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Brillouin (see B a t e s [1963b]) s h o w e d that the c o m p o n e n t of the magnetic m o m e n t μ of a t o m s m u s t be q u a n t i z e d in the direction of the magnetic field H. H e n c e for e a c h a t o m , there are C H . 2, §2] THEORIES OF FERROMAGNETISM 29 t h e s e characteristic q u a n t u m n u m b e r s : L , S, J a n d M , w h e r e M = / , / - 1 , . . , - ( / - 1), - / , a n d t h e c o m p o n e n t s of the magnetic m o m e n t in Η a r e Α ί # μ . Applying t h e M a x w e l l - B o l t z m a n n law gives a 3 a Β V a M = J N 2J Λί #μ 0 3 εχρ(Μ^μ μ ΗΐΙ<Τ) Β 0 Β M.

T o d e t e r m i n e which of t h e allowable t e r m s will r e p r e s e n t t h e lowest energy level of an a t o m , w e rely on H u n d ' s rules, w h i c h are sum­ marized as follows: (1) First select t h e t e r m s of highest S(S = Σ m ) consistent with t h e Pauli principle. (2) A m o n g the t e r m s having the s a m e highest value of 5 , select the o n e with the highest L ( L = Σ mi). (3) F o r the d e t e r m i n a t i o n of / , t w o distinct c a s e s exist: (A) If the subshell is less t h a n half full, set / = \L-S\.

2 + 3 + T h e magnetic m o m e n t of an ion, or a t o m , is given by μ = / * g / i . Since / * is the vector sum of L* and 5 * , in principle the magnetic m o m e n t is derived from b o t h the orbital a n d spin m o t i o n s . If, for s o m e reason to be discussed later, L * = 0, then / * = S* and g = 2. W h e n c e μ = μ = 2 5 * μ , signifying that t h e magnetic m o m e n t is d u e entirely to spin, not to the orbital motion at all. T h e orbital motion a n d therefore its associated angular m o m e n t u m and magnetic m o m e n t are said to be quenched.

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