Brillouin magnetization formula
= Brillouin magnetization formula
{c}
For independent distinguishable moments with angular <momentum> $J$, define $y=g\mu_BB/(k_BT)$. The one-site <partition function> is $Z=\sinh[(J+1/2)y]/\sinh(y/2)$. Its logarithmic derivative gives $\langle\mu_z\rangle=g\mu_B[(J+1/2)\coth((J+1/2)y)-\tfrac12\coth(y/2)]$. At $J=1/2$ this reduces to $(g\mu_B/2)\tanh(y/2)$.