Spontaneous Magnetic Ordering

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. 

If this expression were correct, M would be finite even in a zero-applied field. Lorentz s theory thus predicts that aU substances obeying the Curie law should be ferromagnetic at sufficiently low temperatures. Although this is not tme, Lorentz s theory did predict that spontaneous magnetization, in the absence of an externally applied field, was possible. 

It can be shown that the paramagnetic Curie temperature, at which M vanishes, may be obtained from the vector-valued function M(H), when that function is written as two parametric equations (the parameter being a of Eq. 8.28). The solution is obtained graphically (see, for example, Goodenough, 1966, p. 81) and is found to be  

The familiar Curie-Weiss law (Eq. 8.9), for the magnetic susceptibility in the paramagnetic regime, is obtained from  

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Table 2 Existence (Yes) or absence (No) of spontaneous magnetic order at finite temperature as a function of spin- and lattice dimensionality...

Lappas, A. et al. Spontaneous magnetic ordering in the fuUerene charge-transfer salt (TDAE)Cjo- Science 267, 1799-1802, 1995. 

In Figure 15.26, the frequency of the oscillation, which is approximately proportional to the spontaneous magnetization, is plotted against the temperature [30]. The curve is very close to that expected from a 3D isotropic Heisenbeig spin system. These results of the ZF-/iSR experiments clearly demonstrate the appearance of spontaneous magnetic order in the / -phase crystal of / -NPNN. 

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