Spin moment

The Dirac equation automatically includes effects due to electron spin, while this must be introduced in a more or less ad hoc fashion in the Schrodinger equation (the Pauli principle). Furthermore, once the spin-orbit interaction is included, the total electron spin is no longer a good quantum number, an orbital no longer contains an integer number of a and /) spin functions. The proper quantum number is now the total angular momentum obtained by vector addition of the orbital and spin moments. 

But similar calculations for the iron-group ions show marked disagreement with experiment, and many attempts were made to explain the discrepancies. The explanation is simple in many condensed systems the perturbing effect of the atoms or molecules surrounding a magnetic atom destroys the contribution of the orbital momentum to the magnetic moment, which is produced entirely by the spin moments of unpaired electrons.40... 

Concerning induced orbital moments of U-based intermetallic compounds, many PND experiments have been performed and have shown that the ratio iL/ -is can be used as a measure of the hybridisation [42-44] (in the light actinides, orbital and spin moments are oppositely directed and the neutron magnetic form factors are highly sensitive to the ratio uL/us). Indeed, this ratio is reduced as compared to the free ion expectations (Figure 4). 

The orbital contribution pL has been deduced by combining spin moments ps (all) by the MCP with the magnetization measurement M by an equation pL = ps (all) - M. 

These are summarized together with previous results [4] in Table 1. It is seen from Table 1 that the total moment of each compound is controlled by the orbital moment. Although the magnetic moment increases with going down from X = Se to Te, the absolute value of spin moment decreases while that of orbital moment changes little. These results imply that some orbital quenching happens to occur due to f-d hybridization between U atoms and/or f-p hybridization between U atom and chalcogenide atom. 

The spin moments of both USe and UTe are aligned anti-parallel to the magnetic field. That is to say, the whole magnetization is dominated by the orbital moments of these compounds. 

The spin moments were decomposed into localized 5f component, ps(5f), and diffused components, ps(diff). Combining magnetization measurement with this decomposition, the orbital contribution, pL(5f), has been deduced. ... 

The increase of the total magnetic moment from USe to UTe is the result of the decrease of spin moment from 5f electrons due to the stronger hybridization effects between U atom and Te atom. 

If the unpaired electron is stabilized by resonance or is in a molecular orbital extending over the whole molecule, it must sometimes be detectable elsewhere than on the central carbon atom. The radical in which the central carbon atom is the isotope of mass 13 has been prepared. Whereas carbon 12 has a zero nuclear magnetic spin moment, carbon 13 has a nuclear pin of 0.5 and a magnetic moment of 0.7021 nuclear magnetons. The nuclear magnetic spin moment in an external field gives rise to a nuclear magnetic resonance absorption line, in much the same way as does the unpaired electron. If the unpaired electron... 

Nuclear spins, moments, natural abundances, and resonance frequencies are summarized in a tabulation available from Varian Associates, Palo Alto, California and reproduced in the review article by Pake IS) and the book by Losche 12). 

The magnetic moment arises as a result of interactions between the spin moment of the electron, Ps, and the orbital moment the contribution of the orbital moment is of comparatively minor importance. The magnitude of the overall spin moment depends upon the number of unpaired electrons in the atom, i. e. 

Fe(OH)2 is difficult to investigate because it is so readily oxidized. At room temperature it is paramagnetic and is antiferromagnetic below 33 K (Miyamoto, 1976). Fe(OH)2 has a layer structure. In the antiferromagnetic state all spin moments within a layer are parallel and also parallel to the c-axis spins between adjacent... 

Since the application of pressure may modify strongly the charge density distribution in a solid, and therefore affects the orbital more than the spin moment, magnetic form factors and magnetic anisotropy may become much more pressure-dependent than usually assumed. 

Although attempts have been made to correlate the hyperfine field of a mixed-valence compound with the weighted mean of the Fermi contact-interaction field H, = 220 < Sz > kOe , the orbital and spin-moment contributions Hl and Hd, which may be comparable to H, at Fe(II) ions, make any such correlations dubious ... 

The maximum in susceptibility as a function of temperature can be explained using thermodynamic reasoning. At absolute zero, the spin moments are aligned as antiparallel as possible, yielding a small susceptibility. With increasing temperature, the tendency for disorder or more random alignment of spin moments become greater. 

An example of such a solution spectrum was given in Fig. 1. The dipole contribution to the hyperfine interaction drops out in Eq. (121) leaving the solution A to be primarily determined by the contact term which measures the amount of s character in the spin-moment distribution. 

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