Magnetic symmetry

Fig. 12-7. The Magnetic Symmetry Associated with the Group P62m. The twofold rotations are relative to Z = 1/40.

Magnetic symmetry associated with the group P62m, 757 Magnetic unit cell of MnF2,754 Malkin, I. G, 349... 

Fig. 3. Experimental dipolar shift ratios [for Pr(III)] of lysozyme nuclei plotted against values calculated from the X-ray structure, for a defined direction of the magnetic symmetry axis (see Ref. 5).

The magnetic moment of a particle in a magnetic field B evolves according to the equation of (damped) precession, and in the absence of damping the resonance occurs when the oscillating field frequency exactly equals the precession frequency. For simplicity, we assume the nanoparticles to have an ellipsoidal form with principal axes x, y and z. In this instance, the free energy density in a particle to the first order in the magnetic symmetry can be expressed as [13] ... 

An interesting feature of the NMR spectra of compounds 113 is that they show the magnetic symmetry of symmetrically substituted structures. We have already pointed out (Section VI,A) that this may be the result of a rapid exchange between valence isomers, but it seems more and more accepted that this is a real case of equivalence corresponding to a symmetrical pattern of bonding. 

All results show that for symmetrically substituted compounds, even at low temperatures, the molecules have a total magnetic symmetry on the NMR time-scale, for H as well as for 13C NMR. These results are consistent with either a very rapid equilibrium between valence isomers or with a C2v symmetry, which is now generally accepted. 

Fig. 3. Definition and numbering of the magnetic symmetries whose magnetic dipolar energies are given in Table 1.

The magnetic structures of Ba2CaMnFe2F14 and Ba2CaCoFe2Fi4 could be refined from neutron powder diffractograms recorded below their 3D ordering temperatures (respectively 26 and 30 K) [18,25-26], Both structures can be described with the same magnetic symmetries (Table 3), the transformations of the Sb component being... 

The magnetic symmetry of 1,3-butadiene [5C 1,4) 116.6 ppm 5C 2,3) 137.2 ppm] is broken by the introduction of an amino function at C(l) or C 2). The MINDO/3 calculated charge distribution for 1-dimethylamino- and 2-dimethyl amino-1,3-butadiene in the j-cis and -fran conformation appears in Table 5. The alternation of charge, typical of the enamine system, is maintained when the conjugation is extended, as is 97, the odd-numbered carbons bearing positive charge, and the nitrogen and even-numbered... 

Fig. 11. Influence of transition metal substitutions on the anisotropy (magnetic symmetry) of R2Co]7-based intermetallics of compositions R2(Co) tMJ()17. (After Hamano and Yajima 1978, Ray and Strnat...

Point symmetry group Magnetic symmetry group Number of the tensors nontrivial components ... 

Note that in Eq. (4.62) we neglected the bilinear coupling between magnetization components, found by Dzyaloshinskii for some magnetic symmetries and responsible for so-called weak ferromagnetism in antiferromagnets [106]. 

Fig. 14.145. Magnetic symmetry of R2(Coi-xFe,)i7 phases. Shaded areas indicate values of X where the easy axis of magnetization is in the c-axis (Ray and Strnat, 1972b).

Therefore, on varying the value of the parameter from negative to positive within the interval — 1 < /r < 1, an inversion of the bifurcation scenario with exchange of stability [94] is observed. The bifurcation occurs at the degenerate critical point for fi = Q. The trajectories are displayed on the left of Fig. 7.5. The flow is characterized by the C2v(Cj) = 2mm magnetic symmetry, see Sect. 7.5. 

Magnetic Symmetry of a Molecule in an External Magnetic Field... 

A series of simple rules is obtained taking magnetic symmetry into account ... 

Fig. 7.7 Perspective view of the stagnation graph of the current density vector field in planar ethene C2H4, with magnetic symmetry D2h C2h)- The uniform external magnetic field B is applied in the direction of the C-C bond, coincident with the z axis. Here and in the following figures, green (red) lines denote diamagnetic (paramagnetic) vortices, saddle lines are blue...

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