Bilayer stacking <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> -type altermagnet: A general approach to generating two-dimensional altermagnetism

Abstract

In this paper, we propose a concept of bilayer stacking $A$-type altermagnet (BSAA), in which two identical ferromagnetic monolayers are stacked with antiferromagnetic coupling to form a two-dimensional (2D) $A$-type altermagnet. By solving the stacking model, we derive all BSAAs for all layer groups and draw three key conclusions: (i) Only 17 layer groups can realize intrinsic $A$-type altermagnetism. All 2D $A$-type altermagnets must belong to these 17 layer groups, which will be helpful to search for 2D $A$-type altermagnet. (ii) It is impossible to connect the two sublattices of BSAA using ${S}_{3z}$ or ${S}_{6z}$, a constraint that is also applicable to all 2D altermagnets. (iii) ${C}_{2\ensuremath{\alpha}}$ is a general stacking operation to generate BSAA for an arbitrary monolayer. Our theory not only can explain the previously reported twisted-bilayer altermagnets, but also can provide more possibilities to generate $A$-type altermagnets. Our research has significantly broadened the range of candidate materials for 2D altermagnets. Based on conclusion (i), the bilayer ${\mathrm{NiZrCl}}_{6}$ is predicted to exhibit intrinsic $A$-type altermagnetism. Additionally, we use twisted-bilayer ${\mathrm{NiCl}}_{2}$ and CrOCl as supplementary examples of BSAA. Furthermore, utilizing symmetry analysis and first-principles calculation, we scrutinize their spin-momentum locking characteristic to substantiate their altermagnetic properties.

Topics & Concepts