Exchange Heisenberg

Ding, X.-Q., Bominaar, E.L., Bill, E., Winkler, H., Traitwein, A.X., Driieke, S., Chaudhuri, P., and Wieghardt, K. 1990. Mossbauer and electron paramagnetic resonance study of the double exchange and Heisenberg-exchange interactions in a novel binuclear Fe(II/III) delocalized-valence compound. Journal of Chemical Physics 92 178-186. 

Figure 9. Energy level diagram for reduced FcsSa cluster according to Equation (12) plotted for antiferromagnetic (J > 0) Heisenberg exchange. For B/J > 2 the system ground state have S = 2 and Sab = 9/2. The extra electron was allowed to delocalize between sites A and B.

The Heisenberg exchange coupling constants J can be calculated from the BS DFT solutions utilizing the approaches of Noodleman (87), Ruiz (116), or Yamaguchi (117—119), which differ in the assumptions made regarding the strength of the... 

Low-dimensional Solids. - 2.10.1 Introduction. The magnetic properties of one and two-dimensional arrays of localized spins coupled by Heisenberg exchange interactions have been studied as a rather specialized branch of theoretical physics since the earliest days of quantum mechanics. However, recent advances in theory, and the preparation of real materials that are a good approximation to the theoretical models, have made low-dimensional systems much more central to condensed-matter science. There is enormous scope for synthetic chemistry in this area and, as will be seen later in this section, many new materials have been discovered recently. 

The Hamiltonian of equation (78) corresponds to so-called Heisenberg exchange. In some systems, particularly chains of atoms, it seems that the coupling is restricted to one direction, z. Then the Hex becomes... 

Due to the dependence of / on active nuclear distortions, the Heisenberg exchange interaction, equation (38), summed up over all nearest neighbour centres in a chain, should be added from the start to the energy functional in equation (32). Equation (41) shows, however, that this addition merely leads to the renormalization of the effective force constant Kt in equation (32) by... 

This relationship, known as Bloch s rule, applies in the localized-electron limit where the interatomic spin-spin interaction is described by the superexchange perturbation theory of eq. (23) with 7n J J is the Heisenberg exchange energy. Calculations by Shrivastava and... 

Fig. 23. Schematic energy diagram of the Heisenberg exchange energy J vs. bandwidth W at the crossover from localized-electron to band magnetism, after Zhou and Goodenough (2002a).

Since the leakage factor can be easily calculated from Ti relaxation data, and ys/y is constant, that only leaves the determination of smax before the coupling factor can be directly accessed. For solutions of radicals where Heisenberg exchange is prominent, Emax must be measured as a function of concentration and extrapolated to infinite concentration where smax 26,50 pQr jmmobilized or tethered radicals, nitrogen nuclear spin relaxation effectively mixes the hyperfine states in virtually all cases (small peptides may be an exception) and smax 1 can safely be assumed. 56 Alternately, the determination of smax can be avoided... 

The theoretical model [130] was developed as an extension of the classical theory of dipolar broadening in dilute solid solutions in the absence of exchange interactions [16]. It was suggested in [130] how to determine the dipolar part in the line width by subtraction of the calculated input of Heisenberg exchange interaction of pairs of exchange-coupled ions. Equations were written for the three cubic lattices as a function of ion s concentration for various numbers of cationic sites included in a sphere of radius Rc with the assumption that clustering effects were absent. The results were compared well with experimental data on Cr3+ in MgO powders. 

The geometry of the lattice determines the structure of the Heisenberg exchange parameter matrix. In most cases only nearest-neighbor interactions are taken into account and all non-vanishing Heisenberg exchange parameters axe set equal, i.e. we set... 

On a continuum level, the Heisenberg exchange energy of a cubic material is... 

A. WEISS MOLECULAR FIELD AND HEISENBERG EXCHANGE HAMILTONIAN... 

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