Abstract
The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to. On the other hand, very little is known about semimetallic states emerging in two-dimensional magnetic materials, which present the foundation for both present and future information technology. Here, we demonstrate that including the magnetization direction into the topological analysis allows for a natural classification of topological semimetallic states that manifest in two-dimensional ferromagnets as a result of the interplay between spin-orbit and exchange interactions. We explore the emergence and stability of such mixed topological semimetals in realistic materials, and point out the perspectives of mixed topological states for current-induced orbital magnetism and current-induced domain wall motion. Our findings pave the way to understanding, engineering and utilizing topological semimetallic states in two-dimensional spin-orbit ferromagnets.
Highlights
The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to
The emergence of nodal points in mixed Weyl semimetals (MWSMs) correlates with drastic changes in the mixed topology and it is accompanied by discrete jumps of the momentum Chern number C 1⁄4 1=ð2πÞR Ωkxykdkxdky with respect to the magnetization direction, as well as of the mixed Chern number Z 1⁄4 1=ð2πÞR Ωmybxkdkxdθ with respect to the crystal momentum[30]
Owing to the nature of mixed semimetals incorporating the magnetization direction as an integral variable, we expect pronounced topological magneto-electric effects to which these materials should give rise. Apart from their substantial relevance for technological applications based on magnetic solids, we anticipate that these coupling phenomena can play a key role even in finite systems such as quantum dots[55]
Summary
The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to. Research in the area of topological materials has extended to the class of topological semimetals[4,5,6], which notably include Dirac[7,8,9], Weyl[10,11,12], and nodal-line semimetals[13,14,15] These materials have been theoretically proposed and experimentally confirmed in 3D, revealing remarkable properties such as ultrahigh mobility[16], anomalous magnetoresistance[17,18], and nonlinear optical response[19]. Studying the unique interplay of topological phases with the dynamic magnetization of solids currently matures into a significant burgeoning research field of condensed-matter physics[30,31,32,33] In this context, magnetic interfaces with topological insulators[34] and layered van der Waals crystals[35,36], which can exhibit ferromagnetism at room temperature, constitute compelling and experimentally feasible classes of 2D quantum materials. Besides providing realistic material candidates in which the discussed semimetals could be observed, we suggest possible applications of these states in shaping the magnetic properties of the edges and current-induced domain-wall motion
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