Degeneracy Removal of Spin Bands in Collinear Antiferromagnets with Non‐Interconvertible Spin‐Structure Motif Pair

Abstract

Energy bands in antiferromagnets are supposed to be spin degenerate in the absence of spin–orbit coupling (SOC). Recent studies have identified formal symmetry conditions for antiferromagnetic crystals in which this degeneracy can be lifted, spin splitting,even in the vanishing SOC (i.e., non‐relativistic) limit. Materials having such symmetries could enable spin‐split antiferromagnetic spintronics without the burden of using heavy‐atom compounds. However, the symmetry conditions that involve spin and magnetic symmetry are not always effective as practical material selection filters. Furthermore, these symmetry conditions do not readily disclose trends in the magnitude and momentum dependence of the spin‐splitting energy. Here, it is shown that the formal symmetry conditions enabling spin‐split antiferromagnets can be interpreted in terms of local motif pairs, such as octahedra or tetrahedra, each carrying opposite magnetic moments. Collinear antiferromagnets with such a spin‐structure motif pair, whose components interconvert by neither translation nor spatial inversion, will show spin splitting. Such a real‐space motif‐based approach enables an easy way to identify and design materials (illustrated in real example materials) having spin splitting without the need for SOC, and offers insights into the momentum dependence and magnitude of the spin splitting.

Interplay of altermagnetism and weak ferromagnetism in two-dimensional RuF4

“…A recent discovery of non-relativistic spin splitting in electronic bands of materials with compensated collinear magnetic order opened a new venue in antiferromagnetic spintronics [1][2][3]. These intriguing materials constitute a separate magnetic phase, besides ferromagnets (FM) and antiferromagnets (AF), dubbed the name altermagnets (AM) [4,5] or, alternatively, antiferromagnets with noninterconvertible spin-structure motif pair [6][7][8][9]. Altermagnets display a profusion of diverse physical phenomena, including anomalous Hall effect [10], piezoelectricity [11], and chiral magnons [12]; they can be used for efficient spin-charge interconversion [13], to generate orientation-dependent spin-pumping currents [14] and to proximitize superconductor materials [15][16][17], just to scratch the manifold of their possible applications.…”

The Impact of Local Strain Fields in Noncollinear Antiferromagnetic Films

“…[7][8][9][10] In particular, noncollinear antiferromagnets (AFMs) such as Mn 3 A (A = Sn, Ge, Pt) and Mn 3 AN (A = Ni, Ga, Sn) have been shown to possess intrinsic anomalous Hall effect (AHE), [11][12][13][14][15][16][17] magneto-optical Kerr effect (MOKE), [18][19][20] anomalous Nernst effect (ANE), [21][22][23] and the tunneling magnetoresistance effect [24] which allows for easy readout of the antiferromagnetic state, an obstacle for many collinear antiferromagnetic families, [25][26][27] although encouraging progress with altermagnets may help overcome this bottleneck. [28][29][30][31] Although it is theoretically understood that the AHE may be observed in fully compensated noncollinear AFM with M = 0, [32][33][34][35] experimentally the observation of the anomalous Hall effect in noncollinear AFM systems is accompanied with a small net moment. This moment has been attributed to several sources.…”

Altermagnetic surface states: towards the observation and utilization of altermagnetism in thin films, interfaces and topological materials

“…10 This magnetic phase was called altermagnetism (AM) [10][11][12][13] or antiferromagnetism with non-interconvertible spin-structure motif pair. 14 The presence of AM requires the electronic charge of the spin-up (down) atoms to be mapped in the charge of the spindown (up) atoms without translations, inversion, or their combinations, but only with roto-translations or mirrors. 13,15 Therefore, it is observable for some determined space groups and even more precisely, in the magnetic space groups of type-I and type-III.…”

“…10 This magnetic phase was called altermagnetism (AM) 10–13 or antiferromagnetism with non-interconvertible spin-structure motif pair. 14…”