Yes. It is phenomenological. It doesn't matter whether you describe the phenomenon as magnetization or as bound currents. It is just two different equivalent phenomenological descriptions. Sometimes one or the other approach will simplify a specific problem, but other than that they fundamentally share the same limitations.

The students need to start somewhere to learn the material If they learned the part of it presented in the article, I think more of them would be prepared to study the finer details of things like the exchange effect. There was no attempt here to create any kind of sensationalism. It was actually suggested by Greg B. that I change my original title (which was very undramatic), because it didn't do much to attract the reader's attention.

No, they are not equivalent. One simply describes the magnetic field generated. The other explains why a material becomes a ferromagnet, paramagnet, antiferromagnet, etc.

I think you are talking about Maxwell's equations vs QED.

I am talking about Maxwell's equations formulated in terms of magnetization or in terms of bound currents. Maxwell's equations do not explain magnetization either way, it is phenomenological either way.

I don't know why this is rather difficult to understand. Maybe I'll try it this way:

Quantum magnetism explains why such-and-such a material is a ferromagnet. Once it has become a ferromagnet, it then produces a magnetic field. This magnetic field can then be modeled as being produced by some "surface currents".

Do we have a problem with the statements I made above?

If yes, what is the problem?

If no, then surface currents cannot explain the existence of a permanent magnet/ferromagnet. It can describe the FIELD generated by the magnet, but not how it became a ferromagnet.

If the title of this Insight article reads "Magnetic Fields of Permanent Magnets Described by Magnetic Surface Currents", I would have zero issues with it.

Without the surface currents, magnetized materials would produce rather small magnetic fields, and in addition, there wouldn't be a significant magnetic field inside the material to maintain the magnetization. e.g. Uniformly magnetized discs with the direction of magnetization perpendicular to the face of the disc produce only weak magnetic fields because there are minimal surface currents with this geometry. ## \\ ## Without any surface currents, the exchange interaction, which is energetically much stronger, would still dominate, but by itself, would not explain why it takes such a tremendously strong reverse solenoid current to reverse the direction of magnetization in a permanent magnet. This feature is explained simply by the surface currents. ## \\ ## @ZapperZ Your suggestion for an alternate title, to change the word from "explained" to "described" is perhaps a good one. ## \\ ## The type of discussion I'm still hoping for though is a comparison of the calculations of magnetic "pole" model with those of the "surface current." Even J.D. Jackson's Classical Electrodynamics textbook, which emphasizes the "pole" model, treats ## H ##, (including the ## H ## from the "poles"), erroneously as a second type of magnetic field (besides what he calls the magnetic induction ## B ##). A thorough study of the surface current calculations shows that the ## H ## from the poles in the material is simply a geometric correction factor for geometries other than the cylinder of infinite length. (Mathematically, J.D. Jackson's treatment of ## H ## as a second type of magnetic field works for the purposes of computation, but his ## H ## is actually unphysical. ## H ## is simply a useful mathematical construction that is used to help compute the magnetic field ## B ##. ) ## \\ ## Meanwhile, the article I wrote is intended to help give the student a solid introduction to some E&M fundamentals, rather than trying to explain any details of the exchange interaction.

I would like to post a "link" to a recent thread that gives some additional insight into magnetism phenomena. It is an experiment that involves the Curie temperature, and they really have an interesting experiment. In addition, you might even find of interest the additional experiment that I did with a boy scout compass and a cylindrical magnet that is mentioned near the end of the thread. (see post #21 ) https://www.physicsforums.com/threa...perature-relationship-in-ferromagnets.923380/

I would like to post one additional comment about how the above model with the equation ## M=\chi' B ## is very much an oversimplification of things. This paper was a result of this author's attempts to tie together the "pole model" of magnetism with the "surface current" model. That part was mathematically 100% successful, and showed the two give identical results, with the surface current model providing a more sound explanation for the magnetic fields ## B ## that are generated by a magnetization ## M ##. The assumption of a functional dependence of ## M=M(B) ## is much better at explaining some of the aspects of the permanent magnet than any equation of the form ## M=M(H) ##. This "functional" dependence ## M=M(B) ## is very much unexact though because of the exchange effect. What the magnetization ## M ## decides to do at position ## \vec{r} ## is far too dependent on the magnetization at ## \vec{r}+\Delta \vec{r} ## to be able to assume that ## M ## at position ## \vec{r} ## is responding only to ## B ## at ## \vec{r} ## and nothing else. Any mathematical treatment of this is, however, well beyond the scope of this paper. A quantum mechanical formalism that takes this into account might also be able to explain why some materials make permanent magnets, while others have their magnetization ## M ## return to near zero upon removal of the applied field ## H ##. ## \\ ## An additional comment or two: A Weiss Mean Field Model that uses ## B ## as the applied field (where ## B ## includes the fields from the surface currents) rather than simply just ## H ##, (from the applied field from the current in a solenoid), would be an improvement to the Mean Field discussion found in Reif's Statistical and Thermal Physics textbook. And it should be mentioned, one simple result that the exchange effect has, (where the electron spin is affected not only by the local magnetic field but also by the spin of its neighbors), is to get the spins to cluster so that they tend to respond as a much larger unit, so that ferromagnetic materials have much higher Curie temperatures than what would result from electron spins that were independent of each other. Meanwhile, solutions where the magnetization ## M ## and the magnetic field ## B ## are uniform are rather straightforward. What gets very complex are solutions where the macroscopic ## M ## and ## B ## may be uniform, and even possibly be zero, but where the microscopic fields vary throughout the material. This latter case is well beyond the scope of what I have attempted to treat in the above paper, but is apparently necessary to explain what occurs in the case of ferromagnetic materials where permanent magnets do not result.

I'd say, it's just a mathematical identity. Instead of the magnetization of the permanent magnet you can as well with the magnetization-current density,
$$\vec{j}_{\text{mag}}=2c \vec{\nabla} \times \vec{M},$$
where ##\vec{M}## is the magnetization density of the material.

In classical electrodynamics, I don't see how to make a difference between magnetization and this current density. Of course, physically ferromagnetism is not due to currents but due to the spin orientations (meaning also an orientation of their elementary magnetic moments) of electrons. From the very wording of this sentence it becomes clear that ferromagnetism cannot be understood microscopically within classical electrodynamics, but you need quantum theory. You also need the fermionic nature of the electrons and the related phenomenon of "exchange forces" (which of course is a somewhat unfortunate name, but that's what's stuck in the slang of quantum physicists).

An interesting paper on the state of affairs of ferromagnetism was published around 2011. https://arxiv.org/pdf/1106.3795.pdf It's interesting that someone (Dr. Yuri Mnyukh) who performed numerous experiments on ferromagnetic properties including on the ferromagnetic to paramagnetic transition at the Curie temperature in various materials seemed rather dissatisfied with what was the present understanding of ferromagnetism at that time.