Magnetism: classical spins

We will present the equation of motion for a classical spin (the magnetic moment of a ferromagnetic single-domain particle) in the context of the theory of stochastic processes. The basic Langevin equation is the stochastic Landau-Lifshitz(-Gilbert) equation [5,45]. More details on this subject and various techniques to solve this equation can be found in the reviews by Coffey et al. [46] and Garcia-Palacios [8]. 

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... 

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... 

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... 

The nature of the spin-orbit part of the Hamiltonian operator can be obtained from the classical spin-orbit interaction energy by replacing the classical dynamical variables by their quantum mechanical operators. The magnetic dipole moment of a spinning electron is given by... 

Here S, is a classical spin (dimensionless granule magnetic moment) vector of i-th granule, is a potential of (generally speaking anisotropic, where indices... 

For many cases (e.g. for classical spin or spin 1/2, see Refs. [134, 135] for details), the Eq. (3.120) permits to avoid a solution of the integral equation (3.119), reducing it to the set of transcendental equations for macroscopic quantities like magnetization w = , glassy order parameter and higher order <5"> spin averages of the system. 

Metallic crystals Metallic systems, like Fe impurities in Au, are often cited as classical spin glasses, referring to the pioneering experiment by Cannella and Mydosh (1972) when a cusp in the ac susceptibility, a (T ), in low magnetic fields is observed in these dilute alloys. In such systems, however, the interactions are rather complicated and not precisely known ... 

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