Permanent Magnets Described by Magnetic Surface Currents - Comments

[Charles Link]

Charles Link submitted a new PF Insights post

Permanent Magnets Explained by Magnetic Surface Currents

Continue reading the Original PF Insights Post.

 

[Greg Bernhardt]

Hard work paid off, nice second Insight Charles!

 

[Charles Link]

The explanation given of magnetic surface currents for computing the magnetic fields is also mathematically in complete agreement with the "pole method" that many of the older generation use to compute the magnetic field. This author has done calculations to show the mathematical equivalence of the two methods. The magnetic surface current method provides a much better understanding of the underlying physics while the "pole method", although getting the precisely correct answer for the magnetic field $B$, can easily give incorrect interpretations to what the $H$ from the poles represents, particularly in the material. For a more complete discussion of the pole method, I refer the reader to some calculations that I did connecting the pole method to the magnetic surface current method: https://www.overleaf.com/read/kdhnbkpypxfk This "Overleaf" paper was my very first attempt at Latex, so that some of the typing may appear a little clumsy, but hopefully you find it readable.

 

[ZapperZ]

There is something not quite right with this.

Let's say that I measure some magnetic field geometry. Without knowing the source, and simply looking at the geometry and the boundary conditions, I can come up with a particular geometry of the current source. This is what the article is doing, i.e. deducing the current source based on the fact that there is some configuration of a magnetic field.

But is there really a surface current that is responsible for the magnetic field of a ferromagnet? Or is this simply a model that is made to match the magnetic field geometry?

When I move a magnet into a coil, I get create a magnetic field that opposes the change in the magnetic field experienced by the coil. This opposing magnetic field induces a current in the coil. This is not a "model" current. It is real. If you connect a bulb to the circuit, it'll light up.

So is this surface current real, or is it simply a model that matches the field geometry? If I connect 2 ends a wire to various parts of the surface of the magnet, will I measure a current?

The picture of small, closed current loops to model atomic magnetic moment is highly outdated and not very accurate. Maybe to the first approximation, it might be useful, but that is as far as it can go. There are no current loops, and as far as I know, there are no ferromagnetic surface currents. There are modeled Amperian currents to emulate the magnetic field produced by the magnet, but this isn't real.

The other problem with this scenario is the difference between ferromagnets and paramagnets. If all we care about is this surface currrents, then why, in some material, the magnetization dies off when the external field goes away, while in permanent magnets, they stay aligned. This is one of the topics in quantum magnetism, where, among others, the Heisenberg coupling between nearest neighbor, next-nearest neighbor, next-next-nearest neighbor, etc... magnetic moments comes into play. The determination of the magnetic moment configuration of the lowest energy state is significant to result whether something is a paramagnet, ferromagnet, antiferromagnet, etc. This is the ORIGIN of permanent magnet, not the existence of "surface currents".

Zz.

 

[Charles Link]

There is something not quite right with this.

Let's say that I measure some magnetic field geometry. Without knowing the source, and simply looking at the geometry and the boundary conditions, I can come up with a particular geometry of the current source. This is what the article is doing, i.e. deducing the current source based on the fact that there is some configuration of a magnetic field.

But is there really a surface current that is responsible for the magnetic field of a ferromagnet? Or is this simply a model that is made to match the magnetic field geometry?

When I move a magnet into a coil, I get create a magnetic field that opposes the change in the magnetic field experienced by the coil. This opposing magnetic field induces a current in the coil. This is not a "model" current. It is real. If you connect a bulb to the circuit, it'll light up.

So is this surface current real, or is it simply a model that matches the field geometry? If I connect 2 ends a wire to various parts of the surface of the magnet, will I measure a current?

The picture of small, closed current loops to model atomic magnetic moment is highly outdated and not very accurate. Maybe to the first approximation, it might be useful, but that is as far as it can go. There are no current loops, and as far as I know, there are no ferromagnetic surface currents. There are modeled Amperian currents to emulate the magnetic field produced by the magnet, but this isn't real.

The other problem with this scenario is the difference between ferromagnets and paramagnets. If all we care about is this surface currrents, then why, in some material, the magnetization dies off when the external field goes away, while in permanent magnets, they stay aligned. This is one of the topics in quantum magnetism, where, among others, the Heisenberg coupling between nearest neighbor, next-nearest neighbor, next-next-nearest neighbor, etc... magnetic moments comes into play. The determination of the magnetic moment configuration of the lowest energy state is significant to result whether something is a paramagnet, ferromagnet, antiferromagnet, etc. This is the ORIGIN of permanent magnet, not the existence of "surface currents".

Zz.

I urge you to read through the derivation that Griffiths does for the magnetic potential $A$. He begins with the potential for a single magnetic dipole and then computes the potential $A$ for an arbitrary distribution of magnetic dipoles. It is a rather unique and roundabout proof that gets the result that the potential $A$ consists of two terms: Magnetic currents from $\nabla \times M=J_m/c$ and magnetic surface currents $K_m=c M\ \times \hat{n}$. He does it using SI units, and doesn't really emphasize the very important result. $\\$ In addition, the exchange effect plays an important role in the permanent magnet=otherwise the permanent magnet would only exist at very low temperatures=i.e. near the temperature of liquid helium. The exchange effect causes the spins to cluster, thereby making the unit much more thsan a single electron spin, and causing the Curie temperatures to be of the order of T=1000 degrees Centigrade.

 

[ZapperZ]

I urge you to read through the derivation that Griffiths does for the magnetic potential $A$. He begins with the potential for a single magnetic dipole and then computes the potential $A$ for an arbitrary distribution of magnetic dipoles. It is a rather unique and roundabout proof that gets the result that the potential $A$ consists of two terms: Magnetic currents from $\nabla \times M=J_m/c$ and magnetic surface currents $K_m=c M\ \times \hat{n}$. He does it using SI units, and doesn't really emphasize the very important result.

I have done something similar. This is an exercise the same way I ask my students to compute the centripetal force that is required to keep an electron in "orbit" around a nucleus. But none of this has any bearing on reality.

You could have easily showed me an experiment that actually measured this surface current, and I'll be satisfied with that. But my claim here is that this is nothing more than a model-equivalent, that IF this was modeled by currents, then it will have such-and-such a configuration and value. The magnetic field of permanent magnets is not caused by surface currents.

Zz.

 

[Charles Link]

I have done something similar. This is an exercise the same way I ask my students to compute the centripetal force that is required to keep an electron in "orbit" around a nucleus. But none of this has any bearing on reality.

You could have easily showed me an experiment that actually measured this surface current, and I'll be satisfied with that. But my claim here is that this is nothing more than a model-equivalent, that IF this was modeled by currents, then it will have such-and-such a configuration and value. The magnetic field of permanent magnets is not caused by surface currents.

Zz.

I have already gotten feedback from a well-established E&M professor at the University of Illinois at Urbana-Champaign. (This dates back a year or two already). Please don't be too quick to discard the calculations. Meanwhile, because the surface currents are atomic in nature, they don't experience any ohmic losses. It is impossible to measure them with an ohm meter. There is no actual electrical charge transport in these magnetic surface currents.

 

[ZapperZ]

I have already gotten feedback from a well-established E&M professor at the University of Illinois Champaign-Urbana. Please don't be too quick to discard the calculations.

You don't seem to understand the problem.

There's nothing wrong with the calculation. If you want to model the magnetic field as being generated by a current, then fine! This was never in dispute!

But there is an implicit idea that this surface current is REAL for a permanent magnet. I question this, and I've asked for evidence to support that argument, rather than simply regurgitating the model. An electron has a magnetic moment. It has no "surface current". The requirement for the existence of a current to always produce a magnetic field is not valid.

Zz.

 

[Charles Link]

You don't seem to understand the problem.

There's nothing wrong with the calculation. If you want to model the magnetic field as being generated by a current, then fine! This was never in dispute!

But there is an implicit idea that this surface current is REAL for a permanent magnet. I question this, and I've asked for evidence to support that argument, rather than simply regurgitating the model. An electron has a magnetic moment. It has no "surface current". The requirement for the existence of a current to always produce a magnetic field is not valid.

Zz.

I've given as much rebuttal as I can for the moment. All I can do is ask for others to carefully look over the calculations and provide their opinions.

 

[ZapperZ]

I've given as much rebuttal as I can for the moment. All I can do is ask for others to carefully look over the calculations and provide their opinions.

And I want others to think "Wait, if there's a surface current, then there should be a surface resistance (permanent magnets are not superconductors), and since there's no net potential to maintain this current, this current will decay and die off very quickly. And that means that if the origin of this magnetic field is this surface current, then the magnetic field of a permanent magnet should die off in seconds!

Zz.

 

[Charles Link]

And I want others to think "Wait, if there's a surface current, then there should be a surface resistance (permanent magnets are not superconductors), and since there's no net potential to maintain this current, this current will decay and die off very quickly. And that means that if the origin of this magnetic field is this surface current, then the magnetic field of a permanent magnet should die off in seconds!

Zz.

The origin of these magnetic surface currents is the magnetic moment at the atomic level. These states will persist without experiencing any ohmic losses. This is even the case with the plastic lamination that is used to block the Faraday currents in the ac transformer. The plastic laminations do not block the magnetic surface currents, because there is no actual electrical charge transport. The magnetic field occurs in the transformer from the surface currents, and meanwhile the "eddy" currents are successfully blocked. $\\$ Is there actually an electrical current at the surface? You may be correct in that there perhaps really isn't because there is no electrical charge transport, but assuming the existence of the surface current gives precisely accurate results for all magnetic field computations.

 

[ZapperZ]

The origin of these magnetic surface currents is the magnetic moment at the atomic level. These states will persist without experiencing any ohmic losses. This is even the case with the plastic lamination that is used to block the Faraday currents in the ac transformer. The plastic laminations do not block the magnetic surface currents, because there is no actual electrical charge transport. The magnetic field occurs in the transformer from the surface currents, and meanwhile the "eddy" currents are successfully blocked.

And this is what I meant as it being simply a MODELED current. Haven't I said that there really isn't an actual, real surface current?

I can solve an electrostatic problem of a charge above a conductor plane by using an image charge. Everything about it is accurate. But is there really an image charge? No, there isn't! It is there simply to MODEL the charge distribution on the surface of the conductor. This charge distribution is real. The image charge isn't.

Your surface current can be used to model the magnetic field produced by the magnet. This is NOT is dispute. However, this surface current isn't real, similar to the image charge. It doesn't explain the origin of ferromagnetism. That is my point of contention in your article.

Zz.

 

[Charles Link]

And this is what I meant as it being simply a MODELED current. Haven't I said that there really isn't an actual, real surface current?

I can solve an electrostatic problem of a charge above a conductor plane by using an image charge. Everything about it is accurate. But is there really an image charge? No, there isn't! It is there simply to MODEL the charge distribution on the surface of the conductor. This charge distribution is real. The image charge isn't.

Your surface current can be used to model the magnetic field produced by the magnet. This is NOT is dispute. However, this surface current isn't real, similar to the image charge. It doesn't explain the origin of ferromagnetism. That is my point of contention in your article. Although there may be some additional "local" effects, the magnetic field $B$ used in this equation is basically that of the field from the magnetic surface currents.

Zz.

I didn't include the exchange effect, because that is an additional topic that is very necessary to explain the high Curie temperatures, but isn't needed to explain the magnetic fields that are produced by permanent magnets. To first order, the exchange effect causes a coupling of adjacent spins to create clusters of spins (perhaps 100 or more) that all respond as a unit. Thereby, the $\frac{ \mu_s B}{kT_C}=1$ that gives an estimate of the Curie temperature will have a $\mu_s$ that is much more than a single electron spin. Although there may be some additional "local" effects, the magnetic field $B$ used in this calculation of the Curie temperature is basically that that is computed from the magnetic surface currents.

 

[Charles Link]

@jtbell Might we have your inputs on the topic? In some previous discussions of magnetic surface currents (about a year ago), you were very much a proponent of the concept, where you described in detail the form of the derivation that Griffiths uses in his text.

 

[Dale]

But is there really a surface current that is responsible for the magnetic field of a ferromagnet? Or is this simply a model that is made to match the magnetic field geometry?

In general the goal of science is to provide models that work, and asking "is there really ..." is just a philosophical exercise. If your phisophocal preference is to treat it as just a model and not real then that is fine, it is your choice. You are free to think of it merely as a computational aid and others are free to consider it to be real.

if there's a surface current, then there should be a surface resistance

The J in Ohm's law is the free current. The bound current idea doesn't predict a surface resistance, so its absence isn't contradictory evidence.

 

[vanhees71]

I like the mathematics displayed in this Insights article very much. However one should indeed emphasize that the surface currents are mathematical equivalents to mimic the influence of magnetization of the material in terms of the usual local Maxwell equations, as stressed by @ZapperZ.

 

[fluidistic]

Note that there's an ongoing discussion of this in reddit : https://www.reddit.com/r/Physics/comments/5obsn0/permanent_magnets_explained_by_magnetic_surface/.

 

[Charles Link]

I like the mathematics displayed in this Insights article very much. However one should indeed emphasize that the surface currents are mathematical equivalents to mimic the influence of magnetization of the material in terms of the usual local Maxwell equations, as stressed by @ZapperZ.

The magnetic surface currents are what results from Maxwell's equations, and the result is that the magnetic field that occurs in most magnetic solids is basically from non-local causes. (i.e. from surface currents). If you look at the equation $B=H+4 \pi M$ as presented by the pole method where $H$ includes contributions from the poles (the long cylinder geometry essentially has no poles), you could easily conclude that the magnetic field $B$ is caused by a local magnetization $M$. Calculations with the magnetic surface currents shows that the magnetic field is instead caused by the non-local surface currents. $\\$ For a thin disc shape, the surface currents are minimal and the magnetic field from such a shape is predicted to be rather weak. At least in one set of flat "refrigerator sticker" type magnets that I have, I found by experiment that they actually contain thin rows, spaced about 1/8" apart of alternating + and - magnetization. $\\$ My generation was actually taught the magnetic pole method (1975-1980), and the equivalent magnetic surface current was presented almost qualitatively as an alternative explanation. It wasn't until I did some rather detailed calculations to show/prove that both methods give the exact same result for the magnetic field $B$, that I realized that the surface current theory is a far better approach. In the magnetic pole method that I was taught=(basically from the textbook by J.D. Jackson), there are two different kinds of magnetic fields= $B$ and $H$. In a spherical shaped permanent magnet, the $H$ from the poles points opposite the $M$ in the material. The detailed magnetic surface current theory calculations show that this $H$ in the material is not a magnetic field, but simply a (negative) correction term to the $B$ in the material. (The $H$ of the pole theory is basically a mathematical construction, and not a second type of magnetic field). For the uniformly magnetized sphere $H=-(1/3) 4 \pi M$ and $B=H+4 \pi M=+(2/3) 4 \pi M$ with the $B$ pointing in the direction of the magnetization $M$ in order to maintain it. It was very handwaving arguments that came from the pole method that said the $H$ (in the opposite direction to $M$ was maintaining the magnetization $M$. (They would use the $M$ vs. $H$ hysteresis curve as a reason for how this was possible.) The pole method actually gets the precisely correct answer for the magnetic field $B$, and is a very useful computational tool, but it can easily be misinterpreted. The $H$ contribution from the poles, particularly in the material, is not a second type of magnetic field. From what I learned from a E&M physics professor at the U of Illinois, the "pole" method has now become replaced by the magnetic surface current theory in the curriculum. A computation just using the magnetic surface currents gets the very same result that $B=+(2/3)4 \pi M$ for the magnetic field inside the uniformly magnetized sphere. $\\$ For those who may have studied the "pole" method, I'd be interested in your feedback on what you might think of the surface current method. In the "pole" method, magnetic poles with magnetic pole density $\rho_m$ where $-\nabla \cdot M=\rho_m$ are considered to be sources of $H$, analogous to the polarization charge density $\rho_p$ that arises from $-\nabla \cdot P=\rho_p$ as sources for the electric field $E$. The problem that arises here is the magnetic "poles" are rather fictitious and there is no moving electrical charges/currents to generate the magnetic field in this model. The method does get the correct result for the magnetic field $B$ by employing the equation $B=H+4 \pi M$. It also can be a very good computational tool, where Legendre polynomial type solutions can be employed. (The calculations mentioned above, for the case of a uniformly magnetized sphere, are very difficult to do without Legendre methods, except for the point at the center of the sphere.) Anyway, I welcome your feedback.

 

[Charles Link]

It might be worth mentioning that there are basically two ways to compute the magnetic fields of magnetic materials: The "pole method" and the magnetic surface current method. $\\$ One advantage of the "pole " method is that the mathematics are a little simpler, and for a simple uniformly magnetized bar magnet, all that is needed to compute the magnetic field is to assign a "+" pole to one endface, and a "-" pole to the other, and the magnetic field $H$ from each outside the magnetic obeys the inverse square law. The poles have magnetic surface charge density equal to $\sigma_m=M \cdot \hat{n}$. Inside the magnet, the $H$ points opposite from the $M$, and the magnetic field $B=H+4 \pi M$ will be found to point in the same direction as the magnetization $M$. A second advantage of the "pole" method is that the Legendre polynomial method can be employed for what would otherwise be very difficult calculations.
$\\$ The magnetic surface current method doesn't recognize the existence of any magnetic poles, but instead has a magnetic surface current per unit length $K_m=c M \times \hat{n}$ on the outer surface of the cylindrical magnet, and the magnetic field $B$ is computed everywhere by using Biot-Savart's law. The Biot-Savart integrals used to compute the magnetic field $B$ are much more complex, and it is rather remarkable that these integrals get the exact same answer for the magnetic field $B$ as the simpler "pole" method in all cases. Meanwhile, the magnetic fields are explained in this method as arising from currents=in this case "bound" currents. The agreement between the two methods in the computed magnetic field $B$ is quite remarkable, and the surface current method offers the advantage of explaining the underlying physics=i.e. magnetic fields arise from electrical currents. It is for these reasons that this author finds the magnetic surface current method of calculating magnetic fields in the materials as one that would be quite useful to be emphasized in the physics undergraduate curriculum. $\\$@Dale and @vanhees71 I would enjoy any feedback you might have.

 

[Charles Link]

Note that there's an ongoing discussion of this in reddit : https://www.reddit.com/r/Physics/comments/5obsn0/permanent_magnets_explained_by_magnetic_surface/.

From what I can see of the "reddit" comments, they are a couple of levels below the level of physics that is done at Physics Forums. At Physics Forums, the other members don't always agree with you, but they normally put some careful thought and effort into their ideas and opinions. :) :) :)

 

[Charles Link]

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.

 

[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.

 

[ZapperZ]

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.

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.

 

[Charles Link]

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 $\vec{K}_m=\vec{M} \times \hat{n}/\mu_o$.)

 

[ZapperZ]

The article was not intended to explain everything about ferromagnetism.

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.

 

[Dale]

This model does not explain the origin of ferromagnetism. It can't. It is fundamentally a phenomenological model.

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.

 

[Charles Link]

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.

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.

 

[ZapperZ]

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.

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.

 

[Dale]

No, they are not equivalent.

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.

 

[ZapperZ]

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.

Zz.

 

[Charles Link]

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.

 

[Charles Link]

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/

 

[Charles Link]

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.

 

[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).

 

[Charles Link]

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.

 

[Charles Link]

It might be useful for those interested in the subject of permanent magnets and magnetic surface currents to look through this thread, and, in particular, posts 18 and 19 of this thread, for some additional detail on the subject: https://www.physicsforums.com/threa...-function-of-temperature.950326/#post-6020315

 

[Charles Link]

I'm just now adding this thread to the discussion for the sake of completeness, and see particularly post 73 by @vanhees71 , and even a good part of the later portion of the thread, where the merits and lack of merit of the magnetic surface current model are discussed in much detail, as well as the complete thread, where other details about magnetostatic and electromagnetic concepts are discussed :
https://www.physicsforums.com/threa...electric-induction.962632/page-4#post-6110191