# Permanent magnet's magnetic field arises due to the magnetic dipole moment of the electrons inside the magnet?

THIS QUESTION IS NOT A DUPLICATE OF THIS: Real QM cause of magnetic dipole moment

Because that question asks about the cause of the magnetic dipole moment of an electron.

This question is asking about what causes the permanent magnet's fields to arise.

The two might be related (however even that is not trivial) but the cause of the two is different at the QM level and any answer to the other question will not answer this one.

Now here is a question where on of the answers state that the magnetic fields arise because of spin.

Magnetic field created by the electron spin

The magnetization of for example an iron magnet is almost completely due to the spin moment of the electrons. I have not checked OP's expression, but the field outside a magnet should be the integral over all those electrons.

And there is another question where the answer says that it is caused by the magnetic dipole moment of the electrons.

Does a magnetic field arise from a moving charge or from its spin, or both?

As with the electric dipole, a magnetic dipole of any sort will generate a magnetic field.

So one question says the magnetic field of a permanent magnet arises because of the intrinsic spin of the electrons inside the magnet.

The other one says the magnetic field of a permanent magnet arises because of the magnetic dipole moment of the electrons in the magnet.

I understand that the magnetic dipole moment and the spin of the electron are related.

But the two answers say different things, because the electron's spin is (though related) not the same as it's magnetic dipole moment.

My question is at the QM level and I am trying to find out whether the permanent magnet's fields arise because of

1. the electron's spin

2. the electron's magnetic dipole moment

Question:

1. Which one is right, does the magnetic field of the permanent magnet arise because of the electrons' spin or because of the electrons' magnetic dipole moment?
• It is not a duplicate. That is a question about the magnetic dipole moment, and what causes it. This one is about the cause of the M field, what makes it arise? – Árpád Szendrei Jul 13 '18 at 16:58
• To the extent that this question asks something different to your previous posts, you should edit this post to make that crystal clear. I would also strongly recommend dropping the formatting convention you're using - it makes it extremely hard to parse your questions. There is rather little need for a list-format ramble about what you've read and what you haven't, and the multiple quotes do very little to provide clarity. Cut to the chase of what you're asking from the get-go instead of rambling on and on for a mile before you actually state a question. – Emilio Pisanty Jul 13 '18 at 16:59
• Dear Emilio, yes I edited it. I hope it is clear that the question you linked is asking about the cause of the magnetic dipole moment of an electron. This new question is asking what causes the permanent magnet's magnetic field arise? The cause of one electron's magnetic dipole moment (it might be related somehow) is not the same as the cause of a permanent magnet's field to arise. – Árpád Szendrei Jul 13 '18 at 17:03
• I'm voting to reopen this but I should re-state it - this is an absolute trainwreck of a question, and it probably also deserves to be closed as Unclear What You're Asking while you fix its sprawling rambles. – Emilio Pisanty Jul 13 '18 at 17:30
• You already know that there is no magnetic dipole moment without spin, and vice versa. When somebody says that ferromagnetism is the result of the electron spins interacting in a crystal then he is always referring to the magnetic interaction between the electrons by having the dipoles aligned and not the conservation of angular momentum or some such. – hyportnex Jul 13 '18 at 20:49

hypertnex wrote

You already know that there is no magnetic dipole moment without spin, and vice versa. When somebody says that ferromagnetism is the result of the electron spins interacting in a crystal then he is always referring to the magnetic interaction between the electrons by having the dipoles aligned and not the conservation of angular momentum or some such.

The Bohr model about revolving electrons around the nucleus was changed to a model of smeared electrons in probability volumes around and even inside (with low probality) the nucleus. But the idea about angular momentum is alive and helpful for the description of the electron configurations in atoms and molecules.

The spin was found as it was clear that the description of an electron needs not three but four quantum numbers and the last number has two values only. Only two electrons in any atom could be in the same volume (probability volume, described by a Schrödinger and Dirac) and this behavior was described by spin. The only step you have to do is to acknowledge that the found nearly in the same time magnetic dipole moment of electrons is the reason why two electrons only forming pairs.

The intrinsic spin of subatomic particles has nothing to do with any rotation, this is consensus anywhere. BUT the description of the magnetic dipole moment until now is associated with the rotation of the electron and his electric charge. Strange, to describe the electron as point-like and without inner structure and in the same moment to refer to the magnetic field as the result of the rotation of its electric field.

Where this description comes from? Moving electrons inside a coil are the reason for the induction of a magnetic field. (Before and since Faraday it was found that an electric current induces a magnetic field in coils.) But not the rotation in circles is the deaper reason, but the acceleration which electrons undergo. Under this acceleration an alignment of the magnetic dipoles takes place and this induces the observable magnetic field.

As hypertnex said, intrinsic spin and magnetic dipol moment are related one by one. And I would add, that all the behavior of the electrons in atoms and molecules are describable with their magnetic moments.

Are you saying that the magnetic dipole moment is caused by the electron being around the nucleus (rotating)?

It’s not me who is saying this, it’s from classical electrodynamics:

From classical electrodynamics, a rotating electrically charged body creates a magnetic dipole with magnetic poles of equal magnitude but opposite polarity. This analogy holds as an electron indeed behaves like a tiny bar magnet. One consequence is that an external magnetic field exerts a torque on the electron magnetic moment depending on its orientation with respect to the field.(Electron magnetic moment on Wikipedia)

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Are you saying that the electrons, when accelerating inside a magnet, will align their magnetic dipoles? Is that alignment a certain direction relative to the acceleration?

Not inside magnets but inside a coiled wire (with its acceleration of the electrons due to their circular motion) the induction of a common magnetic field takes place. And under the influence of an external magnetic field the deflection of the moving electrons (movement in a spiral path which is an acceleration) happens. And yes, the alignment of the magnetic dipoles is unambiguous. Electrons and antiprotons get deflection in an external magnetic field in one direction, positrons and protons in the other.

What I do not understand, is in a permanent magnet, nothing is moving (electrons are not moving) and nothing is accelerating. What creates the permanent magnet's magnetic field...?

Some atoms and molecules obeying a stronger summarizing magnetic dipole moment (from the involved electrons and nucleus) as others. The chaotic vibrations of the atoms inside solids prevent the selfinduction of a macroscopic magnetic dipole, but for the atoms with stronger magnetic fields (some rear earth element for example) the selfinduction takes place by room temperature. With rising temperature permanent magnets get destroyed. With falling temperature (less chaotic vibrations) more and more elements could hold the magnetic dipole alignment of their subatomic particles.

• thank you. you say: "BUT the description of the magnetic dipole moment until now is associated with the rotation of the electron and his electric charge." Are you saying that the magnetic dipole moment is caused by the electron being around the nucleus (rotating)? – Árpád Szendrei Jul 14 '18 at 16:41
• And here you say: " But not the rotation in circles is the deaper reason, but the acceleration which electrons undergo. Under this acceleration an alignment of the magnetic dipoles takes place and this induces the observable magnetic field." Are you saying that the electrons, when accelerating inside a magnet, will align their magnetic dipoles? Is that alignment a certain direction relative to the acceleration? – Árpád Szendrei Jul 14 '18 at 16:41
• What I do not understand, is in a permanent magnet, nothing is moving (electrons are not moving) and nothing is accelerating. What creates the permanent magnet's magnetic field as per QM? – Árpád Szendrei Jul 14 '18 at 16:44
• @ÁrpádSzendrei In quantum mechanics, things do not have to be "moving" to have angular momentum. The electron wavefunction around an atom has an orbital angular momentum, even if the electron is not "moving" (whatever that means in terms of a wavefunction). – probably_someone Jul 14 '18 at 19:16
• @ probably_someone you are referreing to OAM. Not spin. we are walking about spin and magnetic dipole moment. I am asking whether the permanent magnet's magnetic field arises due to the acceleration of electrons in the permanent magnet? Or are yuu saying that the field arises because of the OAM of the electrons? – Árpád Szendrei Jul 14 '18 at 19:37