Magnetic spin models

Garrahan and Chandler [230] have recently attempted to rationalize the string-like motion in supercooled liquids based on a completely different concept of dynamic facilitation, derived from the study of magnetic spin models originally developed by Fredrickson and Anderson [231]. Although these spin models seem to exhibit dynamic heterogeneity of some kind and slow relaxation processes, the slowing down of the dynamics in these models is entirely decoupled from the spin model s thermodynamics [116, 230]. In view... 

J. Noolandi (Xerox Research Center of Canada) What is the importance of the long-wavelength modes in your model, and could you clarify the relationship of your model to magnetic spin models ... 

In 1821 Michael Faraday sent Ampere details of his memoir on rotary effects, provoking Ampere to consider why linear conductors tended to follow circular paths. Ampere built a device where a conductor rotated around a permanent magnet, and in 1822 used electric currents to make a bar magnet spin. Ampere spent the years from 1821 to 1825 investigating the relationship between the phenomena and devising a mathematical model, publishing his results in 1827. Ampere described the laws of action of electric currents and presented a mathematical formula for the force between two currents. However, not everyone accepted the electrodynamic molecule theory for the electrodynamic molecule. Faraday felt there was no evidence for Ampere s assumptions and even in France the electrodynamic molecule was viewed with skepticism. It was accepted, however, by Wilhelm Weber and became the basis of his theory of electromagnetism. 

This example shows that dipolar interactions can produce unexpected effects in systems containing polynuclear clusters, so that their complete quantitative description requires a model in which the dipolar interactions between all the paramagnetic sites of the system are explicitly taken into account. Local spin models of this kind can provide a description of the relative arrangement of the interacting centers at atomic resolution and have been worked out for systems containing [2Fe-2S] and [4Fe-4S] clusters (112, 192). In the latter case, an additional complication arises due to the delocalized character of the [Fe(III), Fe(II)] mixed-valence pair, so that the magnetic moments carried by the two sites A and B of Fig. 8B must be written... 

In a condensed system, the local field on a magnetic spin can be considered as a stochastic process. If a constant magnetic field H0 is present in the z-direction, the local field H( ) can be decomposed into the parallel and the perpendicular components. If the constant field is strong enough, this decomposition is meaningful the parallel component Hz(t) causes adiabatic shifts of the resonance frequency, whereas the perpendicular component H t) produces nonadiabatic effects.6 If only the adiabatic part is considered, the problem is just that treated in Section II, and if the local field Hz(t) is assumed to be a Gaussian process, then the Gaussian model of Section III can be adopted. 

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. 

Magnetic susceptibilities of 10a and 10b were measured on a SQUID suscep-tometer in microcrystalline form. %T-T plots are shown in Fig. 9.5. The data were analyzed in terms of a modified singlet-triplet two-spin model (the Blea-ney-Bowers-type), in which two spins (S = V2) couple antiferromagnetically within a biradical molecule by exchange interaction J. The best-fit parameters obtained by means of a least-squares method were 2J/kB = -2.2 + 0.04 K for 10a and -11.6 + 0.4 K for 10b. Although the interaction (2J/kB = -2.2 K) between the two spins in the open-ring isomer 10a was weak, the spins of 10b showed a remarkable antiferromagnetic interaction (2J/kB = -11.6 K). 

The paper is organized as follows. In See.2 we consider the frustrated spin chain at F-AF transition point and describe the exact singlet ground-state wave function as well as details of the spin correlation function calculations. We discuss the phase diagram of this model and its magnetic properties in the AF phase. In Sec.3 the special spin ladder will be considered. A two-dimensional frustrated spin model with the exact ground state is considered in Sec.4. Sec. 5 is devoted to the construction of the electronic models with the SB type of wave function. The results of this paper are summarized in Sec.6. 

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... 

Here, A is introduced to maintain the normalization condition. In many works in the literature, Eq. (9) was easily applied to investigate magnetic properties of various spin models for the bulk materials [35, 36], But, for the applications to the magnetic NPs systems, one needs to define the energy parameters c- appearing in Eq. (9) as... 

Xa-like models have been extended to treat magnetic (spin-polarized) systems (Slater, 1968), in which the electrons are required to be aligned either up or down along some quantization axis. For Xa this extension follows trivially from the observation that HF exchange occurs between electrons of like spin. Thus Slater proposed the spin-polarized expression... 

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