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Spin densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.4, pp. 725-734 [ doi:10.1107/97809553602060000615 ]
... with and spin, respectively. The spin-magnetization density is along z, and is given by is proportional to the normalized spin ...
Introduction
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.10.1, p. 733 [ doi:10.1107/97809553602060000615 ]
Introduction 8.7.4.10.1. Introduction In addition to the usual Thomson scattering (charge scattering), there is a magnetic contribution to the X-ray amplitude (de Bergevin & Brunel, 1981; Blume, 1985; Brunel & de Bergevin, 1981; Blume & Gibbs, 1988). In units of the chemical radius of the electron, the total scattering amplitude is where ...
Magnetic X-ray scattering separation between spin and orbital magnetism
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.10, pp. 733-734 [ doi:10.1107/97809553602060000615 ]
Magnetic X-ray scattering separation between spin and orbital magnetism 8.7.4.10. Magnetic X-ray scattering separation between spin and orbital magnetism 8.7.4.10.1. Introduction | | In addition to the usual Thomson scattering (charge scattering), there is a magnetic contribution to the X-ray amplitude (de Bergevin & Brunel, 1981; Blume, 1985; Brunel & de Bergevin ...
Combined charge- and spin-density analysis
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.9, p. 732 [ doi:10.1107/97809553602060000615 ]
Combined charge- and spin-density analysis 8.7.4.9. Combined charge- and spin-density analysis Combined charge- and spin-density analysis requires performing X-ray and neutron diffraction experiments at the same temperature. Magnetic neutron experiments are often only feasible around 4K, and such conditions are more difficult to achieve by X-ray ...
Comparison between theory and experiment
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.8, p. 732 [ doi:10.1107/97809553602060000615 ]
Comparison between theory and experiment 8.7.4.8. Comparison between theory and experiment Since it is a measure of the imbalance between the densities associated with the two spin states of the electron, the spin-density function is a probe that is very sensitive to the exchange forces in the system. In an ...
Moments of the magnetization density
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.7.2, p. 732 [ doi:10.1107/97809553602060000615 ]
Moments of the magnetization density 8.7.4.7.2. Moments of the magnetization density Among the various properties that are derivable from the delocalized spin density function, the dipole coupling tensor is of particular importance: where Rn is a nuclear position and rn = r - Rn. This dipolar tensor is involved directly in the hyperfine ...
Vector fields
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.7.1, p. 732 [ doi:10.1107/97809553602060000615 ]
Vector fields 8.7.4.7.1. Vector fields The vector potential field is defined as In the case of a crystal, it can be expanded in Fourier series: the magnetic field is simply One notices that there is no convergence problem for the h = 0 term in the B(r) expansion. The magnetostatic energy ...
Properties derivable from spin densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.7, pp. 731-732 [ doi:10.1107/97809553602060000615 ]
Properties derivable from spin densities 8.7.4.7. Properties derivable from spin densities The derivation of electrostatic properties from the charge density was treated in Subsection 8.7.3.4. Magnetostatic properties can be derived from the spin-magnetization density ms(r) using parallel expressions. 8.7.4.7.1. Vector fields | | The vector potential field is defined as In ...
Electronic structure of rare-earth elements
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.6.3, p. 731 [ doi:10.1107/97809553602060000615 ]
Electronic structure of rare-earth elements 8.7.4.6.3. Electronic structure of rare-earth elements When covalency is small, the major aims are the determination of the ground state of the rare-earth ion, and the amount of delocalized magnetization density via the conduction electrons. The ground state |[psi]> of the ion is ...
Beyond the dipolar approximation
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.6.2, p. 731 [ doi:10.1107/97809553602060000615 ]
Beyond the dipolar approximation 8.7.4.6.2. Beyond the dipolar approximation Expressions (8.7.4.74) and (8.7.4.78) are valid in any situation where orbital scattering occurs. They can in principle be used to estimate from the diffraction experiment the contribution of a few configurations that interact due to the operator. In delocalized situations, (8.7.4.74) is ...
International Tables for Crystallography (2006). Vol. C, Section 8.7.4, pp. 725-734 [ doi:10.1107/97809553602060000615 ]
... with and spin, respectively. The spin-magnetization density is along z, and is given by is proportional to the normalized spin ...
Introduction
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.10.1, p. 733 [ doi:10.1107/97809553602060000615 ]
Introduction 8.7.4.10.1. Introduction In addition to the usual Thomson scattering (charge scattering), there is a magnetic contribution to the X-ray amplitude (de Bergevin & Brunel, 1981; Blume, 1985; Brunel & de Bergevin, 1981; Blume & Gibbs, 1988). In units of the chemical radius of the electron, the total scattering amplitude is where ...
Magnetic X-ray scattering separation between spin and orbital magnetism
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.10, pp. 733-734 [ doi:10.1107/97809553602060000615 ]
Magnetic X-ray scattering separation between spin and orbital magnetism 8.7.4.10. Magnetic X-ray scattering separation between spin and orbital magnetism 8.7.4.10.1. Introduction | | In addition to the usual Thomson scattering (charge scattering), there is a magnetic contribution to the X-ray amplitude (de Bergevin & Brunel, 1981; Blume, 1985; Brunel & de Bergevin ...
Combined charge- and spin-density analysis
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.9, p. 732 [ doi:10.1107/97809553602060000615 ]
Combined charge- and spin-density analysis 8.7.4.9. Combined charge- and spin-density analysis Combined charge- and spin-density analysis requires performing X-ray and neutron diffraction experiments at the same temperature. Magnetic neutron experiments are often only feasible around 4K, and such conditions are more difficult to achieve by X-ray ...
Comparison between theory and experiment
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.8, p. 732 [ doi:10.1107/97809553602060000615 ]
Comparison between theory and experiment 8.7.4.8. Comparison between theory and experiment Since it is a measure of the imbalance between the densities associated with the two spin states of the electron, the spin-density function is a probe that is very sensitive to the exchange forces in the system. In an ...
Moments of the magnetization density
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.7.2, p. 732 [ doi:10.1107/97809553602060000615 ]
Moments of the magnetization density 8.7.4.7.2. Moments of the magnetization density Among the various properties that are derivable from the delocalized spin density function, the dipole coupling tensor is of particular importance: where Rn is a nuclear position and rn = r - Rn. This dipolar tensor is involved directly in the hyperfine ...
Vector fields
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.7.1, p. 732 [ doi:10.1107/97809553602060000615 ]
Vector fields 8.7.4.7.1. Vector fields The vector potential field is defined as In the case of a crystal, it can be expanded in Fourier series: the magnetic field is simply One notices that there is no convergence problem for the h = 0 term in the B(r) expansion. The magnetostatic energy ...
Properties derivable from spin densities
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.7, pp. 731-732 [ doi:10.1107/97809553602060000615 ]
Properties derivable from spin densities 8.7.4.7. Properties derivable from spin densities The derivation of electrostatic properties from the charge density was treated in Subsection 8.7.3.4. Magnetostatic properties can be derived from the spin-magnetization density ms(r) using parallel expressions. 8.7.4.7.1. Vector fields | | The vector potential field is defined as In ...
Electronic structure of rare-earth elements
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.6.3, p. 731 [ doi:10.1107/97809553602060000615 ]
Electronic structure of rare-earth elements 8.7.4.6.3. Electronic structure of rare-earth elements When covalency is small, the major aims are the determination of the ground state of the rare-earth ion, and the amount of delocalized magnetization density via the conduction electrons. The ground state |[psi]> of the ion is ...
Beyond the dipolar approximation
International Tables for Crystallography (2006). Vol. C, Section 8.7.4.6.2, p. 731 [ doi:10.1107/97809553602060000615 ]
Beyond the dipolar approximation 8.7.4.6.2. Beyond the dipolar approximation Expressions (8.7.4.74) and (8.7.4.78) are valid in any situation where orbital scattering occurs. They can in principle be used to estimate from the diffraction experiment the contribution of a few configurations that interact due to the operator. In delocalized situations, (8.7.4.74) is ...
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