Magnetic Weyl semimetals: Interplay of band topology and magnetism

Abstract

We review recent theoretical and experimental developments in magnetic Weyl semimetals, focusing on the electromagnetic responses emerging from the interplay of their electronic band topology and magnetism. We begin by introducing the fundamental topological properties of the electrons in Weyl semimetals, and provide an overview of the characteristic phenomena arising from their band topology, such as the anomalous Hall effect and chiral magnetic effect. The materials exhibiting the magnetic Weyl semimetal state, with ferromagnetic ordering, antiferromagnetic ordering, etc., are listed. The possible mechanisms for their magnetism are discussed in connection with the Weyl electrons. Non-uniform magnetic textures and magnetization dynamics are expected to exhibit a topological interplay with the Weyl electrons, manifesting as spinmotive force and spin torques. We also review the magnetotransport phenomena such as domain wall magnetoresistance, studied by mesoscopic scale calculations. Finally, we mention the spin transport properties studied in magnetic Weyl semimetals. The topological nature of Weyl electrons reviewed here is important not only for fundamental physics, but also for the potential application to low-dissipative electronics and spintronics devices.

Figures (40)

• Figure 1: (Color-online) Schematic illustrations of the electronic band structures of (a) metal, (b) insulator, (c) semimetal, and (d) (ideal) Weyl semimetals. The orange dashed lines represent the Fermi level (chemical potential).
• Figure 2: (Color-online) The spin configurations in momentum space for the Weyl fermions with spin-momentum locking, described by the Hamiltonian in Eq. (\ref{['eqn:Weyl_sml']}). Panels (a) and (b) correspond to the Weyl fermions with the positive $(\eta = +)$ and negative $(\eta = -)$, respectively.
• Figure 3: (Color-online) The band structures of (a) the Dirac semimetal state and (b) magnetic Weyl semimetal state, calculated from the Wilson--Dirac model [Eq. (\ref{['eqn:HWD_k']})].
• Figure 4: (Color online) Schematic illustrations of the momentum-space configuration of Weyl points in Weyl semimetal states. Red and blue points correspond to the Weyl points with positive and negative chiralities, respectively. (a) The hypothetical Weyl semimetal state satisfying inversion symmetry but not time-reversal symmetry, which minimally supports a single pair of Weyl points. (b) The ferromagnetic Weyl semimetal Co3Sn2S2, whose 2 Weyl points out of 6 reside on the $k_x k_z$-plane. (c) The hypothetical Weyl semimetal state satisfying time-reversal symmetry but not inversion symmetry, which minimally supports two pairs of Weyl points. (d) The noncentrosymmetic Weyl semimetal TaAs, whose 8 Weyl points out of 24 reside on the $k_x k_y$-plane.
• Figure 5: (Color online) (a) Berry curvature distribution ${\bm b}_-(\boldsymbol{k})$ and (b) Chern number $\nu(k_z)$, calculated from the Wilson--Dirac model on lattice. The Weyl point with chirality $+(-)$ behaves as a sink (source) of the Berry curvature vector field in momentum space.