Topology and anomalous Hall effect in reciprocal space
from spin chirality in real space

Max Hirschberger^1,2

¹RIKEN Center for Emergent Matter Science (CEMS)

²Department of Applied Physics and Quantum Phase Electronics Center (QPEC), The University of Tokyo

In noncollinear magnets (NCM), the winding spin texture defines a topological charge density and, related, an emergent magnetic field that bends the path of conduction electrons. Ab-initio modeling of this emergent electromagnetic phenomenon has remained a challenge for two decades, despite recent progress in large-scale computing.

We summarize our research on various metallic NCM and discuss the varying levels of success in theoretically modeling the electronic structures of these systems, including their emergent electrodynamics. First, Co(Nb/Ta)₃S₆ realize antiferromagnetism with a canted four-sublattice texture, which represents an atomistic analogon (< 2 nm size) to larger skyrmion spin vortices (~20-200 nm) [1,2]. Here, full ab-initio theory is consistent with the observed Hall and Nernst responses and reveals the importance of a spin-space group symmetry of the ordered state [3]. Second, the noncollinear Weyl magnet NdAlSi has a large enhancement of the topological charge as a function of band filling [4]. Finally, in the pyrochlore oxide Nd₂Mo₂O₇, the Hall effect can be described by theory, but questions remain about the thermoelectric effect [5,6].

[1] P. Park et al., Nat. Commun. 14, 8346 (2023)

[2] H. Takagi et al., Nat. Phys. 19, 961 (2023)

[3] N.D. Khanh, M. Hirschberger, et al., under review (2024)

[4] R. Yamada, M. Hirschberger, et al., manuscript in preparation (2024)

[5] M. Hirschberger et al., Phys. Rev. B 103, L041111 (2021)

[6] M. Hirschberger et al., Phys. Rev. B 104, 024436 (2021)