Orbital moments

Bahn, /. way, road, track path orbit trajectory railway breadth (of cloth), bahnbrechend, p.a. pioneer, epoch-making. Bahn-brecher, m. pioneer, -durchmesser, m. orbital diameter, -ebene, /. orbital plane, -elektron, n. orbital electron, bahnen, v.t. beat, smooth, clear (a way). Bahn-hof, m. (railway) station, -impuls, m. linear momentum orbital moment, -sdileife, -schlinge, /., orbital loop, -spur, /, track, -tibergang, m. orbital transition, -zug, m. railway train. 

The values for the atomic saturation magnetization at the absolute zero, ferromagnetic metals iron, cobalt, and nickel are 2.22, 1.71, and 0.61 Bohr magnetons per atom, respectively.9 These numbers are the average numbers of unpaired electron spins in the metals (the approximation of the g factor to 2 found in gyromagnetic experiments shows that the orbital moment is nearly completely quenched, as in complex ions containing the transition elements). 

An anisotropic contribution B from the orbital motion of valence electrons with the quantum number L for the total orbital moment ... 

The value is derived from a zero-field spectrum recorded at 150 K. A q could not be determined at 4.2 K because the compound is in the limit of slow paramagnetic relaxation and the strong unquenched orbital moment forces the internal field into the direction of an easy axis of magnetization. As a consequence, the quadrupole shift observed in the magnetically split spectra results only from the component of the EFG along the internal field and the orientation of the EFG is not readily known dbabh is a bulky N-coordinating amide... 

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). 

Figure 4. Dependence of the ratio u u on the number of 5f electrons for light actinide compounds x free ion values, ° experimental values, form band calculations. The hybridisation between 5f and 3d electrons leads to the reduction of the 5f orbital moments (metallic covalency).

Lebech, B., Wulff, M. and Lander G.H. (1991) Spin and orbital moments in actinide compounds (invited), J. Appl. Phys., 69, 5891-5896. 

Table 1. Separation of spin and orbital moments from magnetic scattering and magnetization measurement in USe and UTe compounds (in bohr magneton unit).

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. 

Mononuclear SMMs of Ln(lll) Ions with Nonzero Orbital Moment... 

Equation (S6.1) is applicable to the salts of lanthanide ions. These have a partly filled 4f shell, and the 4f orbitals are well shielded from any interaction with the surrounding atoms by filled 5.9, 5p, and 6.9 orbitals, so that, with the notable exceptions, Eu3+ and Sm3+, they behave like isolated ions. For the transition metals, especially those of the 3d series, interaction with the surroundings is considerable. Because of this, the 3d transition-metal ions often have magnetic dipole moments corresponding only to the electron spin contribution. The orbital moment is said to be quenched. In such materials Eq. (S6.1) can then be replaced by a spin-only formula ... 

ENDOR on VO(II) complexes is facilitated for several reasons289 (a) the EPR transitions can easily be saturated (ENDOR signals are often observed at 100 K), (b) the large anisotropy of the Av tensor allows for a high orientation selectivity in powder samples, and (c) the V=0 bond may be used as internal reference axis. Moreover, the g tensor is nearly isotropic so that contributions to the hf interactions from an unquenched orbital moment may be neglected (Sect. 5.1). 

The eigenvalue equation corresponding to the Hamiltonian of Eq. [57] can be solved self-consistently by an iterative procedure for each orientation of the spin magnetization (identified as the z direction). The self-consistent density matrix is then employed to calculate the local spin and orbital magnetic moments. For instance, the local orbital moments at different atoms i are determined from... 

The magnetic moments of the Ni clusters are dominated by the contribution from surface atoms.48,69 The analysis of Wan et al. indicates that the orbital and spin local moments of cluster atoms with atomic coordination 8 or larger are similar to those in the bulk (p spin 0.55 and orb 0.05 pB) 73 that is, the orbital moment is almost quenched for internal cluster atoms. In contrast, there is a large enhancement of the spin and orbital moments for atoms with coordination less than 8. This enhancement increases with the coordination deficit, and it is larger for the orbital moment. Wan et al.48 also analyzed the quantum confinement effect proposed by Fujima and Yamaguchi,56 i.e., the... 

Ramsey obtained ay, by first-order and op by second-order perturbation theory (76) variational treatments give similar results (14, 71, 73). The term wp is sometimes called the second-order paramagnetic term and sometimes the high-frequency term (14), because of the dependence of the (temperature-independent) paramagnetism in molecules on the high-frequency matrix elements of the orbital moments (91). 

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. 

For high spin Fe " with five unpaired d electrons and zero orbital angular momentum, both the calculated and measured magnetic moments are 5.9 Bohr magnetons (BM). The measured magnetic moment of Fe of 5.1 to 5.5 BM is, however, higher than the calculated value of 4.9 BM owing to a contribution from the orbital moment of the ion. 

Is due to the orbital moments of the electrons in the complete Radon shell and is expressed as (per mole)... 

The values of spin and orbital moments at two different lattice parameters, bracketing (and very close to) the experimental (normal pressure) value of 4.89 A, are... 

All this opens a vast new field of research for actinide compounds. Besides encouraging high pressure experiments, a search may be foreseen of appropriate compounds of actinides with other elements for which the peculiar properties deriving from these huge actinide orbital moments, and, in particular, their magnetic anisotropy, may result to be enhanced. 

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