# Circulating electrons causes a current

I read that circulating electrons causes a current ( at an atomique scale ) then that causes a magnetic dipole moment for each molecule. How can that create a general magnetic field which creates a magnetization current density J=rotM ( won't the orientation of the molecule's magnetic field be in total random directions?)

I'm not quite sure what you mean, but I think you're talking about atoms and molecules in a solid, especially a crystal, which is a solid where the atoms or molecules are stacked in a regular order. Now, even if the magnetic moments of each atom are oriented randomly at a certain time, over time each moment will pull on its neighbors and patterns will emerge. Think of them as a string of magnets. One would think they'd orient themselves so that every other magnet is pointing north, with the rest pointing south, like so:

N S N S N S ...
S N S N S N ...

in which case everything would cancel out and there would be no magnetic field. As I began answering your question, I realized I didn't remember why this wouldn't be true, so I looked it up on wikipedia:

According to classical electromagnetism, two nearby magnetic dipoles will tend to align in opposite directions (which would create an antiferromagnetic material). In a ferromagnet, however, they tend to align in the same direction because of the Pauli principle: two electrons with the same spin cannot also have the same "position", which effectively reduces the energy of their electrostatic interaction compared to electrons with opposite spin.

In other words, magnets tend to repel the most when you have them close together, but according to quantum mechanics two atoms with the same magnetic moments are unlikely to be close together, so on average there's less pressure on same-aligned dipole moments than oppositely-aligned moments.

That's my guess, anyway.

Yes, you're right. That's at the bottom of the reason for which there is no ferro or antiferromagnetism in classical mechanics at any finite temperature. Or paramagnetism, or diamagnetism for that matter. Only quantum mechanics can explain them. Read Feynman's lectures, vol II, chapter 34-6.