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Why can't we answer this simple question? Where does the magnetic field of a permanent magnet come from? What is different about a magnetizable atom that allows it? Why is it perpetual? Or is it recurrent? Charged particles in motion into wave-flux, then the wave-flux back to charged particles in motion? Primal energy still not explained. To the back side of Mars and physics still cannot explain the basis of a child's toy. tecvia

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    $\begingroup$ Where did you read that physics can't explain this? $\endgroup$
    – Ruslan
    Aug 9, 2013 at 23:38

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Permanent magnets are made of a type of material known as ferromagnets.

Ferromagnets are magnetic because the individual electrons which are tiny magnets – they have a "magnetic moment", we say – tend to orient themselves in the same direction which is why the strength of the electrons adds up. For other materials, it tends to cancel.

The North-South direction of the magnet "hiding" inside an electron is aligned with the electron spin, its intrinsic rotation around the axis. The magnitude of the magnetic moment and the magnitude of the spin are determined and constant – characteristic properties of the electron. Only the direction is variable and quantum mechanics implies that once an axis is chosen, the spin (and magnetic moment) may only be "up" or "down" (clockwise or counter-clockwise rotation but nothing in between).

Ferromagnets align the electron spins in the same way because by the Pauli exclusion principle, the same orientation of the spin of two electrons implies that their other properties such as positions have to be different. The identity of the two spins automatically implies that the the "wave function" encoding the probability distribution of the electrons' positions has to be antisymmetric. When it's antisymmetric, it's very small for nearly coincident positions of the electrons (zero for equal positions) which is why the electrons are unlikely to be close to each other. Because of the Coulomb electric repulsion, this "protection against small distance" reduces the total energy by something called "the exchange energy" – the explanation of what it means is this whole paragraph and more – and that's why the same orientation of the electron spins is preferred.

If there were no spin, there would be no ferromagnets. Permanent magnets therefore demonstrate at least two properties of Nature that would be prohibited if it were governed by classical physics: internal angular momentum of point-like particles; and their complete indistinguishability. The classical or high school intuition is enough to imagine a ferromagnet as a pile of many tiny magnets (the electrons) oriented in the same direction but it is not really enough to honestly understand why the electrons "like" that configuration. Quantum mechanics is needed for that.

(There are also permanent magnets that are not of a ferromagnetic, but a ferrimagnetic material, in which the strength of the electrons does not fully add up, but cancels in part. Examples are ferrite magnets and some minerals)

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    $\begingroup$ This is a great answer at the level at which the OP posed the question. The Bohr–van Leeuwen theorem proves more formally that permanent magnetism can't be a classical phenomenon: en.wikipedia.org/wiki/Bohr%E2%80%93van_Leeuwen_theorem $\endgroup$
    – user4552
    Aug 9, 2013 at 16:26

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