One-dimensional magnetism and Rashba-like effects in zigzag bismuth nanoribbons

Discoveries of low-dimensional quantum materials have renewed interest in some of the fundamental phe-nomena, such as magnetism and Rashba-type spin orbit coupling. In particular, exploring these phenomena by themselves and/or in combination within one-dimensional (1D) systems is of interest for fields as disparate as spintronics and biology. For example, a better understanding of Rashba-type spin orbit coupling in 1D systems may be used to explain spin-selective electron transport in long helical molecules. In this paper, using first principle calculations, we show that each edge of a zigzag nanoribbon composed of a bismuth (Bi) bilayer is a truly 1D structure that naturally combines both 1D magnetism and Rashba-type spin orbit coupling in a single system. In particular, we study the combined effects of exchange and spin-orbit coupling in nanoribbons that are: (i) ideal freestanding, (ii) placed on a hexagonal boron nitride substrate, and (iii) decorated with N atoms. The edges of the Bi zigzag NRs can display ferromagnetic, antiferromagnetic, or noncollinear ordering, resulting in a broken quantum spin Hall state. The interplay of Rashba and exchange effects in different magnetic phases can result in different spin-dependent transport regimes.