Topological Magnets: Functions Based on Berry Phase and Multipoles

Macroscopic responses of magnets are often governed by magnetization and, thus, have been restricted to ferromagnets. However, such responses are strikingly large in the newly developed topological magnets, breaking the conventional scaling with magnetization. Taking the recently discovered antiferromagnetic (AF) Weyl semimetals as a prime example, we highlight the two central ingredients driving the significant macroscopic responses: the Berry curvature enhanced because of nontrivial band topology in momentum space, and the cluster magnetic multipoles in real space. The combination of large Berry curvature and multipole enables large macroscopic responses such as the anomalous Hall and Nernst effects, the magneto-optical effect, and the novel magnetic spin Hall effect in antiferromagnets with negligible net magnetization, but also allows us to manipulate these effects by electrical means. Furthermore, nodal-point and nodal-line semimetallic states in ferromagnets may provide the strongly enhanced Berry curvature near the Fermi energy, leading to large responses beyond the conventional magnetization scaling. These significant properties and functions of the topological magnets lay the foundation for future technological development such as spintronics and thermoelectric technology. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 13 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.