I am reading a book on Skyrmions, and I am at the part where the interaction of skyrmions with electrons is discussed. The chapter speaks of Spin-Transfer Torque (STT) and makes the following statement about magnetic metals:

In magnetic metals, the outer-shell electrons of magnetic atoms participate in the formation of the localized moment $\mathbf{n}$, as well as acting as mobile carriers of the electric current. The two types of electrons (i.e., localized and itinerant) originating from the same atom are bound by the Hund’s coupling $$ -J_H \mathbf{n} \cdot \left( \psi^\dagger \mathbf{\sigma} \psi \right) $$

In the above, $\psi$ is the spinor field, given by $$\psi = (c_{\uparrow} \text{ } c_{\downarrow})^T$$ and $\mathbf{\sigma}$ is the vector of Pauli matrices. $J_H$ is a coupling constant. My questions are:

  1. How can there be both an electron which creates a localized moment while another acts as a mobile carrier in the same shell of the same atom of the material?
  2. How can one see that indeed the term referenced is the term that enforces Hund's rules? (I'm assuming this is what is meant by Hund's coupling)

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