Crystal Ground State Research Articles

The Advantage of Internal Force Calculations in the X‐Ray Crystal Structure Analysis

AbstractAccording to the Hohenberg‐Kohn‐theorem the valence electron density (VED) determines the electronic ground state of crystal. The VED can be constructed measuring the X‐ray scattering amplitudes. Parametric density models are developed in order to complete the experimental data and to enable a generalization of the solved structure parameters. Caused by experimental and methodic errors various density models are able to describe the experimental data with comparable accuracy. However, electrostatic criterions can be applied in order to select a density model, which describes also the dynamical structure–property connections of semiconductor. A quantitative calculation of internal forces is possible by use of the generalized Berlin‐Theorem. The electrostatic model contains the ion–ion‐ and the electron–ion interaction in the crystal. The latter one can be calculated in the Fourier space using experimental or theoretical structure amplitudes. A model is proposed specially designed for diamond and zincblende structure compounds. The elastic properties of covalently bonded materials are described sufficiently precise by a bond charge model, taking into account the variation of amount and extension of the bond charge by deformation of lattice. The so fitted VED response of binary compounds can be transfered to solid solutions in order to interprete quantitatively the measured internal deformations in such materials.

Theoretical Calculation of Compton Profiles for Simple Ionic Crystals. II. Evidence against the Prevalent Picture of O2-in MgO

The electronic ground state of the MgO crystal is studied on the basis of the Heitler-London picture. The electron density in momentum space is calculated by using the 2nd-order cluster approximation mentioned in the preceding paper of this series. In the present study two extremes are chosen from available wavefunctions of the O 2- ion, all now available ones having the free ion-like symmetry 1 S. It is shown quantitatively that neither of the obtained electron-momentum densities is consistent with both of the observed isotropic Compton profile and cohesive energy. The present results indicate that the difficulty will be removed by adopting non-spherically distorted wavefunctions for O 2- .

Crystal field in Tm 2Ni 17

The compound Tm 2Ni 17 was studied by means of 169Tm Mössbauer spectroscopy in the temperature range 4.2–300 K. From an analysis of the spectra it was derived that the second order crystal field potential V 0 2 is negative for both Tm sites, favoring an easy c-axis magnetization at low temperature and an J = ¦±6 > crystal field split ground state.

161Dy Mössbauer Effect in Dy2Fe14B

AbstractThe 161Dy Mössbauer effect is measured in the tetragonal compound Dy2Fe14B at various temperatures between 4.2 and 300 K. The spectra are analysed in terms of two subspectra associated with the two crystallographic Dy sites in the structure of Dy2Fe14B. It is found that the crystal field split ground state corresponds to Jz = −15/2 for both the types of sites. The results of bulk magnetization measurements and the temperature variation of hyperfine field and quadrupole splitting are used to derive values of the magnetic coupling constant between the Fe moments (JFeFe) and the rare earth and iron moments (JFeR).

Quantum-mechanical ground state of crystals with dipole-dipole and exchange interactions

This paper deals with the quantum-mechanical ground state of crystals with dipole-dipole and exchange interactions. The approximation used is that the wave function is a product of the eight-spin wave functions of the magnetic ion supercells. The wave functions of the supercells are assumed to have the same form. Thus spin correlations for magnetic ions in the same supercell are taken into account, whereas in common mean-field theory this effect is neglected. Correlations between ions in different supercells are not taken into account. The eight-spin wave functions are constructed by using the theory of irreducible representations of the translation group. An additional simplification results by taking advantage of the classical solution of the problem. The method developed here is applied for a determination of the ground state of cerous magnesium nitrate, the results of which appear in the following paper.

Electron Structure and X‐Ray Absorption Spectra of Potassium Chloride I. Band Structure Approach

AbstractThe conduction band (CB) structure of potassium chloride in a rather wide energy region is calculated by means of the augmented plane wave (APW) method. The important features of CB are the hybridization and interaction of nearly free electron bands with K d‐ and Cl d‐bands. These effects lead to the appearance of many contrast peaks in the energy distribution of the density of K p‐and Cl p‐states. These distributions are compared with the experimental X‐ray K‐spectra in KCl. As a result of this comparison it is concluded that the band theory of an ideal crystal ground state is insufficient for an adequate quantitative explanation of the X‐ray absorption spectra in alkali halides. The assumption is made that one must take in account the deep core hole influence on the final‐states spectrum.

The coherent non-linear light propagation in crystal in the exciton range of the spectrum

The phenomenon of self-induced transparency (SIT) in the exciton range of the spectrum consists of the propagation through the crystal of solitary wave packets of coherent excitons and photons with anomalous small losses. In the running frame of reference at the site occupied by the soliton a single aperiodic transformation of photons into excitons and a reverse motion of the energy into the field takes place. The solutions of the SIT equations have been received in the slowly-varying amplitude approximation. Taking into account the phase modulation, the authors have shown the appearance of the branch of the carrier wave frequency with anomalous dispersion not only at the given pulse width but at the given pulse amplitude. They have also found the exact solution of the above mentioned equations taking into account the effect of saturation of the dipole momentum transition from the crystal ground state to the exciton state. It leads to the increasing of the soliton time width, to the decreasing of its amplitude and worsens the SIT observation.

Two-photon transitions to exciton states in semiconductors. Application to CuCl

We show that excitons in semiconductors are described by an effective Hamiltonian containing a nonlocal potential. In order to preserve the gauge invariance of the multiphoton transition rates in such systems, we show that a corrective term due to the nonlocal character of the potential has to be added to the standard electron-photon interaction. As an application, we calculate in the velocity and length gauges the two-photon transition rates between the crystal ground state and the $2p$ Wannier exciton in CuCl, and we show analytically and numerically their gauge invariance. We also estimate the contribution to the two-photon absorption coefficient due to transitions to $2p$ excitons in CuCl and we find a general agreement with experiment.

Two-photon transitions to exciton states in semiconductors

We consider the gauge invariance of the two-photon transition rate from the crystal ground state to exciton states in semiconductors in the framework of the Wannier model. We show that the non-locality correction in the velocity gauge is essential to preserve the gauge invariance. As a numerical example, we calculate in the length and in the velocity gauge the transition rates for the two-photon direct creation of 2 p excitons in a two-band semiconductor.

The ground state of rhombohedral crystals in an external magnetic field

This paper deals with the ground state of spin systems in an external magnetic field interacting with dipole–dipole and exchange interactions. The Luttinger and Tisza approach is adopted. By using group theoretic techniques a simplified form of the equation and constraints results. It is shown that the ground state problem can be solved by using only two out of the eight constraints. Application has been made in the case of cerium magnesium nitrate (CMN). It is found that in general the magnetic moment increases with the magnetic field but it is not parallel to it. Above a critical field hc the crystal goes into the metamagnetic state. Comparison is made with the experimental results.

Strong spin-phonon interaction. I. Quantum mechanics of domain walls

The ground state of a three-dimensional crystal with strong spin-phonon interaction is shown to possess a domainlike structure with domains separated by walls. Under the action of an external magnetic field, the walls are shown to acquire dynamical properties. These properties are investigated and the possibility of evidencing experimentally the quantum-mechanical motion of domain walls is briefly discussed, together with the connection between strong-spin phonon models and the dynamic clusters found in displacive materials with double-well atomic potentials.

New variational treatment of the ground state of solid helium

We use a new variational method recently proposed for treating the ground state of quantum crystals to calculate properties of solid $^{4}\mathrm{He}$. Key improvements over previous variational calculations include avoiding a low-order cluster expansion in determining the density distribution function, and using a quite general and correctly symmetrized single-particle wave function. The variational calculation, which is unrestricted, predicts the correct solidification density within 10%, but the binding energy is about 0.5\ifmmode^\circ\else\textdegree\fi{}K too low possibly because of a superposition approximation. The pressure is in good agreement with experiment. The density distribution function has a Lindemann ratio of 0.24 in accordance with expectations, but the corresponding single-particle wave function is much more spread out. The important implications this result has for the possible existence of Bose-Einstein condensation in solid $^{4}\mathrm{He}$, and also for the size of the exchange integral in solid $^{3}\mathrm{He}$, are briefly discussed.

Theory for the ground state of quantum crystals

We propose a new variational method for treating the ground state of quantum crystals which is free from the ills associated with cluster expansion procedures. Its application to solid 4He and neutron star matter produced satisfactory results.

Quantum-mechanical ground state of crystals with dipole-dipole and exchange interactions

Quantum-mechanical ground state of crystals with dipole-dipole and exchange interactions

The ground state of crystals with dipole-dipole and exchange interactions in an external magnetic field

The Luttinger and Tisza approximation for magnetic ions of crystals interacting with an external magnetic field and through dipole-dipole and exchange interactions is considered. The method of Luttinger and Tisza for finding the ground-state energy is applied and the solutions of the resulting set of equations are presented. In contrast to the case of zero field, not all solutions which satisfy the weak constraint automatically satisfy the strong constraint when an external magnetic field is present. Applications are made to the ground state of cerium magnesium nitrate. It is found that for low fields the solutions of the Luttinger and Tisza equations give the minimum energy spin configurations only when the field is in the yz plane or its rotationally equivalent planes. It is shown that for fields below a critical value the ground state of cerium magnesium nitrate is partly ferromagnetic and partly antiferromagnetic.

Suitability of Jastrow functions of WKB type to cluster calculations of the quantum crystal ground state

The effect of choosing a Jastrow function of the WKB formexp (−k/r5) for use in the Nosanow cluster calculation of the quantum crystal ground state is studied via a previously developed exact one-dimensional model. The computed convergence rates confirm the inability of this form to resum the cluster expansion so as to provide a meaningful variational minimum.

On the ground state of crystals with dipole-dipole and exchange interactions II: The general solution of the Luttinger-Tisza approximation

The general solution of the Luttinger-Tisza approximation for the ground state of crystals with dipole-dipole and exchange interaction is given for crystals with two equivalent magnetic ions (or atoms) per unit cell. (It is an extension of an earlier paper where the solution of the same problem was given for crystals with only one magnetic ion (or atom) per unit cell.) It is shown that this is the most general case to which the Luttinger-Tisza theory is applicable since in all other cases the so-called weak constraint can be shown not to be equivalent to the strong constraint. As an example we apply the theory to the crystal DyCl 3·6H 2O.

Polarization dependence of the two-photon absorption coefficient in crystals

The theory of two-photon absorption with provision for exciton effects is built on the basis of general principles without using any model of electronic states of the crystal. Electron-phonon interaction is neglected. The splitting of exciton levels into levels of transverse and longitudinal excitons is taken into account. The polarization dependence of two-photon absorption coefficient of allowed two-photon dipole transitions from the ground state of crystal for all 32 crystallographic classes is calculated. The results obtained are compared with the experimental data available.

On the ground state of crystals with dipole-dipole and exchange interactions

A complete solution is given of Luttinger and Tisza's method for finding an approximation to the ground state of a quantum-mechanical system of dipoles on a Bravais lattice, interacting through dipolar and exchange forces. The results are applied to cerium magnesium nitrate and a layered, antiferromagnetically ordered ground state is predicted for this crystal.

Far-Infrared Spectra and Zeeman Effect of Rare-Earth Double Nitrates

The far-infrared spectra of several rare-earth double nitrates have been observed over the range 30–170 cm−1. The frequencies of the low lying phonon modes have been determined by comparison of the spectra of the diamagnetic and paramagnetic salts. The absorptions due to the crystal field split ground states of the rare-earth ions have been positively identified by observations of the Zeeman effect. The experimental energies and g values have been compared with the predictions of earlier crystal field calculations based on approximate symmetries. Some of these are in reasonable agreement with the experimental results, but none of them provides a consistent description of the ground state levels for all the ions studied.