I've read that ferromagnetism is a quantum mechanical phenomenon and

[sci-guy]

I've read that ferromagnetism is a quantum mechanical phenomenon and have some questions:

1) Is it an example of quantum coherence, like laser light, superconductivity, etc.?

2) Since it depends on electron alignment amongst the iron atoms of the magnet, and since electrons have both particle and wave properties, is it equally correct to speak of ferromagnetism as resulting from a "structural alignment of electrons" or some kind of "wave energy alignment" (or "wave coherence," if it's an example of quantum coherence). Or is there some more precise way to describe it?

 

[shawl]

Ferromagnetism is a quantum mechanical phenomenon because it is originated from the asymmetry of wave function exchanging between two fermions, i.e. electrons, which can not be understood in the classical mechanism.

 

[sci-guy]

Thanks, but I'm not sure that answers my main question:

Is it an example of the specific quantum principle of "coherence," in which the macroscopic ferromagnetism can be defined by a single wave function?

 

[shawl]

Ferromagnetism is caused by the wave properties of electrons. There is nothing can be related to the coherence in the origination of Ferromagnetism.

But we do study the spin dynamics of a chain of magnetic lattice by the "spin wave theory".

Please link to the following URL, you may get what you want

https://jilawww.colorado.edu/pubs/thesis/lewandowski/ch5.pdf

and

http://en.wikipedia.org/wiki/Spin_wave

 

[DrDu]

Thanks, but I'm not sure that answers my main question:

Is it an example of the specific quantum principle of "coherence," in which the macroscopic ferromagnetism can be defined by a single wave function?

Of course there is coherence. The orientation of a spin at site i is correlated with the orientation at any other site j, how far away it may be.
These long range correlations are thought to be the most distinctive characteristic of ordered phases like magnetism, superconductivity, crystals etc.
And in fact, P W Anderson found a description of superconductors which closely resembles the description of a ferromagnet in which the Cooper pairs are described by spin operators.

 

[sci-guy]

Thanks for the spin wave reference; I didn't know about that. But unless I missed something, there's some disagreement on the implication:

There is nothing can be related to the coherence in the origination of Ferromagnetism.

Of course there is coherence.

From what little I could comprehend about spin waves, it seems to me that they DO indicate quantum coherence, in that the ferromagnetism depends on the coherent (i.e. in-phase) spin waves of the electrons. This coherence is like other examples (laser light, superconductivity, etc.) in that the quantum state of all the electrons can be defined by a single wave function.

Sorry if I've butchered this; I'm no scientist -- just trying to understand it so I can explain basic conccepts to laypeople.

 

[sci-guy]

So, is ferromagnetism quantum coherence or not?

 

[shawl]

Of course there is coherence. The orientation of a spin at site i is correlated with the orientation at any other site j, how far away it may be.
These long range correlations are thought to be the most distinctive characteristic of ordered phases like magnetism, superconductivity, crystals etc.

What you said is called " correlation " and the system you mentioned are strong correlation system. Where tolds us the phase of spin A is correlated to spin B, which is different from the "coherence".

He is asking whether or not the ferromagnetism comes from the coherence of electrons.

It will be great to look for the answer in books like " magnetism ".

We usually say ferromagnetism comes from the quantum mechanism because it is due to the asymmetry exchanging of electron wavefunctions that is hard to explained by classical physics.
But it has not yet been related to the concept of coherence. At least not in the explanation of ferromagnetism.

 

[shawl]

In understanding the Ferromagnetism theory, you'd better look in Heisenberg theory.
Heisenberg is the first man using the asymmetry exchanging of electron wavefunction to explain successfully the origination of magnetism (including Ferro- and Antiferro- magnetism).

 

[DrDu]

What you said is called " correlation " and the system you mentioned are strong correlation system. Where tolds us the phase of spin A is correlated to spin B, which is different from the "coherence".

The ground state of a ferromagnet of spins 1/2 with orientation of the magnetization given by the polar angles theta and phi can be described as a coherent state $$\Psi=\prod_i (\cos(\theta)+\sin(\theta) e^{i\phi}\sigma_+) |0>$$ where i runs over all sites and |0> is the state with all spins pointing in z-direction. This is a coherent superposition of eigenstates of the total S_z operator.

 

[sci-guy]

I'm still not clear about my second question, which is the relation between wave coherence and particle/structural coherence. Must electrons be "physically aligned" (if that's a valid expression) in order to have the same spin state?

 

[sci-guy]

An analogy might be the Earth (analogous here to an electron) which, by virtue of its "spin" (axial rotation), has its magnetic field oriented in a particular direction. We can envision many Earth's grouped together, like electrons in a lump of iron. So long as the Earth's are randomly aligned (i.e. their poles face random directions), their magnetic fields cancel and there is no "macroscopic" magnetic effect. But if all Earth's are aligned according to the same north-south pole axis, spinning the same direction, their magnetic fields constructively interfere with each other, adding up to a macroscopic magnetic field. Therefore, it's the physical alignment of the material Earth's that is responsible for the macroscopic magnetism.

Is this essentially how electrons generate macroscopic magnetism in ferromagnets? That seems to be what's suggested by this:

http://en.wikipedia.org/wiki/Ferromagnetism#Origin_of_magnetism
http://en.wikipedia.org/wiki/Ferromagnetism#Magnetic_domains

I just want to be sure that I'm not misunderstanding what's meant by "alignment" -- I'm sure it has meaning on different levels (including alignment, or coherence, of energy or wave states), but does it also imply a physical alignment?

 

[DrDu]

Sci-guy, yes, that picture of the aligned microscopic momenta is correct.