Ferromagnetic spin

Yamamoto, Y Miura, T Suzuki, M., Kawamura, N Miyagawa, H Nakamura, T Kobayashi, K Teranishi, T. and Hori, H. (2004) Direct observation of ferromagnetic spin polarization in gold nanopartides. Physical Review Letters, 93, 116801. 

While mononuclear octahedral Ni11 complexes often show relatively broad signals, nuclear relaxation enhancement and sharp signals may be observed in related dimer species 350,351 This has been taken advantage of for a detailed NMR investigation of a series of weakly ferromagnetically spin-coupled dinuclear octahedral Ni11 centers.352... 

Their n-conjugated backbone provides a ferromagnetic spin interaction over a long chain. The spins can interact not only with their neighboring spins, but also with more remote spins. This is very important because this interaction makes the spin coupling insensitive to the spin defect. 

It is relatively common for DFT calculations to not explicitly include electron spin, for the simple reason that this approximation makes calculations faster. In materials where spin effects may be important, however, it is crucial that spin is included. Fe, for example, is a metal that is well known for its magnetic properties. Figure 8.10 shows the energy of bulk Fe in the bcc crystal structure from calculations with no spin polarization and calculations with ferromagnetic spin ordering. The difference is striking electron spins lower the energy substantially and increase the predicted equilibrium lattice constant by 0.1 A. 

The fully ionic solids (region I) afforded band insulators, 1 1 Mott insulators with ground states of antiferromagnets (E b(21) and F b(22) in Fig. 1) or spin-Peierls systems, ferroelectrics, ferromagnets, spin-ladders, and nonlinear transport materials (switching and memory). 

In Chap. A, we have seen that, in the Stoner model, (ferromagnetic) spin-polarization of electrons originates two electron states E+ and E from each electron state E of a non-spin-polarized electron band, the difference between the two being (E+ - E ) = Im, where I is the Stoner parameter and m = n+ - n is the magnetization density. 

In the case of Fe(OEC)Py susceptibility measurements indicated a S = 3/2 ground state for the metal atom (p = 3.80 BM) but this characterization is not in agreement with Mossbauer data (8Fe = — 0.09 mms 1, AEq = 3.88 mms"1) which correspond rather to those observed for the Fe4+ complexes. The hypothesis has been considered that the complex would be an Fe4+ corrole anion radical the magnetic properties (S = 3/2) of which would result from ferromagnetic spin coupling of Fe4+ (S = 1) with a macrocycle anion radical (S = 1/2) [27]. Theoretical studies are necessary to completely characterize the electron distribution in the complex. 

Fig. 11. Variation with x of the magnetic moment per Mn ion in Bohr magnetons at 4 K (straight line represents ferromagnetic spin-only value) and magnetic-ordering temperatures (crossed circles) for LaMri xGax()3, after Goodenough et al. (1961).

Now we recall the discussion on the magnetic order in a ferromagnetic spin system through the molecular-field approximation as is described in the usual textbook [10], In the spin system of S = the magnetization M at the temperature T is described as... 

Figure 8. A fragment of two-dimensional rectangular lattice with N=L+1. The shaded circle corresponds to the region with ferromagnetic spin ordering around the segment with an additional electron (the shaded ellipse).

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