Orbital moment quenching

Orbital moment quenching The eigenfunctions of the angular moment operator r are the spherical harmonics, characterized by the quantum numbers I and m. 

The procedure is best illustrated with a simple example. For this purpose, we fall back on the model system used before in the discussion of the orbital moment quenching. The external potential stabilizes the Pz orbital with respect to the degenerate px and py orbitals by an amount of AE as shown in Fig. 2.2. Using the explicit notation for spatial and spin part, the zeroth-order wave functions are... 

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). 

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. 

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 ... 

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... 

It is important to mention that a reduction of ligand field symmetry can strongly alter the magnetic properties of ions If the symmetry of a 3d1 system with an Oh-symmetric ligand field is reduced (e.g., by an orthorhombic distortion), the entire orbital moment will be quenched and spin-only magnetism is observed. 

In the model of localized magnetic moments for the spin-only state (orbital moment is quenched) the interrelation between the effective magnetic moment and the moment in the magnetically ordered state is given by... 

This compares well with the experimentally determined value (approximately 3 x 105Am 1). The discrepancy is probably due partly to the assumption that Ni0Fe203 has the ideal inverse spinel structure and partly to the incomplete quenching of the orbital moment. 

Goldenbero s measurements show that the magnetic moment, of K5Mn(GN)g is i 05/utB> which is less than the calculated value for one unpaired electron. From the above jwssible structure this cannot be due to electron spin, so it is evidently due to incomplete quenching of the orbital moment. 

Externa] fields from other atoms and ions may effectively quench the orbital moment in these complexes. For the heavier transition metals and the lanthanides, the orbital contribution is larger and must be taken into account. Because we are usually concerned... 

The magnetic moments of many Cu complexes fall within the range 1.8- 2.2/i3 and are compatible with the presence of one unpaired electron with variable quenching of orbital moment. Most Ag complexes are also paramagnetic otherwise paramagnetism is uncommon in complexes of... 

The complex ion CrOBrj" has been isolated as the relatively stable bipy" salt. The value of //, 1.75 BM, and the g value, 1.999, show, as expected, that the orbital moment is quenched in a low-symmetry ligand field, the distortion being caused by the strong metal-oxygen bond. 

It is well-known that the geometry has a large influence on the size of the orbital moment. Densely packed cubic structures normally quench the orbital moment considerably (note the mentioned exception of US, where strong s-o coupling overcomes the crystal field effects). At the surface, however, both spin and orbital moments are enhanced in most cases due to the reduced coordination. The most pronounced effect is observed for ad-atoms, where moments in the order of the atomic moments can be found. Figure 12 illustrates this behavior for the case of iron atoms placed in different geometrical surroundings. Note, that the OP correction yields an essential enhancement in all cases. 

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