Magnetic moment formula

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... 

Consider the orbital angular momentum of a free-ion term. Here L = 3 and the orbital degeneracy is 7. Application of Van Vleck s formula (5.8) predicts an effective magnetic moment. 

This formula shows a smooth decrease of p toward the bulk magnetic moment with increasing N. However, the experimental results graphed in Figure 1 indicate that the variation of p with N has a more complex, oscillatory behavior. Its explanation requires a detailed consideration of the geometry of the cluster and a better treatment of its electronic structure. 

Here p is the stellar dipole magnetic moment and M is the mass accretion rate through the disk. For this formula we assume a purely dipolar field higher multipoles weaken the dependence on M because the field is effectively stiffen... 

Person 1 Calculate the net magnetic moment per unit cell for copper ferrite. Remember that there is more than one formula unit (CuFe204) per unit cell in the inverse spinel structure. 

Griffith el al. (Ill, 112) have shown that the blue compounds obtained by the interaction of nitric oxide and nickel carbonyl in the presence of water or an alcohol (68) have the general formula Ni(NO)(OR)3, and are probably tetrahedral. The N—0 stretching frequency of 1828 cm-1 in Ni(NO)(OH)3 indicates coordination of N0+ the spectra show absorption at 15,500 cm-1, in agreement with other such complexes, but the magnetic moment of Ni(NO)(OH)3 is only 2.97 B.M., which indicates considerable distortion. 

Caroli s analysis shows that the fall-off as cos(2/cFr+ff)/r3 is valid under more general conditions. This formula is used in Chapter 3 to derive the so-called RKKY interaction between magnetic moments embedded in a metal. 

Here we have in mind such materials as EuS with a comparatively high concentration of Gd atoms to give a degenerate electron gas, and a large number of metallic transitional-metal compounds where ions of mixed valence exist (in the latter there may be uncertainty about whether the electrons are in a conduction (4s) band or the upper Hubbard band described in Chapter 4). In such a case a new interaction term arises between the moments which is via the conduction electrons. This is the so-called RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction, which is an oscillating function of distance (Ruderman and Kittel 1954, Kasuya 1956, Yosida 1957 for a detailed description see Elliott 1965). This derives from the formulae of Chapter 1, Section 5. Consider an atom with magnetic moment in a given direction then the wave functions of conduction electrons with spin up and with spin down will vary with distance in different ways, so that... 

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