Permanent magnets - why spontaneous symmetry breaking? I am not a physicist. I'm curious about the cause of permanent magnetism in ferromagnetic materials. So far, I have formed the impression that a macroscopic net magnetic dipole moment is formed from the collective alignment of electron magnetic dipole moments (in suitable metals). But why do the electron spins align? My first instinct would be that such an ordered state forming spontaneously would seem inconsistent with the second law of thermodynamics. I have learned that below the Curie temperature, the spherical symmetry that one might expect of the magnetization direction is spontaneously broken, resulting in a magnetic anisotropy - a magnetic dipole moment. But I still don't understand why this spontaneous symmetry breaking occurs in the first place. Is there a way to explain this to a non-physicist?
 A: First I will write some general remarks about spontaneous appearance of orientation. After that I go to the question specifically.
Take the following demonstration:
Take a large plate, in the middle slightly lower than the perimeter, gradually sloping down.
Place small spheres randomly (ball bearing balls work quite will for that kind of demonstration).
Because of the (gentle) slope the spheres will bunch up in the center, but with very little structure in the arrangement. At the level of all spheres together there will be no recognizable orientation in the distribution.
Then apply a bit of shaking, giving the spheres just enough motion to allow them to slide relative to each other. You will then see the spheres gradually settle in single hexagonal arrangement of all the spheres, because that is the closest packing. The hexagonal arrangement does have a sense of orientation (modulo the 6-fold symmetry of hexagonal arrangement).
I regard that as an instance of spontaneous symmetry breaking. The initial state was full 360 symmetry; all around the circle there was no orientation standing out. Hexagonal arrangement narrows that down to a subset of 6 orientations.


As to magnetization:
I found an interesting bit of information in the following entry (part of a series) titled: Spontaneous magnetism/magnetization
The author mentions involvement of spin-spin coupling, a quantummechanical phenomenon. This spin-spin coupling is an interaction that goes beyond just the magnetic interaction.

For the case of magnetization: I'm not sure whether the circumstances for spontaneous symmetry breaking actually have opportunity to occur.
In geology there is the phenomenon of magnetism in rocks that  have originated from upwelling of magma where tectonic plates move apart. That is, when the magma has sufficient content of ferromagnetic elements, then as the rock cools down the structure becomes permanently magnetized, aligned with the Earth's magnetic field at the time of that material solidifying. So that has the Earth's magnetic field initiating the orientation.
In general, there will always be some presence of magnetic field, either from close by or far away. And if there is a pre-existing magnetic field then the alignment that occurs does not meet the formal criterion of being a spontaneous occurrance.
A: a macroscopic net magnetic dipole moment is formed from the collective alignment of electron magnetic dipole moments (in suitable metals). But why do the electron spins align?
The magnetic dipole is something that the electron has permanently. It is even a constant. If you put the connection with spin in the background for a short time, it becomes clear what happens in ferromagnetic materials.
Above the Curie temperature, the thermal motions of the subatomic particles destroy the self-organisation of the magnetic alignment of these particles. Below the Curie temperature, on the other hand, the mutual alignment of the magnetic dipoles prevails.
I have already pointed out several times in this forum that emphasising the electron as an electric charge and not also as a magnet should actually be outdated. The electron, like the proton and the antiparticles, are charges as well as dipoles to the same extent.
The consideration of the spin in ferro- and other magnetic alignments is not purposeful. The consideration of magnetic dipoles is sufficient and purposeful.
A: Your questions is not at all obvious. A similar question was made to Richard Feymann. Here it is his answer: https://www.bing.com/videos/search?q=richard+feynmann+magnetism&docid=608050619608737724&mid=4BE8AC651C02CC66FEDD4BE8AC651C02CC66FEDD&view=detail&FORM=VIRE
First, electrons have an spin moment, it is a quantum quantity, but it could explained classically as if the electron has an intrisic orbital momentum. This breaks spherical symmetry. The spin can point up or down, i.e., classically means that the sense of motion of the spin is Clock wise or counter clock wise. Electrons are the basis of atom bonding and interatomic interaction. Magnetic field are of much lower magnitude than electrical fields. So the reason that you can find electrons pointing in the same direction has to do with the way the coulomb interaction between electrons is configured within the solid  where electrons are. It must be added the fact that, in quantum mechanics, there is no way to distinguish between particles since there are no trayectories as in classical mechanics. This gives rise to different statistics for the electrons, Fermi statistics. But also to a different resulting interaction: the exchange interaction. Then, if the system has an imbalance in the density of spin up and down due to holes in the related valence bands, the system can be magnetic due to the way the electrons colectively are coupled by the coulomb interaction and the excahnge interaction. Solid state books gives an example of that using only two electrons. The system could give rise to a singlet state With zero net spin, or a triplet spin with 1 net spin. The triplet state is magnetic. This is not the only way spins can be ordered. Insulators and metallic materials can be magnetic. The most ancient known magnetic material is ferrite, Fe3O4, which is actually a very complicated to explain magnetic material which have different magnetic phases at different temperatures, No wonderr tehn, that Magnetism in materials is so important subject due to the rich varieties of kinds of magnetic behaviors can be found in solids
