Ferromagnetism with mobile spins How can electron spins in Iron at room temperature have ferromagnetic order even though they are travelling at very high speeds?
One could argue that spin and motion are completely uncorrelated and hence you can have superfast electrons that still somehow manage to orient their spins - but then how do you explain domains?
 A: In ferromagnetic materials there is an unpaired electron in the outermost orbital, giving an overall magnetic moment equal to one electron spin to the atom. In a ferromagnetic bulk crystal, these orbitals can overlap between neighbouring atoms which causes the spontaneous magnetisation through the exchange interaction. This interaction is incredibly short range, just a few Angstrom (approx nearest neighbour atoms only) and so cannot be entirely responsible for domain structure. The important aspect of the exchange interaction for domain structure is an effective restoring torque on the spins between neighbouring atoms. Imagine the spins as rungs on a rope-ladder, if you try to misalign one rung the ones next to it will move slightly and if you let go, the torque will restore alignment. (A similar torque exists for the anisotropy in the crystal).
The next important contribution for domains is how the overall magnetic order in the material aligns. The internal magnetisation $M$ must terminate at the surfaces of the material, so if we take the usual $B = \mu_0 [H+M]$, and take the divergence:
$\nabla\cdot B = \mu_0 [\nabla\cdot H + \nabla \cdot M] $
so:
$ \nabla \cdot H = -\nabla \cdot M$
All this means is that all magnetisation which terminates at the surface must produce a  stray field, $H$. In short, the production of the stray field corresponds to a cost in energy $\frac{1}{2\mu_0}\int H^2 dV$ which can be minimised by reducing the amount of $M$ which terminates at the surface. The consequence is that the minimum energy state for the magnetic order is certainly not for all the spins to align with one-another in most cases. This is why we see twists and turns in the magnetic order, 'Domain structure'.
So basically, the exchange interaction provides a method for spins to align with one another on the short scale and the minimisation of the stray field shapes the larger structure across whole domains. (Other contributions can come from external magnetic fields and magneto-crystalline anisotropy).
I may have gone off topic there but I hope it answers some part of your question :)
A: It's because the electrons in the conduction band are correlated, motion and spin are not uncorrelated since pauli principle is acting, if the spins are opposite the motion can be more "free", but if they point towards the same direction they can be closer (conterintuitevely) Exchange interaction
