Localized magnetic moments

It is clear that an ah initio calculation of the ground state of AF Cr, based on actual experimental data on the magnetic structure, would be at the moment absolutely unfeasible. That is why most calculations are performed for a vector Q = 2ir/a (1,0,0). In this case Cr has a CsCl unit cell. The local magnetic moments at different atoms are equal in magnitude but opposite in direction. Such an approach is used, in particular, in papers [2, 3, 4], in which the electronic structure of Cr is calculated within the framework of spin density functional theory. Our paper [6] is devoted to the study of the influence of relativistic effects on the electronic structure of chromium. The results of calculations demonstrate that the relativistic effects completely change the structure of the Or electron spectrum, which leads to its anisotropy for the directions being identical in the non-relativistic approach. 

Figure 6.6 (a) Calculated local anisotropy axes on Dy(lll) sites (dashed lines) and the local magnetic moments in the ground state (arrows), (b) Temperature dependence of the /T product for Dy3-isoscelles complex. 

Blue arrows show the orientation of the local magnetic moments in the ground state on Dy and Cu ions, (b) A comparison between measured (empty squares) and calculated... 

Here Zp is the Fermi energy, that is, the energy of the highest occupied level Zc is a limiting atomic coordination number below which the local magnetic moment of that atom adopts the value pdim of the dimer, and one can choose... 

The spin-dependent local electronic occupations (wr,a) and the local magnetic moments p, = (( /a ) - ( oq)) are self-consistently determined... 

Figure 5.12. A revised Periodic Table of the/and d series. According to Smith and Kmetko (1983) this table of the d and/transition elements shows the cross-over between itinerant, fully bonding electrons and fully localized electrons usually forming local magnetic moments.

The appearance of magnetic properties in multi layer graphene has been studied [204, 227, 244-248]. Using graphene based activated carbon fibers it has been found that these materials show a Cuire-Weiss behavior, giving evidence of the presence of localized magnetic moments at its edges (see Fig. 28) [249]. 

As in the case of transition metals magnetism, the question of localized magnetic moments has been debated for some time and is still open. 

The mixed-valence iron oxides provide an experimental test-bed for studying the evolution of charge-transfer processes from the localized-electron to the itinerant-electron regimes. Moreover, it is possible to monitor the influence of the charge transfer on the interatomic magnetic coupling since the iron ions in oxides carry localized magnetic moments. 

An analysis of the correlation between the magnetic and geometrical structures of AunTM+ clusters, and a detailed study of the local magnetic moment of the TM impurity will be published elsewhere ... 

Fig. 3.6 Binding energy curves for the hydrogen molecule (lower panel). HF and HL are the Hartree-Fock and Heitler-London predictions, whereas LDA and LSDA are those for local density and local spin density approximations respectively. The upper panel gives the local magnetic moment within the LSDA self-consistent calculations. (After Gunnarsson and Lundquist (1976).)...

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.

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