Re: paramagnetism

[Stan Dodds <dodds@RICE.EDU>]

I don't think the data exist because the 'right' system probably
doesn't exist. Consider the two families of atoms with unpaired spins,
rare earths and transition metals (3d).

For the rare earths, J is a good quantum number, so the simple theory
you would like to use is applicable. Unfortunately nature has not
supplied rare earths with J=1/2.

For the 3d transition metals, electrostatic effects from the
surrounding crystal structure ('crystal fields') are important. This
has the effect of partially or totally 'quenching' the orbital angular
momentum when L is not zero, so the free-atom J is not an accurate
description of the atom in the lattice. Instead, the effective
magnetic moment is determined by the spin S and the residual orbital
momentum.

The examples taken from Henry are well chosen for illustrative
purposes. Gd3+ with J=7/2 is simple, essentially a free atom in the
crystal. Fe3+ shows J=5/2, fairly exactly, because L=0 already. Cr3+
has S=3/2 and L=3 as a free atom, but susceptibility measurements
indicate a moment consistent with net spin 3/2, so it works OK. The
two ions with S=1/2, Ti3+ and Cu2+ have measured moments that deviate
noticeably (5-10%) from the spin-1/2 calculation, indicating
incomplete quenching.

The situation with the 4d or 5d elements may be more favorable,
although the increasing importance of spin-orbit coupling is a further
complication for them. Also, there is much less experimental data on
these systems.

For these reasons, I don't think you will find spin-1/2 data
comparable to that shown by Henry, although there may be other types
of systems, such as dilute organic free radicals, that would show
simple paramagnetism.

Hope this helps.

Stan

> Books on thermal physics and solid-state physics frequently show
> data (graphs of magnetization vs. B/T) on saturation of paramagnetic
> salts at low temperature.  In fact, these books all show the
> *same* data, from a 1952 paper by Henry, for systems with
> J = 3/2, 5/2, and 7/2.  Does there exist similar data for a
> J = 1/2 system (which is much easier to analyze mathematically)?
> If anyone out there can point me to a reference for such data,
> I'll be eternally grateful.  Thanks in advance,
>
> Dan Schroeder
> dschroeder@cc.weber.edu