Left-handed Ferromagnet

The dynamics of the total magnetization in metallic ferromagnet is studied theoretically taking into account the relativistic spin-orbit interaction. It is found that its quantum dynamics is seriously influenced by the band crossings near the Fermi energy, and sometimes the direction of the precession can be reversed from what expected from the commutation relation $[S^{x},S^{y}]= i\hbar S^{z}$ ($h = 2\pi \hbar$: Planck constant), i.e., the left-handed ferromagnet can be realized.