# Itinerant electron systems

As far as I understand, in a primitive picture insulators are localized systems, and metals are itinerant electron systems.

What I do not get: I have, e.g., 3d itinerant magnets like:

Ni ([Ar] 4s2 3d8 or [Ar] 4s1 3d9 ),
Fe ([Ar] 4s2 3d6), and
Co ([Ar] 4s2 3d7).

Why does it make sense to speak about 3d electron shells, if the electrons are not localized to the atomic nucleus but they are itinerant, i.e., there are distributed over the whole crystal (it can be described by the probability function of the Bloch waves).

Confinement to atomic nucleus does not make sense to me, since (weak correlated) metals behave as a free electron gas.

• Okay, I like your answer. What I still do not get, is spin-orbit interaction for itinerant systems. Normally, in the rest frame of the electron, the atomic nucleus orbits around the electron producing a magnetic field to which couples the spin of the electron. However, for itinerant systems it is not true that the nucleus orbits the electron. But the spin-orbit equation $H_{LS}\propto \vec L \cdot \vec S \frac 1{r}\frac{dU}{dr}$ holds true, anyway. So what does $r$ mean for itinerant systems? Maybe, I should open a new question. – cerv21 Nov 27 '17 at 14:17