Transition from antiferromagnets to altermagnets: Symmetry-Breaking Theory

Abstract

Considering the similarity of the real-space configurations for the opposite spin sublattices in both antiferromagnets (AFM) and altermagnets (AM), the relationship between them should be profound. In this work, we demonstrate that AFM and AM can be connected with spin groups and their subgroups. Consequently, the breaking of the combined inversion or translation operation with time-reversal symmetry (PT or tT) in AFM will induce transition from AFM to AM. We systematically list all collinear spin point groups and space groups that can realize the transition for the three types of AFMs: PT-type, tT-type and PT-tT-type. Moreover, we propose that Floquet engineering using circularly polarized light and surface cutting engineering are effective approaches to break PT and tT symmetries of AFM, respectively, achieving the transition. Interestingly, the features and magnitude of altermagnetic spin splitting can be tuned by adjusting various parameters of Floquet engineering. Our work not only establishes a theoretical framework for the transition from AFM to AM, but also provides practical approaches utilizing the achievements in AFM for a hundred years to obtain AM, significantly expanding the scope of altermagnetic materials for both theoretical studies and future practical applications.

Figures (4)

• Figure 1: The evolutionary relationship between point groups and their subgroups. The point groups with inversion symmetry are denoted by pink boxes, while those without inversion symmetry are represented by arctic blue boxes. Transition pathways from groups with inversion symmetry to their subgroups without it are indicated by both green and purple lines. However, only the green lines may describe the transition from antiferromagnetic to altermagnetic phases.
• Figure 2: AFMs to AMs by Floquet engineering in $PT$ antiferromagnetic honeycomb lattice. (a) Antiferromagnetic honeycomb lattice. Blue and red represent the spin-up and spin-down sublattices, respectively. (b) The spin-degenerate energy bands in antiferromagnetic honeycomb lattice. (c) Floquet hopping of the honeycomb lattice. (d) The energy band structure with left circularly polarized light intensity 1.0/Å. The inset illustration shows 2D Brillouin zone (BZ) with altermagnetic spin splitting. Blue and red represent spin-up and spin-down, respectively.
• Figure 3: AFMs to AMs by Floquet engineering in $G$-type antiferromagnet Cr$_2$O$_3$. (a) and (b) Crystal structure and the 3D BZ of the $G$-type AFM Cr$_2$O$_3$, respectively. (c) The BZ plane at $k_z = 0$ exhibits altermagnetic spin splitting. (d) Energy bands under left circularly polarized light ($\hbar \omega$ = 15 eV) with an intensity of 0.35/Å, where blue and red denote spin-up and spin-down states, respectively.
• Figure 4: Surface engineering-induced transition from AFMs to AMs in $\bm{t}T$ antiferromagnetic materials AMnN (A = K, Rb, Cs; N = P, As, Bi). (a) Crystal structure and (b) 3D Brillouin zone (BZ) of AMnN. (c) Surface 2D BZ and altermagnetic spin splitting. (d) Slab band structure of KMnP with 15 layers along the $z$-direction, where blue and red represent spin-up and spin-down states, respectively.