Exchange coupling, Heisenberg

Exchange coupling, Heisenberg, 43 265-270 Exchange energy, 38 438-439 Exchange reactions, see also specific elements binuclear complexes, formation of, 10 183-188, see also Binuclear complexes one-equivalent, 10 154-178, 188-212 of actinide ions, 10 177, 178 of cerium, 10 176, 177, 206, 207, 211 of chromium, 10 163-168, 174, 175, 188-198, 206, 208... 

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... 

The quantum mechanical mechanisms that underlie exchange coupling are complex, but can be modeled by a phenomenological Hamiltonian that involves the coupling of local spin operators Sa and SB, the so-called Heisenberg-Dirac-Van... 

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. 

Table 5 Spin levels (Ei,i = 1 ), /T (in cm. K/mol) values at (in °K) corresponding to maximum anisotropy of the main values of the susceptibility /ii(ii = xx, yy, zz) tensor, /avr[Xav = (l/3)(Xxx + Xyy + Xzz)] and anisotropic D12 and A12 tensor parameters of a Fe -CN-Cu" model complex with and without trigonal Jahn-TeUer distortions from model calculations accounting for the difference of Je and Jb2 exchange coupling parameters (exchange anisotropy) or alternatively, assuming an isotropic Heisenberg exchange (1 = 1e = 1b2)...

Fig. 8. Orientational dependence of the average (spin-independent) exchange interaction energy AE = Via) ,

B. Heisenberg Exchange Coupling in Tetranuclear Species (Including a Useful Set of Microsoft BASIC Subroutines for Calculating Coupled Spin States, Energies, and Susceptibilities)... 

The magnetic properties of Cs4Ni3CdF12 (12R) and Cs5Ni4CdF15 (10H) were shown to agree with a model of exchange-coupled units, on a large temperature scale [3]. The interactions are well-described by the Heisenberg Hamiltonian... 

---