Altermagnetism of ultrathin CrSb slabs

TL;DR

This work probes how altermagnetic spin splitting in CrSb evolves as the material is reduced to ultrathin slabs, using first-principles calculations across (0001), (100), and (110) orientations. The results reveal a strong orientation dependence: the (110) slab preserves a large exchange-driven splitting comparable to bulk (~$0.4$ eV) with SOC playing a negligible role, while the (0001) slab loses the exchange-driven AM and only retains a small SOC-induced ~ $70$ meV anisotropy, and the (100) slab becomes fully spin-degenerate in the ultrathin limit. Enhanced in-plane AFM exchange in the (110) geometry underpins this robustness, suggesting CrSb(110) as a prime platform for ultrathin altermagnetic spintronics. The findings highlight how spin-group symmetries and exchange topology govern altermagnetism at the nanoscale, with potential near-term realizations via CrSb(110) epitaxial films.

Abstract

Altermagnets exhibit momentum-dependent spin splitting without net magnetization, combining characteristics of both ferromagnets and antiferromagnets, making them highly interesting for spintronics applications. CrSb is a prime candidate with a high Néel temperature ($\sim700$~K) and a large exchange-driven splitting of $\sim0.6$--1~eV. Using ab-initio calculations, we consider slabs of various orientations in the ultrathin limit. We find that (100) oriented slabs have spin-degenerate bands. In (0001) oriented slabs, the exchange-driven altermagnetic spin splitting collapses, but including spin-orbit coupling restores a residual anisotropic splitting of $\sim70$~meV. In contrast, the (110) oriented slabs show an altermagnetic spin splitting of $\sim400$~meV, and emerges as a robust candidate for realizing large, exchange-driven altermagnetism

Figures (8)

• Figure 1: Structural illustration of the hexagonal CrSb bulk system along the (a) $ab$-plane and (b) $ac$-plane. (c) Illustration of two symmetry operations connecting the opposite spin sub-lattices in the CrSb system.
• Figure 2: Illustration of different considered magnetic configurations: (a) FM, (b) AFM-1 (layered (001)), (c) AFM-2 (layered (100)), and (d) AFM-3 (layered (110)). Blue/red spheres denote spin-up/down Cr atoms.
• Figure 3: (a) First BZ of hexagonal bulk CrSb. (b) Scalar-relativistic band structure of the bulk along high-symmetry lines, and (c) along low-symmetry lines. (d) Band structure including SOC along low-symmetry lines.
• Figure 4: Spin-polarized bands along low-symmetry paths for (a) Cr$_2$Sb and (b) hcp-Cr. Spin-up and spin-down atoms are shown in blue and red.
• Figure 5: (a) Structural models of CrSb(0001) slabs: asymmetric Sb$|$Cr termination (left) and symmetric Cr$|$Cr termination (right). (b) Band structure of CrSb(0001) slabs with symmetric Cr$|$Cr termination from scalar-relativistic spin-polarized calculations showing spin-degenerate bands, and (b) with SOC. The color bar denotes the spin character of the bands.