Anomalous Hall Effect and Topological Defects in Antiferromagnetic Weyl Semimetals: Mn3Sn/Ge

Abstract

We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and Z6 vortex lines, in the antiferromagnetic Weyl semimetals Mn3Sn and Mn3Ge with negative vector chirality. We argue that these materials possess a hierarchy of energies scales which allows a description of the spin structure and spin dynamics using a XY model with Z6 anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies the presence of Z6 vortex lines, the double-domain pattern in the presence of magnetic fields, and the ability to control domains with current. We also introduce a minimal electronic model which allows efficient calculation of the electronic structure in the antiferromagnetic configuration, unveiling Fermi arcs at domain walls, and sharp quasi-bound states at Z6 vortices. Moreover, we have shown how these materials may allow electronic-based imaging of antiferromagnetic microstructure, and propose a possible device based on domain-dependent anomalous Hall effect. PACS numbers:The Hall effect has long been a nucleation center for geometry and topology in the physics of solids. In the 1950s, prescient work of Karplus and Luttinger identified Berry curvature of electron wavefunctions as the heart of the anomalous Hall effect (AHE) in ferromagnets [1,2]. In the 1980s, topology entered with the discovery of the quantum Hall effect. These ideas came together in the mid-2000s to unveil broad applications to electronic systems in the form of topological insulators, superconductors [3,4] and semimetals with topological Weyl (and other) fermion excitations [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The AHE re-appears as one of the key emergent properties of topological semimetals, and coming full circle, most ferromagnets are now believed to host Weyl fermions to which their AHE is at least in part attributed.The dissipationless nature of the Hall effect also makes it interesting for applications. Uses based on ferromagnets may, however, be limited by the difficulty of miniaturization posed by large fields generated by the magnetization. For this reason, antiferromagnetic realizations of AHE may be of practical interest, but the microstructure, dynamics, and AHE of antiferromagnets are relatively uninvestigated. Here we attack these issues in the family of noncollinear antiferromagnets including Mn 3 Sn and Mn 3 Ge, for which a strong AHE was predicted and then experimentally verified to exist [19][20][21]. First principles calculations further indicate that in Mn 3 Sn and Mn 3 Ge there are Weyl nodes around the Fermi level [22,23]. We argue that these materials possess a hierarchy of energies scales which permits a description of the microstructure and spin dynamics as an XY model with Z 6 anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies a rich domain structure, the presence of Z 6 vortex lines, and the ability to control domains with current. We further introduce a ...

Spin Hall effect emerging from a noncollinear magnetic lattice without spin–orbit coupling

“…Large AHE in room temperature has recently been reported in Mn 3 Ge and Mn 3 Sn [22,23]. These materials also exhibit other exotic phenomena including the Weyl semimetal phase [38], magneto-optical Kerr effect [39], anomalous Nernst effect [40], and topological defects [41]. Distinct from hexagonal Mn 3 X compounds, the Mn 3 Ir (space group Pm m 3 , No.…”

Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal

“…In particular in Mn 3 Sn, six magnetic domains and the associated various types of topological defects could be possible including a vortex type of point defect around which the six domains meet. It is a future subject to investigate the possible current-induced AF domain wall motion 37 . Finally, the topological aspect of the magnetic state (magnetic Weyl state) of Mn 3 Sn, which has been recently pointed out by theoretical 38 and experimental 39 studies, would make it interesting to investigate the Berry curvature effects in the MOKE at low frequency, and further make the topological defects even more attractive as the bulk-edge correspondence for such a magnetic Weyl semimetallic state may lead to a Fermi arc in a magnetic domain wall, and contribute to the MOKE signal in an unconventional fashion 37, 40 .…”

The study of magnetic topological semimetals by first principles calculations

“…Therefore, W 1,2,7,4 have other three partners, W 9 has other one partner, while W 3,5,6,8 have other seven partners according to Noting that the symmetries are slightly broken by a tiny net magnetic moment, hence the coordinates will be slightly shifted from where they are expected to be. Mn 3 Sn(Ge) [148,149]. Recently, the proposed dynamics of the textures in the non-collinear antiferromagnets provide a theoretical mechanism for driving domain walls in Mn 3 Sn(Ge, Ir) [150], which is a platform to study the interplay between the magnetic Weyl nodes and the domain walls.…”