Effective spin Hamiltonian

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... 

The effective spin Hamiltonian for energetically well isolated and orbitally nongene-rate ground states of transition metal ions with spin S is generally given by [1, 41, 103] ... 

Any set of energetically well-isolated levels can be described by an effective spin Hamiltonian operator by choosing S to match the corresponding number of levels. This can be just one isolated Kramers doublet of a high-spin multiplet if the... 

Then, there are model Hamiltonians. Effectively a model Hamiltonian includes only some effects, in order to focus on those effects. It is generally simpler than the true full Coulomb Hamiltonian, but is made that way to focus on a particular aspect, be it magnetization, Coulomb interaction, diffusion, phase transitions, etc. A good example is the set of model Hamiltonians used to describe the IETS experiment and (more generally) vibronic and vibrational effects in transport junctions. Special models are also used to deal with chirality in molecular transport junctions [42, 43], as well as optical excitation, Raman excitation [44], spin dynamics, and other aspects that go well beyond the simple transport phenomena associated with these systems. 

E are the projections of the electron orbital angular momentum on the molecular axis and the subscript is the projection of the total electron angular momentum on the molecular axis directed from the heavy atom to fluorine. It is convenient to describe the spin-rotational spectrum of the ground electronic state in terms of the effective spin-rotational Hamiltonian following [90, 117] ... 

In [90] the conclusion was made, that the accuracy in calculations of the parameters of the effective spin-rotational Hamiltonian is close to 20%. However, further ab initio calculations showed the situation is more complicated. 

A special focus will be on phenomenological Hamiltonians involving electronic spin interactions. For this it is necessary to define atomic surrogate spin operators—so-called local spin operators—that may be directly related to the effective spins in... 

Dirac and Heisenberg showed how the same state of affairs could be reproduced by an effective spin-Hamiltonian... 

D. Maynau, P. Durand, J. P. Duadey, and J. P. Malrieu, Phys. Rep. A, 28, 3193 (1983). Direct Determination of Effective-Hamiltonians by Wave-Operator Methods. 2. Application to Effective-Spin Interactions in -Electron Systems. P. Durand and J. P. Malrieu, in Advances in Chemical Physics (Ah Initio Methods in Quantum Chemistry—I), K. P. Lawley, Ed., Wiley, New York, 1987, Vol. 67, pp. 321-412. Effective Hamiltonians and Pseudo-Operators as Tools for Rigorous Modelling. 

The Spin Hamiltonian Effective Approach to the Vibronic Effects - Selected Cases... 

In the actual construction the vibronic constant taken as the coordinate derivative of non-diagonal matrix element in equation (5) took a form depending on the spin-Hamiltonian effective parameters ... 

The aim of this work is to elucidate these problems. To this end, we calculate the effective spin Hamiltonian of the 5f2—5f2 superexchange interaction between the neighboring U4+ ions in the cubic crystal lattice of UO2 and we calculate T5 <%> eg, rs f2g(l) ancl r5 f2g(2) linear vibronic coupling constants. These data are then used to draw a more definite conclusion about the driving force of the phase transition and especially about the actual mechanism of the spin and orbital ordering in U02. 

The fact that the phase transition in UO2 has the first-order character and the ordered magnetic moment of 1.74 /ab is considerably lower than the paramagnetic moment (about 3 /ab) is qualitatively consistent with the ratio of the strength of the bilinear and biquadratic parts of the effective spin Hamiltonian (8) of the 5f2-5f2... 

The general NMR effective spin Hamiltonian has the following form ... 

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