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.
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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)
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.