Classical spin model

Due to the nature of the magnetic ions involved, both having a 6At fundamental term, the magnetic chains of Ba7MnFe6F34 are likely to be well described by an isotropic classical spin model, similar in principle to the one developed by Fisher [7] for the simple chain. This later uses however the recurrence relation (written here with trivial notations) ... 

The isotropic classical spin model for chains of rings already used for Ba7MnFe6F34 could be applied successfully to Ba2CaMnFe2F]4 [18,25] considering now the basic magnetic unit drawn in Fig. 23. The special role devoted to the nodal... 

Let us consider a MV dimer — d" in which for the sake of definiteness we assume that n < 4 (less than half-filled d-shells). The main features of the phenomenon can be understood in the framework of the classical spin model [77]. As distinguished from a quantum spin, a classical spin represents the infinite spin limit for which all the directions in the space are allowed. From the classical point of view, for Hund s configuration of the ion the extra electron lines up its spin, Sg, parallel to the spin sq of the d" ion (spin core). In the classical limit, 1/2, so that max 2 0 and 0. These two extremes correspond to parallel and antiparal-... 

Fig. 7 Spin dependence of the double exchange in a classical spin model...

We analyzed the temperature dependence of 1/Ti using the semi-classical BPP model for the effect of molecular motion on 1/Ti [32]. In this model, 1/Ti can be related to the values of correlation time, Tc, which is the characteristic time between significant fluctuations in the local magnetic field experienced by a spin due to moleciflar motions or reorientations of a molecule. As usual, it is assumed that Tc follows Arrhenius-hke behavior ... 

Much of our understanding of critical phenomena is based on the Landau-Ginzburg model of a ferromagnet. This model concentrates on the local magnetization, represented by an m-component vector field Sa (r), a = 1,..., m. often called a classical spin field . The interaction of the spin field is described by the Landau-Ginzburg Hamiltonian... 

This kind of representation for a single nuclear spin is absolutely equivalent to the classic vector model. 

The Stokes parameters for the polarization of an electron beam can be represented in a Cartesian basis which also provides a convenient pictorial view for the polarization state of an electron beam. Since the polarization of an ensemble of electrons requires the determination of spin projections along preselected directions, the classical vector model of a precessing spin will first be discussed. Here the spin is represented by a vector s of length 3/2 (in atomic units) which processes around a preselected direction, yielding as expectation values the projections (in atomic units, see Fig. 9.1)... 

In most instances, the magnetic structure of a compound can be understood to be based on interacting localized spin centers, such as classical 3d/4d/5d transition metal ions and 4f lanthanide or 5f actinide cations with unpaired electrons. Note that while the assumption of localized moments is valid for many compounds comprising such spin centers, even partial electron delocalization in mixed-valence coordination compounds renders many localized spin models inapplicable. 

To account for quantum mechanical effects, an approximate quantum model that reproduces the findings of the two classical spin-based approaches was constructed in a next step.37 One foundation of this model was the finding that several (nonfmstrated) molecular antiferromagnets of N spin centers 5 (which can be decomposed into two sublattices) have as their lowest excitations the rotation of the Neel vector, that is, a series of states characterized by a total spin quantum number S that runs from 0 to N x 5. In plots of these magnetic levels as a function of S, these lowest S states form rotational (parabolic) bands with eigenvalues proportional to S(S +1). While this feature is most evident for nonfmstrated systems, the idea of rotational bands can be... 

The Yamanouchi-Kotani basis is best suited if we want to solve the Heisenberg problem in the complete spin space. However, the number of spins that can be handled this way, soon reaches an end due to the rapid growth of the spin space dimension f(S,N). Even with the present day computers, the maximum number of spins that can be treated clusters around N = 30. For larger values of N one must resort to approximate treatments, one of which, as described hereafter, is based on the idea of resonating valence bonds (RVB) coming from the classical VB model developed by Pauling and Wheland back in the early 1930 s [37, 51]. In essence,... 

The vector model is a way of visualizing the NMR phenomenon that includes some of the requirements of quantum mechanics while retaining a simple visual model. We will jump back and forth between a classical spinning top model and a quantum energy diagram with populations (filled and open circles) whenever it is convenient. The vector model explains many simple NMR experiments, but to understand more complex phenomena one must use the product operator (Chapter 7) or density matrix (Chapter 10) formalism. We will see how these more abstract and mathematical models grow naturally from a solid understanding of the vector model. 

The second term is —3JN/16, when Tj is a two-dimensional classical spin, and is —3JN/% in the quantum-spin case. A total number of sites is N. This model is proposed as a orbital state for the layered iron oxide, [5, 6, 26], and is also recently proposed in study of the optical lattice [27-29]. A similar orbital model in a honeycomb lattice termed the Kitaev model is recently well examined. [30,31] Let us introduce the Fourier transformation for the orbital pseudo-spin operator. The Hamiltonian (15) is represented in the momentum space, [5,27]... 

Luiten, E., and Blote, H.W.J. Classical critical behavior of spin models with long range interactions. Phys Rev. B, 1997, 56, p. 8945-58. 

In this section we will generalize the Monte Carlo methods described in section 2 for classical spin systems to quantum spin systems. As an example we will use the spin-1/2 quantum Heisenberg o XXZ models with Hamiltonian... 

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