastostatics — of a specific but yet fairly general class of particulate microstructures which allow to compute exactly the homogenized response of the resulting composite materials. The theory is applicable to any choice of elastic dielectric behaviors (with possibly even or odd electroelastic coupling) for the underlying matrix and particles, and any choice of the one- and two-point correlation functions describing the microstructure. In spite of accounting for fine microscopic information, the required calculations amount to solving tractable first-order nonlinear (Hamilton-Jacobi-type) partial differential equations.As a first application of the theory, explicit results are worked out for the basic case of ideal elastic dielectrics filled with initially spherical particles that are distributed either isotropically or in chain-like formations and that are ideal elastic dielectrics themselves. The effects that the permittivity, stiffness, volume fraction, and spatial distribution of the particles have on the overall electrostrictive deformation (induced by the application of a uniaxial electric field) of the composite are discussed in detail.

Modelling of hysteretic behavior of piezoceramic materials under electrical loading

The purpose of this study is to model the hysteretic behavior of piezoceramic materials under electrical loading. Remanent strain and remanent polarization are chosen as internal variables. A domain orientation distribution is used to describe the evolution of these variables by bridging the characteristics of microscopic domain distribution into macroscopic behaviors. This model is able to calculate electric displacement, longitudinal, and transversal strains as a function of uniaxial electrical field. Good quality of the formulation is demonstrated through comparison with experimental data of the literature. In addition, results confirm our hypothesis of isochoric deformation of piezoceramics under electrical loading.

Random field induced order in low dimension

We address an unresolved issue in the physics of low-dimensional many-body systems: the question of whether or not a random field can produce order at low temperatures for statistical mechanical systems possessing continuous internal symmetries. Concretely, we verify that the XY model in a uniaxial random field orders in two and three dimensions. The direction the system orders is perpendicular to the randomness for any choice of symmetry breaking field with nonzero projection perpendicular to the randomness. The result is particularly relevant in two dimensions, where there are a number of competing effects —quasi–long-range order of the pure system and strong fluctuations of the random field. While we consider only classical systems explicitly, the effect is robust and our work has implications for quantum systems as well, producing ordered phases in any dimension.

Brownian dynamic simulations and experiments of MR fluids

The use of computational techniques in magnetorheology is not new. I general, these approaches assume dipolar magnetic interactions, hard sphere repulsions, and no-slip conditions. In this contribution we focus on the dynamics of the equilibrium state in the presence of uniaxial DC fields. To achieve this goal we make use of Brownian Dynamic Simulations. We highlight the importance of the Brownian forces versus magnetic dipolar interaction in the range of low magnetic field strengths. We monitor the formation of columnar structures and their dynamics, in competition with the Brownian motion, until a hexatic crystal phase appears at high field strengths for monodisperse systems. The shear viscosity is computed from the Einstein relation and eventually compared with experimental data at very low-shear rates. A reasonably good agreement between both data sets is observed.

The generalized method of quantitative description of the uniaxial anisotropy in weak ferromagnet rhombohedral calcite type structure crystals with S-state ions

The method for investigation of the uniaxial and hexagonal anisotropies in weakly ferromagnetic rhombohedral FeBO3 crystals with the Fe2+ magnetic impurity with the use of the single-ion and pair approximation has been developed. In the framework of this method, a quantitative discrepancy between theoretical and experimental data on a uniaxial field has been eliminated. The energy contributions to the hexagonal anisotropy that are caused by the Dzyaloshinsky–Moriya interaction, the crystal field of Fe3+ ions and the temperature dependence of this anisotropy were analytically treated. The experimental temperature dependence of the hexagonal anisotropy of FeBO3 crystals is explained. It is shown that the compensation point and the typical temperature dependence of the hexagonal anisotropy result from the competition of the contributions of Fe3+ and Fe2+ ions. It is shown that respective considerable contributions to the anisotropy of Fe3+ and Fe2+ ions are made by the cubic symmetry and the uniaxial symmetry of the exchange “single-ion” type. The anisotropy constants for FeBO3 crystal was obtained by using the described results. It was shown, that for the calcite type structure crystals (iron borate and manganese carbonate) with S-state ions, the single ion and pair models (which previously raised doubts in their validity and accuracy) describe the experimental data good enough.

Polarized luminescence from Jahn-Teller split triplet states of self-trapped excitons in PbMoO4

The green luminescence from the triplet states of a self-trapped exciton (STE) located on a tetrahedral (MoO${}_{4}$)${}^{2\ensuremath{-}}$ ion in PbMoO${}_{4}$ splits into three bands, I, II, and III, as a result of the symmetry lowering of the (MoO${}_{4}$)${}^{2\ensuremath{-}}$ ion due to a Jahn-Teller effect. Time-resolved luminescence measurements have been performed for polarizations with the electric vector parallel to the crystallographic $c$ axis ($\mathbf{E}\ensuremath{\parallel}\mathbf{c}$) and perpendicular to it (E\ensuremath{\perp}c) in a temperature range between 8 and 225 K. All three bands are confirmed to exhibit significant polarizations. The main band II at 520 nm is polarized with $\mathbf{E}\ensuremath{\parallel}\mathbf{c}$ at low temperatures ($T$ 75 K) but changes its polarization from $\mathbf{E}\ensuremath{\parallel}\mathbf{c}$ to E\ensuremath{\perp}c at $T$ > 125 K. Band III at 600 nm is polarized with E\ensuremath{\perp}c at $T$ = 170 and 225 K. The degree of polarization of these two bands does not depend on the polarization of excitation light. On the other hand, band I at 405 nm is polarized with E\ensuremath{\perp}c ($\mathbf{E}\ensuremath{\parallel}\mathbf{c}$) under the excitation by photons polarized parallel (perpendicular) to the $c$ axis, in the range of $T$ = 150--225 K. The observation of polarized luminescence provides convincing evidence for further lowering of the symmetry of (MoO${}_{4}$)${}^{2\ensuremath{-}}$ ions due to a uniaxial crystal field in addition to the Jahn-Teller distortion. The sublevels of the triplet STE state responsible for the PbMoO${}_{4}$ luminescence are identified on the basis of group-theoretical considerations.

Two-dimensional colloidal networks induced by a uni-axial external field

Based on Monte Carlo and Molecular Dynamics computer simulations we investigate the aggregation patterns and dynamics of model colloidal mixtures consisting of particles with either one or two, oppositely oriented, induced dipole moments. The mixtures are confined to two spatial dimensions. Our model is inspired by recent optical-microscopy experiments involving polystyrene particles with (and without) gold patches. For a broad range of parameters, we find the model systems to self-assemble via a two-step scenario involving first percolation along the field, followed by a percolation transition in the transverse direction. The resulting two-dimensional networks are characterized by strongly hindered translational dynamics.

Linear trinuclear Zn(ii)–Ce(iii)–Zn(ii) complex which behaves as a single-molecule magnet

Linear Zn(II)-Ce(III)-Zn(II) complex, which involves only one 4f electron as a spin source, behaves as an SMM. Easy-axis magnetic anisotropy for the ground (2)F(5/2) state of Ce(III) was achieved by a uni-axial crystal field, which is formed with four phenoxo oxygens as axial donors with the other five oxygens as equatorial donors.

Relation between the grafting density of liquid crystal macromolecule and the symmetry of self-assembled bulk phase: coarse-grained molecular dynamics study

I consider a generic coarse-grained model suitable for the study of bulk self-assembly of liquid crystal (LC) macromolecules. The cases include LC dendrimers, gold nanoparticles modified by polymer chains with terminating LC groups and others. The study is focused on the relation between a number of grafted chains, $N_{\rm ch}$, and the symmetry of the self-assembled bulk phases. Simple space-filling arguments are used first to estimate stability intervals for a rod-like, disc-like and spherulitic conformations in terms of $N_{\rm ch}$. These are followed by coarse-grained molecular dynamics simulations for both spontaneous and aided self-assembly of LC macromolecules into bulk phases. In spontaneous self-assembly runs, essential coexistence of rod-like and disc-like conformations is observed (via analysis of the histograms for the molecular asphericity) in a broad interval of $N_{\rm ch}$, which prevents the formation of defect-free structures. The use of uniaxial and planar aiding fields is found to improve self-assembly into monodomain phases by promoting conformations of respective symmetry. Strong shape-phase relation, observed experimentally, is also indicated by the simulations by the coincidence of the stability intervals for the respective conformations with those for the bulk phases.

A model for alignment between microscopic rods and vorticity

Numerical simulations show that microscopic rod-like bodies suspended in a turbulent flow tend to align with the vorticity vector, rather than with the dominant eigenvector of the strain-rate tensor. This paper investigates an analytically solvable limit of a model for alignment in a random velocity field with isotropic statistics. The vorticity varies very slowly and the isotropic random flow is equivalent to a pure strain with statistics which are axisymmetric about the direction of the vorticity. We analyse the alignment in a weakly fluctuating uniaxial strain field, as a function of the product of the strain relaxation time τs and the angular velocity ω about the vorticity axis. We find that when ωτs ≫ 1, the rods are predominantly either perpendicular or parallel to the vorticity.

Theory of Fe and Mn 2p X-ray absorption for RbMn[Fe(CN)6

We calculate the Fe 2p X-ray absorption spectrum (XAS) of RbMn[Fe(CN)6] in the ferromagnetic (FM) and photo-induced (PI) phases based on the calculation for the low-temperature (LT) and high-temperature (HT) phases. We use a configuration-interaction full-multiplet theory for a Fe(CN)6 cluster model and take account of the influence of adjacent Mn spins on the Fe(CN)6 cluster as an exchange field acting on the N 2p level. We predict that the Fe component of the magnetic moment can be decided by the Fe 2p XAS in the FM phase. In the PI phase, we predict a remarkable incident photon polarization dependence of the Fe 2p XAS.We examine the effect of a uniaxial crystal field on the Fe 2p XAS because RbMn[Fe(CN)6] in the LT phase takes the tetragonal structure which is one of factors for the temperature-induced valence transition. We also calculate the Mn 2p XAS of RbMn[Fe(CN)6] in the HT phase using a Mn(CN)6 cluster model. The average Mn 3d electron count is somewhat larger than the formal Mn valence (Mn2+) because of ligand-to-metal charge transfer.

Tunable thermal transport and thermal rectification in strained graphene nanoribbons

Using molecular dynamics (MD) simulations, we study thermal transport in graphene nanoribbons (GNR) subjected to uniform uniaxial and nonuniform strain fields. We predict significant thermal rectification (over $70%$) in a rectangular armchair GNR by applying a transverse force asymmetrically. The heat flux is larger from the less stressed region to the more stressed region. Furthermore, we develop a theoretical framework based on the nonequilibrium thermodynamics to discuss when thermal rectification under a stress gradient can occur. We conclude with a discussion of details relevant to experiment.

Experimental study of the x-ray linear dichroism of NiO films grown on Fe(001)

X-ray linear dichroism (XLD) effects at the Ni ${L}_{2}$ edge of NiO films grown on Fe(001) were studied systematically as a function of NiO thickness (${d}_{\mathrm{NiO}}$), temperature, interfacial modulation, and Fe magnetization directions. We found that the Ni XLD signal exhibited an unusual dependence on ${d}_{\mathrm{NiO}}$. The XLD effect persists above the N\'eel temperature and exhibits a similar ${d}_{\mathrm{NiO}}$-dependence as the behavior at room temperature. On the other hand the Ni XLD signal reverses its sign as the Fe magnetization is switched by 90${}^{\ensuremath{\circ}}$. We propose a possible mechanism such that the Fe magnetostriction induces the NiO uniaxial crystal field to dominate the XLD magnitude in the NiO/Fe(001) system.

Interface magnetism of iron grown on sulfur and hydrogen passivated GaAs(001)

Sulfur (S) and hydrogen (H) atom passivated GaAs(001) templates were used for deposition of ultrathin crystalline Fe films using molecular beam epitaxy, where the Fe thickness ranged from 10 to 45 atomic layers. Reflection high-energy electron diffraction patterns showed that the S- and H-passivated surfaces had no and very weak (1 × 2) superlattice reconstructions, respectively. This indicates that these GaAs(001) templates have a square-like symmetry. Magnetic anisotropies were investigated using the in-plane angular dependence of ferromagnetic resonance at 36 GHz. The in-plane cubic and uniaxial anisotropies and perpendicular uniaxial field were described by bulk and interface contributions, indicating that the Fe films have a high lattice coherence. The magnetic properties of the Fe films were compared to those grown on more commonly used GaAs(001) templates having a (4 × 6) reconstruction with an As-rich in-plane uniaxial symmetry. The Fe films grown on S-passivated templates exhibited unique magnetic properties caused by a decreased lattice spacing compared to the bulk Fe.

Noncollinear Fe spin structure in (Sm-Co)/Fe exchange-spring bilayers: Layer-resolved57Fe Mössbauer spectroscopy and electronic structure calculations

Magnetization reversal in nanoscale (Sm-Co)/Fe (hard/soft) bilayer exchange-spring magnets with in-plane uniaxial magnetic anisotropy was investigated by magnetometry, conversion-electron M\ossbauer spectroscopy (CEMS) and atomistic Fe spin-structure calculations. Magnetization loops along the easy direction exhibit signatures typical of exchange-spring magnets. In-field CEMS at inclined \ensuremath{\gamma}-ray incidence onto thin (2 nm) ${}^{57}$Fe probe layers embedded at various depths in the 20-nm-thick natural (soft) Fe layer provides depth-dependent information (via the line-intensity ratio ${R}_{23}$ as a function of the applied field $H$) about the in-plane rotation of Fe spins. A minimum in the ${R}_{23}$-vs-$H$ dependence at (${H}_{\mathrm{min}}$, ${R}_{\mathrm{min}}$) determines the field where Fe magnetic moments roughly adopt an average perpendicular orientation during their reversal from positive to negative easy-axis orientation. A monotonic decrease of ${H}_{\mathrm{min}}$ with distance from the hard/soft interface is observed. Rotation of Fe spins takes place even in the interface region in applied fields far below the field of irreversible switching, ${H}_{\mathrm{irr}}$, of the hard phase. Formation of an Fe-Co alloy is detected in the interface region. For comparison, the noncollinear Fe spin structure during reversal and the resulting ${R}_{23}$ ratio were obtained by electronic-structure calculations based on a quantum-mechanical Hamiltonian for itinerant electrons. The coupling at the hard/soft interface is described by the uniaxial exchange-anisotropy field, ${h}_{\mathrm{int}}$, as a parameter. Our calculated ${R}_{23}$ ratios as a function of the (reduced) applied field $h$ exhibit similar features as observed in the experiment, in particular a minimum at (${h}_{\mathrm{min}}$, ${R}_{\mathrm{min}}$). ${R}_{\mathrm{min}}$ is found to increase with ${h}_{\mathrm{int}}$, thus providing a measure of the interface coupling. Evidence is provided for the existence of fluctuations of the interface coupling. The calculations also show that the Fe spin spiral formed during reversal is highly inhomogeneous. In general, our simulation of the Fe spin structure is applicable for the interpretation of experimental results on layered exchange-spring magnets.

Ferromagnetic resonance phenomenon of magnetic thin film under a perpendicular field

Regarding ferromagnetic resonance frequency as a function of the perpendicular external magnetic field, the ferromagnetic resonance phenomenon is investigated. The results show that for the case where the external magnetic field is parallel to the its plane and the magnetic thin film has a perpendicular uniaxial magnetiocrystalline anisotropy, magnetic resonance frequency is divided into two categories, i.e., low frequency branch and high frequency branch, their specific relation depends on the magnetic anisotropy of the magnetic film; when external magnetic field is perpendicular to the systemic plane, the magnetic resonance frequency displays only a branch with the change of external magnetic field. In general, the magnetic resonance frequency decreases with the increase of the external magnetic field nonlinearly and monotonically. However, when the ratio between the cubic magnetocrystalline anisotropic field Hk1 and uniaxial magnetocrystalline anisotropic field Ha is about 2/3 Hk1/Ha < 1, the magnetic resonance frequency increases with the increase of external magnetic field, which is in good agreement with the experimental results. The results show that through magnetic resonance spectrum, the vertical magnetic anisotropy in magnetic thin film can be distinguished.

Multi-axial fatigue initiation at inclusions and subsequent crack growth in a bainitic high strength roller bearing steel at uniaxial experiments

The behaviour of inclusion initiated fatigue was studied for a high strength bearing steel with a bainite micro-structure. The analysis included experiments and numerical simulations. It was realized that the stress-state was multi-axial in the matrix material that met the inclusion also for a uniaxial far field stress. Fatigue initiation risk at the interface between the inclusion and matrix material was therefore predicted with the Findley multi-axial critical plane criterion. The fatigue parameters were determined from independent experiments on smooth specimens with tensile surface stress gradients. Crack growth from the inclusion to final rupture was modelled as a penny shaped crack with closure compensated effective material parameters. The growth simulations suggested that the majority of the fatigue life was consumed as fatigue crack initiation at the non-metallic inclusion.

Luminescence study of self-trapped excitons in CdMoO 4

Luminescence properties of CdMoO 4 crystals have been investigated in a wide temperature range of T=5–300 K. The luminescence-excitation spectra are examined by using synchrotron radiation as a light source. A broad structureless emission band appears with a maximum at nearly 550 nm when excited with photons in the fundamental absorption region (<350 nm) at T=5 K. This luminescence is ascribed to a radiative transition from the triplet state of a self-trapped exciton (STE) located on a (MoO 4) 2− complex anion. Time-resolved luminescence spectra are also measured under the excitation with 266 nm light from a Nd:YAG laser. It is confirmed that triplet luminescence consists of three emission bands with different decay times. Such composite nature is explained in terms of a Jahn–Teller splitting of the triplet STE state. The triplet luminescence at 550 nm is found to be greatly polarized in the direction along the crystallographic c axis at low temperatures, but change the degree of polarization from positive to negative at T>180 K. This remarkable polarization is accounted for by introducing further symmetry lowering of tetrahedral (MoO 4) 2− ions due to a uniaxial crystal field, in addition to the Jahn–Teller distortion. Furthermore, weak luminescence from a singlet state locating above the triplet state is time-resolved just after the pulse excitation, with a polarization parallel to the c axis. The excited sublevels of STEs responsible for CdMoO 4 luminescence are assigned on the basis of these experimental results and a group-theoretical consideration.

Evolution of magnetic anisotropy and thermal stability during nanocrystal-chain growth

We compare measurements and simulations of ferromagnetic resonance spectra of magnetite nanocrystal-chains at different growth-stages. By fitting the spectra, we extracted the cubic magnetocrystalline anisotropy field and the uniaxial dipole field at each stage. During the growth of the nanoparticle-chain assembly, the magnetocrystalline anisotropy grows linearly with increasing particle diameter. Above a threshold average diameter of D ≈ 23 nm, a dipole field is generated, which then increases with particle size and the ensemble becomes thermally stable. These findings demonstrate the anisotropy evolution on going from nano to mesoscopic scales and the dominance of dipole fields over crystalline fields in one-dimensional assemblies.

Simulation of a two-dimensional model for colloids in a uniaxial electric field

We perform Monte Carlo simulations of a simplified two-dimensional model for colloidal hard spheres in an external uniaxial ac electric field. Experimentally, the external field induces dipole moments in the colloidal particles, which in turn form chains. We therefore approximate the system as composed of well-formed chains of dipolar hard spheres of a uniform length. The dipolar interaction between colloidal spheres gives rise to an effective interaction between the chains, which we treat as disks in a plane, that includes a short-range attraction and long-range repulsion. Hence, the system favors finite clustering over bulk phase separation, and indeed we observe at low temperature and density that the system does form a cluster phase. As the density increases, percolation is accompanied by a pressure anomaly. The percolated phase, despite being composed of connected, locally crystalline domains, does not bear the typical signatures of a hexatic phase. At very low densities, we find no indication of a "void phase" with a cellular structure seen recently in experiments.