The temperature dependence of paramagnetic susceptibility

As described in Section 12.1.2, the temperature dependence of the susceptibility of paramagnetic compound is given by the Curie law, Equation (12.3). The Curie law is indicative of the presence of isolated paramagnetic ions or atoms in the material. 

In classical physics, the magnetic dipole can lie in any direction with respect to the magnetic field. In real atoms this is not possible, and the direction of the magnetic moment vector can only take values such that the projection of the vector on the magnetic field direction, z, has values of Mj, where Mj is given by  

The classical case, in which the magnetic dipole moments can rotate freely, is equivalent to a continuum of energy levels with J tending to infinity. In this case, the magnetisation is given by  

This has the same form as the Curie equation, and the Curie constant is given by  

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The temperature dependence of paramagnetic susceptibility is shown in Figure 33.5 and follows the Curie law ... 

Figure 12.1 Various styles showing the temperature dependence of paramagnetic susceptibility. The plane defined by the vertical and horizontal axes Is divided Into two regions of FM and AFM interactions by the solid curve following the Curie law. The dotted curves show the susceptibilities in the presence of FM or AFM interactions.

Figure 12.4 The temperature dependence of paramagnetic susceptibility of the 2,4,6-tri-ferf-butylphenoxy radical crystal. 

Figure 12.5 The temperature dependence of paramagnetic susceptibilities of the galvinoxyl crystal (inset) and the 6 1 mixed crystal of galvinoxyl and hydrogalvinoxyl (main frame).

Figure 12.9 (a) The temperature dependence of paramagnetic susceptibility and (b) the magnetization isotherms of the a-HNN crystal. The solid curves represent the fitting results by the dimer model with Jlkg = -11 K. 

Figure 12.14 The temperature dependence of paramagnetic susceptibility (left) and the magnetization isotherms (right) of DEAPNN. gpePoH/IJI = 11 corresponds to [igH = 20 T. The thin lines represent the theoretical calculation with Jlkg = -2.45 K. For magnetization, the calculation at 0 K is shown.

Figure 12.23 The temperature dependence of paramagnetic susceptibility of the triradical, TNN. The isolated radical is in the quartet ground state, but the maximum of susceptibility of the orystal locates cn the theoretical curve for dcublet species. 

Magnetic (Natural) Multipoles. Magnetic dipole. In 1905 Langevin, when aiming at an explanation of Curie s law, i.e. of the temperature dependence of magnetic susceptibility in paramagnetics, attributed a priori and classically a permanent magnetic moment to the microsystems. 

Penney and Schlapp (35) many years ago discussed the influence of crystal field on the temperature dependence of magnetic susceptibility x in paramagnetic materials. X may be computed from the fundamental Van Vleck equation (36)... 

The temperature dependence of the molar susceptibility of a paramagnetic substance follows the Curie-Weiss law (if the magnetic field is not too strong) ... 

The temperature dependence of the molar magnetic susceptibility (x) of an assembly of paramagnetic spins without interaction is characterized by the Curie behavior with x = C/T where C = /Vy2( 2.S (.S + l)/3k. It is a very common situation in the organometallic chemistry of radical species when the spin density is essentially localized on the metal atom. Since, in most cases, this atom is surrounded by various innocent ligands, intermolecular interactions are very weak and in most cases are reflected by a small contribution described by a Curie-Weiss behavior, with x = C/(T 0) where 0 is the Curie-Weiss temperature. A positive value for 0 reflects ferromagnetic interactions while a negative value — the most common situation — reflects an antiferromagnetic interaction. 

Even for complexes that do not exhibit spin crossover, the temperature dependence of magnetic properties can provide very important information. Pierre Curie established in 1895 that paramagnetic susceptibility is inversely proportional to the absolute temperature (Fig. 11.57a) ... 

The Curie paramagnets [e.g., octahedral Fe(III) complexes] are rather rare, and the temperature dependence of the magnetic susceptibility requires more parameters, depending on the actual spacing of the low-lying energy levels. Let us enumerate the MPs associated with the SH formalism ... 

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