Local moment

Within the general trend in the behavior across the actinide series, their alloys, and their metallic compounds from superconductors to local moment magnets, the only serious irregularity occurs in some plutonium compounds. These compounds should be magnetic but turn out to be temperature independent paramagnets. 

The problem could be stated from another point of view. In an isostructural series the uranium and neptunium compounds tend to be itinerant electron magnets or band magnets (like iron) and their orbital contribution is at least partially quenched. For much heavier actinides we know that the compounds will make local moment magnets with orbital contributions. It is quite possible that in between these two clear cut forms of magnetism that the intermediate case could be dominated by fluctuations, and no recognizable form of magnetism would occur. To state that the... 

Site Localized moment Spin proportion Occupation parameter ... 

That way, the Distributed Electrostatic Moments based on the ELF Partition (DE-MEP) allows computing of local moments located at non-atomic centres such as lone pairs, a bonds and n systems. Local dipole contributions have been shown to be useful to rationalize inductive polarization effects and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a n character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. 

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... 

Figure 13 Ground state structures and local spin magnetic moments (in pB) of Mn5 and Mn7 determined by DFT calculations. For Mng, the structure and local moments correspond to a relevant isomer 0.07 eV above the ground state. Some bond lengths are also given, in A. Reproduced with permission from Ref. 103.

Superexchange describes interaction between localized moments of ions in insulators that are too far apart to interact by direct exchange. It operates through the intermediary of a nonmagnetic ion. Superexchange arises from the fact that localized-electron states as described by the formal valences are stabilized by an admixture of excited states involving electron transfer between the cation and the anion. A typical example is the 180° cation-anion-cation interaction in oxides of rocksalt structure, where antiparallel orientation of spins on neighbouring cations is favoured by covalent... 

Fig. 3.8 Left-hand panel The on-site atomic energy levels for up and down spin electrons due to the exchange splitting Im where / and m are the Stoner exchange integral and local moment respectively. Right-hand panel The local magnetic moment m, as a function of //2 / where / and h are the exchange and bond integrals respectively. Compare with the self-consistent LSDA solution in the upper panel of Fig. 3.6.

The c/a ratio is greater than for V02, which implies that the n band (i.e. that with d-orbital lobes in the basal plane) is more occupied than in V02 (Goodenough 1971, p. 352). But we think that if it were not ferromagnetic, the n band, in contradistinction to V02, would be wholly above the Fermi energy. The Hubbard correlation term U, however, produces localized moments for the 3d2 states, as explained in Chapter 3, and these, if oriented ferromagnetically, would just fill the tjj band. The filled band (for spin-up electrons) will now overlap the n band, allowing ferromagnetic interaction of Zener or RKK Y type between the d2 moments, as described in Chapter 3. The T2 term in the resistivity could be explained as in Chapter 2, Section 6. 

Dispersion is a considerably more difficult modeling task. As first noted in Section 2.2.4, dispersion is a purely quantum mechanical effect associated with the interactions between instantaneous local moments favorably arranged owing to correlation in electronic motions. In order to compute dispersion at the QM level, it is necessary to include electron correlation between interacting fragments, which immediately sets a potentially rather high price on direct computation. More difficult still, however, is that the continuum model by construction does not include the solvent molecules in the first place. 

However, Eq. (2.21) is not very convenient in the context of intramolecular electrostatic interactions. In a protein, for instance, how can one derive the electrostatic interactions between spatially adjacent amide groups (which have large local electrical moments) In principle, one could attempt to define moment expansions for functional groups that recur with high frequency in molecules, but such an approach poses several difficulties. First, there is no good experimental way in which to measure (or even define) such local moments, making parameterization difficult at best. Furthermore, such an approach would be computationally quite intensive, as evaluation of the moment potentials is tedious. Finally, the convergence of Eq. (2.20) at short distances can be quite slow with respect to the point of truncation in the electrical moments. 

In most instances, the magnetic structure of a compound can be understood to be based on interacting localized spin centers, such as classical 3d/4d/5d transition metal ions and 4f lanthanide or 5f actinide cations with unpaired electrons. Note that while the assumption of localized moments is valid for many compounds comprising such spin centers, even partial electron delocalization in mixed-valence coordination compounds renders many localized spin models inapplicable. 

In this case, setting Tn as 3.18 K as determined from the low field measurements, the critical field Hq at which Tn goes to zero is estimated to be Hq = 23 kG. This estimated absolute value of Hq matches the magnitude of order which is expected for local moment antiferromagnets Hq b n/a b-... 

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