Figure 1: Schematic band structure and Weyl fermion in ferromagnets.
From: Weyl fermions and spin dynamics of metallic ferromagnet SrRuO3
(a) The energy (ɛ) dispersions of up () and down () spin bands with the exchange splitting Jex. ɛF is the Fermi energy. The band crossings ɛn(k)=ɛm(k) occur when the overlap of the up and down spin bands are finite. In the presence of the spin–orbit interaction, which mixes the up and down spins, the band crossings turn into the anti-crossings with the gap opening (red curve). (b) Band structure near the Weyl point k0. The band dispersions with fixed kz are shown in the kx–ky plane. The gap closes at the Weyl point k=k0. (c) Distribution of the emergent magnetic field b(k) near a Weyl point. The flux penetrating the area S is given by the solid angle subtended by S, and the total flux is 2πη. Therefore, Weyl fermion acts as a monopole or anti-monopole of the emergent magnetic field depending on the chirality η=±1.
