Single Ions in Crystals

Neglecting any spin-orbit coupling, what would be the observed orbital angular momenta of octahedral-site Co, Ni, Ni, Cr, Cr +, Mn +, and Cu + cations. 

Ion Number of d electrons Configuration L of unpaired electrons [/(/+1)] / in units of h 

a is a dimensionless parameter that is a measure of the ratio of the magnetic energy (the Zeeman energy) tending to align the magnetic moment to the thermal energy  

Alternatively, when gfi H/kT I, M NgjJu J. The magnetization derived from the BriUouin function have been tabulated for spin values to j in half-integral steps and for y= 00 (Darby, 1967). As stated earlier, the classic analog to Eq. 8.30 (in which g /A y(y -b 1) is replaced with the square of the magnetic moment, /r ) was first derived by Langevin. However, in classical mechanics the moments can be continuously aligned 

Using Eqs. 8.26, 8.28, and 8.29, show that the magnetization of a paramagnet in an externally applied field is given by Langevin s expression (Eq. 8.8).  

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