Magnetic susceptibility and electron spin resonance ESR

These complementary techniques are applied by inorganic chemists to the study of materials containing unpaired electrons. In such materials, we can identify ions (usually of the d or f block elements) as paramagnetic centres. The unpaired electrons may be appreciably delocalised over other atoms, however, and there may be considerable interaction between electrons on neighbouring centres, often to the extent that we have to look at a whole crystal and not at individual ions/ molecules in describing the magnetic properties. 

Consider a substance where the unpaired electrons are deemed to reside in d orbitals, localised - as in CF theory - upon ions of a transition element, n on each centre. The total spin 5 of each ion is equal to nil. If a 

It should be apparent that the magnetic susceptibility x of a paramagnetic sample (corrected for diamagnetism) should be infinite at absolute zero (with perfect alignment of the magnetic dipoles, or 100% population of the lowest Zeeman state) and zero at infinite temperature (random alignment of dipoles, equal population of Zeeman states). An obvious expression which embodies these conditions is  

This is the Curie law (Pierre, not Marie), C being a constant for a given sample. Better agreement with experimental data is obtained with the modified Curie-Weiss expression  

The magnetic susceptibility is thus a temperature-dependent property of a bulk substance. It is meaningless to specify the susceptibility of a single molecule or complex ion. For convenience, inorganic chemists prefer to answer the question How paramagnetic is this substance in terms of the magnetic moment peff defined by the relation  

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