1
$\begingroup$

If we consider the magnetization for paramagnetic materials, then we obtain $$M = -n\frac{\partial F}{\partial B} \propto B_J(x),$$ where $$x \equiv g\left( JLS\right) \cdot J \cdot \frac{\mu_B\cdot B}{k_B T}$$ is an auxiliary variable and $B_J( \ . )$ the Brillouin function. Now, what exactly is $J$ in this context? I thought that $\hat J = \hat L \ \oplus \ \hat S $, s.t. $J$ would be its quantum number. But then, how can $J$ be an integer, as is shown in the plot in our lecture: enter image description here

$\endgroup$

1 Answer 1

1
$\begingroup$

Well, I can't see why it bothers you. Mathematically we have all these combinations, with different degeneracies, of S (1/2, 1,...) Physically, integer S can be achieved either by decimating pairs of spin-1/2 particles (where a m=0 sector is accessible) or by considering a bosonic paramagnet, obtained by analyzing the unit cell of some crystal lattice, that sometimes has bosonic character; if this guy has spin-1 and its ground-state is singlet-like, there is a physical realization. I'd like people to add concrete examples of materials that behave like this in nature.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.