Magnetism, molecular field theory

Luckhurst G R 1985 Molecular field theories of nematics systems composed of uniaxial, biaxial or flexible molecules Nuclear Magnetic Resonance of Liquid Crystals ed J W Emsiey (Dordrecht Reidel)... 

There are further models which do not introduce new ideas but use the above frame for more complicated types of interactions. Bari and SivardiSre215) discussed a two sublattice model in analogy to the molecular field theory of antiferromagnetism. In this case there are two different interaction constants, viz. the intrasublattice and the intersublattice interaction. They also expand the one-sublattice model by an Heisenberg type magnetic interaction term between the HS states. Such an interaction may only become important for degenerate spin states. 

The field dependence of magnetization and of the susceptibility of a weakly anisotropic antiferromagnet - according to the molecular field theory - is described in Fig. 33 and the H = f(T) diagram in Fig. 34. 

Applying superposition approximations to the Ising model, one finds an evidence for the phase transition existence but the critical parameter to is systematically underestimated (To is overestimated respectively). Errors in calculation of to are greater for low dimensions d. Therefore, the superposition approximation is effective, first of all, for the qualitative description of the phase transition in a spin system. In the vicinity of phase transition a number of critical exponents a, /3,7,..., could be introduced, which characterize the critical point, like oc f-for . M oc (i-io), or xt oc i—io for the magnetic permeability. Superposition approximations give only classical values of the critical exponents a = ao, 0 = f o, j — jo, ., obtained earlier in the classical molecular field theory [13, 14], say fio = 1/2, 7o = 1, whereas exact magnitudes of the critical exponents depend on the space dimension d. To describe the intermediate order in a spin system in terms of the superposition approximation, an additional correlation length is introduced, 0 = which does not coincide with the true In the phase... 

Ohkoshi, S., Abe, Y., Fujishima, A. and Hashimoto, K. (1999) Design and preparation of a novel magnet exhibiting two compensation temperatures based on molecular field theory. /. Phys. Rev. Lett., 82, 1285-1288. 

The significance of 6 is most easily demonstrated by application of the mean or molecular field theory (MFT). The central idea here is that magnetic moments on neighboring atoms give rise to an internal or exchange or molecular field, H , in addition to any applied field as in (8)... 

Molecular field theory (MFT) is the simplest theory of ordered magnetic moments in solids. Proposed in 1907 by P. Weiss, its main assumption is... 

Since 1946 there has been in process of development at Northwestern University a new method for the elucidation of structure in certain classes of catalytically active inorganic solids. This method depends upon an application of magnetic moment and molecular field theory to the oxidation state, coordination, and atomic environment of the active element. It is this development which is described below. 

Fig. 5. Magnetic cluster spontaneous moment, /a, in Bohr magnetons, as a function of temperature. The solid line is the curve from molecular field theory for spin 5.

Fig. 7. Variation of the sub-lattice magnetization in the antiferromagnet GdV04 below = 2.4955(5)K. O from NMR frequency of V (J=i) (Bleaney et al. 1981c). Mossbauer data (Cook and Cashion 1979). — Molecular field theory.

The molecular field theory has been quite successful in describing the magnetic properties of many simple ferro-ferri- and antiferromagnetic spin arrangements in solids. According to this, the expression for the magnetic ordering temperature of various types of order and crystal structures is... 

If the spins in a lattice are aligned spontaneously in the same direction thus producing a finite magnetization, the ordered state is ferromagnetic. In the molecular field theory of ferromagnetism, the existence of an internal field ifi , is assumed which is proportional to the magnetization... 

Fig. 302. (NH4)2CuBr4 2H2O (a) and Rb2CuBr4 2H2O (b). Field dependence of magnetization M/Mq measured at T=4.2 K. The dashed curves represent the Brillouin function for S=. The solid curves are fits to molecular field theory [74V1].

The molecular field theory of this particular system has been worked out by Blume (1966) in order to explain the magnetism of UOa. Only for relatively small level separation Fi-Fs is the phase transition of second order. Larger level separation leads either to a first order phase transition or no transition depending on the coupling strength. 

The magnetic properties of the rare earth metals systems with localized magnetic moments, can be described by means of the molecular field theory. In the frame of this model the Curie temperature Tq and the paramagnetic transition temperature Tp may be expressed as (Smart 1966)... 

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