Fitting the magnetic susceptibility

The method utilises a subroutine for the minimisation of a function of one variable. This can be done either without or with the calculation of the gradient. For one-dimensional minimisation without evaluating a derivative  

In the simplest version, the Powell method utilises the unit vectors as a set of directions. Using one-dimensional minimisation, the algorithm moves along the first direction to its minimum, then from there along the second direction to its minimum, etc. The whole process is repeated as many times as necessary until the function stops decreasing. All the direction set methods consist of prescriptions for updating the set of directions as the method proceeds. 

Alternative optimisation algorithms are accessible. Among them the MINUIT system of the CERN centre is often utilised [13]. A rather new approach is based on genetic algorithms [14-16]. 

A reduced FORTRAN code to fit the magnetic susceptibility is available on request from the author [17]. The optimisation algorithms selected there cover the simulated annealing method combined with the simplex method. 

For Curie paramagnets analytic functions were derived the Brillouin function and its classical analogue, the Langevin function. 

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The above statements apply to an assembly of independent spins. Deviation from proportionality, if any is observed, suggests the presence of cooperative magnetic phenomena, i.e. ferro-, antiferro-, ferri-, meta-, micto-magnetism, and so on. The magnetic susceptibility at above the spinordering temperature (Tq) can be usually fitted by the Curie-Weiss expression (18) with the Weiss temperature 0 > 0 for the sample with dominant... 

Nevertheless, the calculation of is an important issue. In experiment, it is considered as an empirical parameter fitted to experimental data so that the corresponding Heisenberg Hamiltonian describes the experimentally observed magnetic behavior (100,101). Although it would be more desirable from a quantum chemical point of view to directly calculate experimentally accessible properties, e.g., the magnetic susceptibility (102), the quantum chemical calculation of Ky provides a means to compare experimental and calculated results—though in a somewhat indirect fashion. 

The lattice parameters of PrNi2B2C (Siegrist et al. 1994b, see fig. 29) fit well the linear relationship derived for the other rare earth based borocarbides (except CeNi2B2C). Therefore the valence state of Pr in PrNi2B2C is close to 3+. The magnetic susceptibility... 

Ginsberg et al.2917 made a detailed analysis of the average magnetic susceptibility of nickel(II) dimers and fitted the temperature dependence of the magnetic susceptibility of [Ni2(en)4X2]Y2 (X, Y = Cl, Br X = NCS, Y = I). The model Hamiltonian they used is... 

A detailed study of the magnetic behavior of 18 Fe(R2Dtc)3 complexes with various R groups was carried out as a function of temperature and pressure (226). The magnetic susceptibility data as a function of temperature were fit by... 

The most spectacular example of such a directed chemical approach toward quantum magnetism is Cu2Te205Br2, a system with weakly connected Cu2+ tetrahedra, as sketched in Fig. 2a) [39], The magnetic susceptibility data given in Fig. 2b) show a broad maximum at Tmax=30 K and a decrease at low temperatures, a behavior that is consistent with weakly coupled tetrahedra of AF coupled spins. A fit to this temperature dependence gives a typical energy scale for the intra-tetrahedra coupling of J=40 K for this compound. A kink at Tc=14.4 K in the susceptibility marks a transition [32],... 

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