Magnetic site exchange

In some molecules, nuclei such as protons undergo magnetic site exchange.31 In the case of spin- nuclei, random magnetic site exchange between two equally... 

The description of nanomagnets requires new approaches. First, nanostructures are not periodic and tend to have large surface-to-volume ratios. Because of this the magnetization is not uniform across the nanostructure, local magnetic moments differ from site to site, exchange coupling varies throughout the nanostructure, and the anisotropy can be quite different from bulk or surface anisotropies. Second, it is hard to define properties in the similar fashion as in the bulk or as in case of molecules. 

Fig. 3. Calculated NMR lineshapes for equally populated two-site exchange as a function of the dimensionless parameter a = nf rA. The abscissa is the dimensionless relative offset parameter, x = A/// (see Eq. (18)). (a) a = 4 (b) a = 2 (c)a=l (d) a = l/ /2 (e) a = 0.5 (f) a = 0.2. Spectra (a) and (f) are near the slow and fast exchange limits, respectively. Reproduced with permission from R. K. Harris, Nuclear Magnetic Resonance Spectroscopy A Physicochemical View, p. 124, Longman Scientific and Technical, Harlow, 1986.

First the behavior of the LDA+U results versus U were studied (on-site exchange was kept fixed at 1 eV). The dependence of the magnetic moment on U (obtained from the FPLO code) for FM ordering is shown in Fig. 1. Recall that the ordered array of Na ions in our cell gives two crystallographically... 

Dd-m equals zero exactly if the two magnetic centers are centrosymmetric or lie on an n-fold axis of C symmetry with n >2, so many compounds are imaffected by this term. It is most commonly observed when adjacent magnetic sites are related by a screw axis. The effect of this term is to align adjacent spins at right angles to each other, but it only occms when the exchange interaction is also present and rendering the spins either parallel or antiparallel. The result is for the spins to be canted alternately to either side of their mean axis... 

X and X must be magnetically equivalent, that is they exchange magnetic sites with one another. The most plausible mechanism for such an exchange is the inversion of the carbanion 4 5, that is isoelectronic with an amine. The activation energy for this process... 

Molecular magnetic susceptibility (x) data for 1 and 2 powders (Fig. 4) were fitted to the theoretical expression for the susceptibility of an exchange-coupled triangle with three identical V magnetic sites,... 

Cotton, F. A., Chemical Applications of Group Theory, 2nd ed., Wiley-Interscience, 1971. Cotton, F. A., Quart. Rev., 1966, 20, 389 (reviews polyhedra of transition metal atoms). Emsley, J. W., J. Feeney and L. H. Sutcliffe, High Resolution Nuclear Magnetic Resonance Spectroscopy, Vol. 1, Pergamon Press, 1965 (Chapter 9 covers basic theory of the effect of site exchange on nmr line shapes). 

The treatment of exchange amongst more than two sites is possible by means of the McConnell equations and it can be seen that for the slow-passage solutions Bn algebraic equations result, where n is the number of distinct Larmor frequencies or magnetic sites available. The McConnell equations have been used by Meiboom (1961) in the problem of proton transfer in water amongst seven possible Larmor frequencies. In this case, the population of one Larmor frequency in H20 greatly exceeds the other six in The result obtained by Meiboom by... 

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