Poisson Relation Research Articles

In-plane epitaxy-strain-tuning intralayer and interlayer magnetic coupling in CrSe2 and CrTe2 monolayers and bilayers

Mismatched lattice-constants at a van-der-Waals epitaxy interface often introduce in-plane strains to the lattice of the epitaxial layer, termed epitaxy-strain, where the strains do not follow the intra-layer Poisson's relation. Here, we presented the magnetic phase diagrams of the CrSe2 and CrTe2 mono- and bi-layers under epitaxy-strain up to 8 %, as predicted using density-functional-theory calculations. They show that the in-plane epitaxy-strain manipulates either the intra- or inter-layer magnetism of them. The in-plane strain varies the interlayer distance, defined using an inter-layer Poisson's ratio, which governs the inter-layer magnetism in two opposite ways depending on the in-plane magnetism. The tunability of the intra-layer magnetism is a result of competing intra-layer Cr-Cr super-exchange interactions. A graphene substrate was introduced to examine the validity of our diagrams in practice. Our work also gives a tentative explanation on the controversially reported magnetizations in CrSe2 and CrTe2 epitaxial mono- or bi-layers under epitaxy-strains.

Magnetic Curvatures of a Uniformly Magnetized Tesseroid Using the Cartesian Kernels.

In recent years, the gravitational curvatures, the third-order derivatives of the gravitational potential (GP), of a tesseroid have been introduced in the context of gravity field modeling. Analogous to the gravity field, magnetic field modeling can be expanded by magnetic curvatures (MC), the third-order derivatives of the magnetic potential (MP), which are the change rates of the magnetic gradient tensor (MGT). Exploiting Poisson’s relations between (n+1)th-order derivatives of the GP and nth-order derivatives of the MP, this paper derives expressions for the MC of a uniformly magnetized tesseroid using the fourth-order derivatives of the GP of a uniform tesseroid expressed in terms of the Cartesian kernel functions. Based on the magnetic effects of a uniform spherical shell, all expressions for the MP, magnetic vector (MV), MGT and MC of tesseroids have been examined for numerical problems due to singularity of the respective integral kernels (i.e., near zone and polar singularity problems). For this, the closed analytical expressions for the MP, MV, MGT and MC of the uniform spherical shell have been provided and used to generate singularity-free reference values. Varying both height and latitude of the computation point, it is found numerically that the near zone problem also exists for all magnetic quantities (i.e., MP, MV, MGT and MC). The numerical tests also reveal that the polar singularity problems do not occur for the magnetic quantity as a result of the use of Cartesian as opposed to spherical integral kernels. This demonstrates that the magnetic quantity including the newly derived MC ‘inherit’ the same numerical properties as the corresponding gravitational functional. Possible future applications (e.g., geophysical information) of the MC formulas of a uniformly magnetized tesseroid could be improved modeling of the Earth’s magnetic field by dedicated satellite missions.

Forward modeling magnetic fields of induced and remanent magnetization in the lithosphere using tesseroids

A newly developed software package to calculate the magnetic field in a spherical coordinate system near the Earth's surface and on satellite height is shown to produce reliable modeling results for global and regional applications. The discretization cells of the model are uniformly magnetized spherical prisms, so called tesseroids. The presented algorithm extends an existing code for gravity calculations by applying Poisson's relation to identify the magnetic potential with the sum over pseudogravity fields of tesseroids.By testing different lithosphere discretization grids it is possible to determine the optimal size of tesseroids for field calculations on satellite altitude within realistic measurement error bounds. Also the influence of the Earth's ellipticity upon the modeling result is estimated and global examples are studied.The new software calculates induced and remanent magnetic fields for models at global and regional scale. For regional models far-field effects are evaluated and discussed. This provides bounds for the minimal size of a regional model that is necessary to predict meaningful satellite total field anomalies over the corresponding area.

Strain induced variations in band offsets and built-in electric fields in InGaN/GaN multiple quantum wells

The band structure, quantum confinement of charge carriers, and their localization affect the optoelectronic properties of compound semiconductor heterostructures and multiple quantum wells (MQWs). We present here the results of a systematic first-principles based density functional theory (DFT) investigation of the dependence of the valence band offsets and band bending in polar and non-polar strain-free and in-plane strained heteroepitaxial InxGa1-xN(InGaN)/GaN multilayers on the In composition and misfit strain. The results indicate that for non-polar m-plane configurations with [12¯10]InGaN//[12¯10]GaN and [0001]InGaN//[0001]GaN epitaxial alignments, the valence band offset changes linearly from 0 to 0.57 eV as the In composition is varied from 0 (GaN) to 1 (InN). These offsets are relatively insensitive to the misfit strain between InGaN and GaN. On the other hand, for polar c-plane strain-free heterostructures with [101¯0]InGaN//[101¯0]GaN and [12¯10]InGaN//[12¯10]GaN epitaxial alignments, the valence band offset increases nonlinearly from 0 eV (GaN) to 0.90 eV (InN). This is significantly reduced beyond x ≥ 0.5 by the effect of the equi-biaxial misfit strain. Thus, our results affirm that a combination of mechanical boundary conditions, epitaxial orientation, and variation in In concentration can be used as design parameters to rapidly tailor the band offsets in InGaN/GaN MQWs. Typically, calculations of the built-in electric field in complex semiconductor structures often must rely upon sequential optimization via repeated ab initio simulations. Here, we develop a formalism that augments such first-principles computations by including an electrostatic analysis (ESA) using Maxwell and Poisson's relations, thereby converting laborious DFT calculations into finite difference equations that can be rapidly solved. We use these tools to determine the bound sheet charges and built-in electric fields in polar epitaxial InGaN/GaN MQWs on c-plane GaN substrates for In compositions x = 0.125, 0.25,…, and 0.875. The results of the continuum level ESA are in excellent agreement with those from the atomistic level DFT computations, and are, therefore, extendable to such InGaN/GaN MQWs with an arbitrary In composition.

Gravimagnetic similarity in anomaly formulas for uniform polyhedra

Gravitational and magnetic anomalies of an arbitrary target body are linked through Poisson's differential relation. For a uniform polyhedral target, Poisson's relation reduces to an algebraic link between gravity and magnetic anomaly formulas. The derivation is given in tensor form. It identifies for each target facet edge a vector function, in terms of which the gravitational and magnetic potential and field anomaly formulas are similarly expressed as appropriately weighted linear combinations. This similarity unifies the theory of uniform polyhedral anomalies. It benefits analysis and construction of software that naturally embraces all anomalies in a single code. The analysis is exemplified by a discussion of singularities and by the adaptation of three gravity‐field algorithms to the remaining gravitational and magnetic cases, while retaining the respective computational advantages of the former gravity‐field algorithms.

Gravitational attraction of solids of revolution: Part 2: General expressions

A general integral expression is formulated for the gravitational attraction due to any solid of revolution based on the attraction of vertical, semi-infinite, circular, cylindrical shells. The expression accommodates solids with radial variation of density. For solids with constant density, further generalization to arbitrary orientation is made through coordinate transformation that considers both vertical and radial components of attraction. Special solutions for solids with simple geometry are listed. Practical applications are demonstrated by forward gravity modelling the effects of volcanic islands (cylindrical core bounded by an outer exponentially trending surface) and inclined finite-length cylinders. Corresponding expressions for the magnetic case are discussed in terms of using Poisson's relation.

A geological interpretation of the gravitational and magnetic fields of the northern and middle Caspian, based on estimates of their ratios

A geological interpretation of the gravitational and magnetic fields is a method based on Poisson's relation between the gravitational and magnetic potentials. Within the northern and middle Caspian there are parts of the crust with different types of spatial relation between the density and magnetic-action boundaries, corresponding to different structural-tectonic elements of platforms of different ages. The authors locate the southern boundary of the East European Platform; they distinguish the Scythian and Turanian plates: in the Paleozoic base of the Scythian plate they distinguish a graben of the axial zone and a limb of the Donets- Caspian fold system; they determine the position of the upper Paleozoic downwarps filled with volcanic-clastic strata at the edges of the Rostov -Kochubeyev zone of the pre-Permian basement and on the slopes of the middle Caspian massif. —Authors.

Solutions for the Static Junction†

ABSTRACT The characteristic non-linear differential equation which arises from Poisson's relation for the static distribution of charge is analysed for its solutions when either rather loose or restrictive boundary conditions provail. While the former admits a number of closed form solutions, an inverse series solution, appropriate particularly for diverse impurity distributions in the p-n junction, is developed for the spatial variation of the electrostatic potential.

Parametric Solution for the Diode Space Charge at Relativistic Energies†

ABSTRACT Transformation of the basic equations that describe the behaviour of the diode space charge “including Poisson's relation” into a time-dependent form allows straightforward solution in the relativistic domain. The parametric solution lends itself to securing various approximate explicit results and readily yields the extreme relativistic limit of a current linearly dependent upon anode voltage.