Re: Mechanism Underling Ferromagnetism

[Allen Miller <amiller@SUHEP.PHY.SYR.EDU>]

I'll make an attempt on Mark Sylvester's question as to the mechanism
underlying ferromagnetism. We need to see if it is favorable for the
electron spins of a selected pair of electrons to be aligned or
anti-aligned.

If we ignore Coulomb interactions experienced by the electrons, then
anti-alignmnet is favored. This can be seen by noting that in this case,
all of the energy of the electrons is kinetic. No energy is shared, so
single-electron states can describe the situation. Now, for each state of
"up" spin, there is a state of the same kinetic energy of "down" spin, So,
if the these states are the lowest-energy state available, the latter
state is also available, if the former is. The electron pair can be
"placed" in these two states. The net magnetic moment is zero.

So, from this argument, we will never get ferromagnetism, unless we take
into account the Coulomb repulsion between the two electrons. This
repulsion favors alignment. The outcome of alignment vs. anti-alignmnet
is decided by this competition, and the winner varies, when we compare one
elemental metal against another.

Why does Coulomb repulsion favor alignment? The reason is due to an
interplay between the PAuli Exclusion Principle and the Coulomb repulsion.

Due to the Exclusion Principle, parallel-spin electrons tend to stay
apart. This is the "Fermi hole". Otherwise, they would be occupying the
same state, violating the Pauli principle. By staying apart, their Coulomb
repulsion energy is diminished. This lowers the total energy of the
system. At low T, this produces the alignment.

At high T, one needs to maximize the entropy, as well as keep the energy
low. Electron spins that are aligned have a high degree of order, and
hence low entropy. So, beyond the Curie temperature, spin anti-alignment
is preferred and the ferromagnetism is lost.

Allen Miller,
Physics,
Syracuse University


On Sun, 6 Jun 1999, Mark Sylvester wrote:

> At 20:31 05/06/99 -0600, Ken Fox wrote:
> > There are new appliances in my neighbors kitchen with stainless front.
> > Very classy. However they no longer have refrigerator art gallery as
> > magnets do not stick. Is there no soft iron in stainless fronts of these
> > new appliances? I am confused and hope you can guide me.
>
> I rediscovered the fact that stainless steel is not ferromagnetic a few
> years ago when visiting Trieste synchrotron with a physics class. We were
> looking at the beam tube passing between the poles of very expensive
> magnets, when we were told that the tube was made of stainless steel
> ("inox" in Italian - a good word).
>
> What is the mechanism underlying ferromagnetism? I know about atomic
> dipoles and domains; what I'm asking is the nature of the thing that makes
> the difference between paramagnetic and ferromagnetic materials. This is
> presumably a large-scale QM manifestation, which, like superconductivity,
> occurs at sufficiently low temperature. What is it that makes it a lower
> energy state for a bunch of iron atoms to align their magnetic dipoles to
> form a domain?
>
> Mark
>
>
> Mark Sylvester
> United World College of the Adriatic
> 34013 Duino TS
> Italy.
> msylvest@spin.it
> tel: +39 040 3739 255