Curie paramagnet behavior

Fig. 3 Example comparisons of X versus T behavior for a ferromagnet (left) and a sample with antiferromagnetic exchange (right) to theoretical Curie paramagnet behavior.

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. 

Fig. 11.59 Variation of magnetic susceptibility with temperature for diamagnetic, paramagnetic, ferromagnetic, and antiferromagnetic substances. Transitions to paramagnetic behavior for ferromagnetic and antiferromagnetic substances occur at the Curie (Tc) and Neel (TN) temperatures, respectively.

The Weiss constant applies a minor perturbation of the Curie Law a small FM exchange yields 6 > 0 K and an AFM exchange yields 9 < 0 K. In a Curie-Weiss plot, a negative x-intercept means AFM interactions are present, and a positive x-intercept means FM interactions. For large enough 9, these plots deviate from linearity at lower temperatures (upward for 9 < 0, downward for 9 > 0). It is best not to overinterpret small Weiss constants where 9 < 0.5 K or so, save to note that they imply nearly isolated paramagnetic behavior. From mean-field theory, one can approximate 9 = 2z JMF/k,46 where is an... 

This, in turn, accounts for the deviation from Curie-law behavior in many paramagnetic materials, as described in the last section. Before a discussion on the nature of exchange interactions, a phenomenological model of ferromagnetic behavior by Weiss is presented, which precedes the understanding of its quantum mechanical origin. 

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