# Insights Permanent Magnets Described by Magnetic Surface Currents - Comments

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1. Jan 20, 2017

Additional comment on this subject: I am hoping some of the readers take the time to calculate and compare the results from the magnetic "pole" model with those from the magnetic "surface current" model. (e.g. for the cylindrical and spherical geometries for uniform magnetization.) The universities don't seem to be emphasizing this material very much these days in the curriculum because there is so much other material to learn, but I think the reader may find it quite interesting that these two very different methods give identical answers for the magnetic field $B$ both inside and outside of the material.

2. Feb 2, 2017

### Raxxer

This works well to explain the details to the lay-man, though I will admit that it seems logical that a permanent magnet could exist because of the positions of electrons in said ferromagnetic materials and their symmetries.

3. Feb 2, 2017

### ZapperZ

Staff Emeritus
Unfortunately, this is the exact reason why I had problems with this model. While you may use it to arrive at the magnetic field that a particular geometry of permanent magnet can generate, your conclusion that this somehow explains how "... a permanent magnet could exist because of the positions of electrons in said ferromagnetic materials and their symmetries...." is not correct. This model does not explain the origin of ferromagnetism. It can't. It is fundamentally a phenomenological model.

Zz.

4. Feb 2, 2017

The article was not intended to explain everything about ferromagnetism. A very important part of the ferromagnetism is the exchange interaction which couples adjacent spins to each other (to have it be very energetically favorable for them to be co-aligned.) The exchange interaction also is what makes ferromagnetism exist to very high temperatures (the Curie temperature), rather than occurring at only very low temperatures (as would be the case without the exchange interaction.) In any case, I think most physics students should find it worthwhile reading, and it is a topic that seems to have become deemphasized in the curriculum because there are so many other things to learn. It certainly should be an improvement over the magnetic "pole" model that is taught in many of the older E&M textbooks. $\\$ As stated previously in the discussions above, I have done lengthy calculations that show the precise equivalence of the magnetic field $B$ computed from the "pole" model and "surface current" model in all cases. If the student has extra time, I would even recommend they study the magnetic "pole" model as well, because it is mathematically simpler and also very useful for computations of the resulting magnetization and magnetic field using Legendre polynomial methods, such as a sphere of magnetic material in a uniform magnetic field. $\\$ For a very simple problem involving magnets, you can start with a cylinder of radius "a" and length $L$ with uniform magnetization $\vec{M}=M_o \hat{z}$ (pointing along the axis of the cylinder). The problem is to calculate the magnetic field $\vec{B}$ everywhere both inside and outside the cylindrical magnet using both the magnetic "pole" method and magnetic "surface current" method. If the student can do this, they have a good start at understanding the mechanics of computing the magnetic fields for problems involving magnetic materials. $\\$ (Using MKS units with $\vec{B}=\mu_o \vec{H}+\vec{M}$, this problem can even be quantified with $M_o=+.75$, a very typical value for a permanent magnet. For MKS units, the surface current per unit length $\vec{K}_m=\vec{M} \times \hat{n}/\mu_o$.)

Last edited: Feb 2, 2017
5. Feb 2, 2017

### ZapperZ

Staff Emeritus
And this, to me, is the SOURCE of the confusion, and the reason why I objected to the article. Not only did it not explain everything about ferromagnetism, I also claim that it explains nothing about ferromagnetism. It describes the FIELD generated by a ferromagnet, but it says nothing about ferromagnetism.

Ferromagnetism is the material, the formation of magnetic ordering within the material. The result of such ordering is the magnetic field. The title of the article is severely misleading when you claim "Permanent Magnets Explained by Magnetic Surface Currents". This was my objection from the very beginning - the use of that language! Claiming that "permanent magnets explained by magnetic surface currents" means that the origin of this permanent magnet is this surface currents. Even you have admitted that this isn't true, but yet, the misleading title, and the first sentence in the article made it sound as if this IS the "explanation" for a ferromagnet.

It isn't. It is a way to "explain" the FIELD generated by the ferromagnet. It doesn't explain how ferromagnetism happens. You may think this is a trivial and subtle point, but it isn't, as can already be seen by the misunderstanding made by previous "lay-man" post. If this was an internal note among physicists, I wouldn't have wasted my time because we all know the full story. But this is meant for students and also people who do not have enough understanding of physics to be aware of such things as quantum magnetism. They will walk away thinking that a permanent magnet becomes one due to all these surface currents. That is wagging the dog!

Zz.

6. Feb 2, 2017

### Staff: Mentor

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.

7. Feb 2, 2017

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.

8. Feb 2, 2017

### ZapperZ

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

Zz.

9. Feb 2, 2017

### Staff: Mentor

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.

10. Feb 2, 2017

### ZapperZ

Staff Emeritus
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.

Zz.

11. Feb 2, 2017

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.

Last edited: Feb 2, 2017
12. Sep 4, 2017

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/

13. Dec 23, 2017

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.

Last edited: Dec 23, 2017
14. Dec 25, 2017

### vanhees71

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).

15. Dec 25, 2017