Magnetic moment density

Examples of p(r) are energy density, charge density, current density (see Section 4.6), difference density (difference between a final density and an initial density), electric moment density, magnetic moment density, local reactivity functions (see Section 4.5.2), force density, etc. Note that, for ensuring the stability of matter, the net force density must vanish everywhere in space. The concept of a PDF has generated many significant developments in interpretative quantum chemistry. 

Except in the few cases where a fairly large set of data has been collected on single crystals, and the magnetic moment density in the unit cell obtained by... 

We omit the explicit radial dependence of d and x (but note that the origin is the center of the metal wavefunction but x is ligand centered) and assume that they are unchanged from the free ion situation. This assumption is not essential, however, as a neutron scattering experiment provides information on the radial distribution as well as the magnitude of the magnetic moment density. 

Another important quantity related to the current density distribution is the nuclear magnetic moment density distribution (or magnetization density distribution) m(r) = r x j(r), which integrates to the magnetic moment = f d r m(r) briefly mentioned above. Finally, the magnetic induction field, generated by the nuclear current density distribution, can be obtained from the vector potential or from the current density distribution as... 

Titanium trifluoride [13470-08-17, TiF, is a blue crystalline solid that undergoes oxidation to Ti02 upon heating in air at 100°C (see Titanium compounds). In the absence of air, disproportionation occurs above 950°C to give TiF and titanium metal. TiF decomposes at 1200°C, has a density of 2.98 g/cm, and is insoluble in water but soluble in acids and alkafles. The magnetic moment is 16.2 x 10 J/T (1.75 -lB). 

Uranium dioxide [1344-57-6], UO2, is found ki nature as the mineral pitchblende and as a component ki uraninite. The crystalline soHd melts at 2878°C and is paramagnetic with a room temperature magnetic moment of 3.2 )Xg. The density has been found to range from 10.79 to 10.95 g/cm, lower values are... 

Figure 1.1. Nuclear precession nuclear charge and nuclear spin give rise to a magnetic moment of nuclei such as protons and carbon-13. The vector n of the magnetic moment precesses in a static magnetic field with the Larmor frequency vo about the direction of the magnetic flux density vector Bo...

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

Table 2 Fermi energy Ep (Ryd), density of states jVg, (per cell) and band contribution to the total energy Ep (Ryd) for 5DVF and SDWj at i = 0.5 (four-atom cell). The magnetic moment is Oz-directed.

Figure 5. Temperature development of the electronic density of states in fee FeaNi with the temperature dependent input taken from the Ginzburg-Landau theory (magnetic moments are given per atom).

The muffin-tin potential around each atom in the unit cell has been calculated in the framework of the Local-Spin-Density-Approximation using the ASW method. The ASW method uses the atomic sphere approximation (ASA), i.e. for each atom a sphere radius is chosen such that the sum of the volumes of all the overlapping spheres equals the unit cell volume. The calculation yields the expected ferromagnetic coupling between Cr and Ni. From the self-consistent spin polarized DOS, partial and total magnetic moment per formula unit can be computed. The calculated total magnetic moment is 5.2 pg in agreement with the experimental value (5.3 0.1 e calculations presented here have been performed... 

Much of the Pt Mossbauer work performed so far has been devoted to studies of platinum metal and alloys in regard to nuclear properties (magnetic moments and lifetimes) of the excited Mossbauer states of Pt, lattice dynamics, electron density, and internal magnetic field at the nuclei of Pt atoms placed in various magnetic hosts. The observed changes in the latter two quantities, li/ (o)P and within a series of platinum alloys are particularly informative about the conduction electron delocalization and polarization. 

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