First-order Zeeman effect

Figure 27 Splitting of a free-ion state into 27+1 components by a magnetic field (a) for J even, (b) for J odd (i) for the first-order Zeeman effect (ii) including the second-order Zeeman effect...

For a state showing only the first-order Zeeman effect the magnetization as a function of field strength is given by the Brillouin function (equation 57). 

The Zeeman effect must be mentioned in the case of nitrogen it behaves normally when 77 = 0 but, in the general case of a non-zero asymmetry, the Zee-man part of the hamiltonian no longer commutes with the quadrupolar part and there appears to be no first-order Zeeman effect, The second-order treatment of the perturbation yields the following values for the transition frequen cies 81 ... 

Owing to the special form of the eigenwave functions for t] f=0, and in accordance with the absence of first-order Zeeman effect, it may be shown that the magnetic dipolar contribution to nitrogen resonance line width is very small33,34). Lines are consequently narrow for many of the compounds studied, a very convenient feature when weak effects, like the Stark effect, are to be studied35). 

The magnetic moment tends toward zero at low temperatures because, as shown in Figure 2, there is no first-order Zeeman effect in Tg. At the level of approximation presented here the moments arising from the orbital and spin motions cancel. 

In an octahedral field, the ground state is split by spin-orbit coupling into a lower quartet Eg and a higher doublet f-. There is no first-order Zeeman effect for Eg and thus the g factor is zero. 

In these expressions, w is a numerical coefficient which is a complicated function of both C and t. H is the field strength—that is, the first-order Zeeman splitting is proportional to the field strength—and P is the Bohr magneton. The first-order Zeeman effect has removed all degeneracies. Inclusion of the second-order Zeeman effect gives... 

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