Spin-layer coupling in an altermagnetic multilayer: A design principle for spintronics
Jianke Tian, Jia Li, Hengbo Liu, Yan Li, Ze Liu, Linyang Li, Jun Li, Guodong Liu, Junjie Shi
Abstract
The discovery of collinear symmetric-compensated altermagnets (AM) with intrinsic spin splitting provides a route toward energy-efficient and ultrafast device applications. Here, using first-principle calculations and symmetry analysis, we construct a series of AM $\mathrm{C}{\mathrm{r}}_{2}\mathrm{S}X$ ($X$ = O, S, Se) monolayers and explore the spin splitting in $\mathrm{C}{\mathrm{r}}_{2}\mathrm{S}X$ multilayer. A spin-layer coupling design principle for predicting electronic spin behavior in odd and even layers is mapped out based on the comprehensive analysis of spin group symmetry. The spin-splitting behavior related to the ${\mathcal{M}}_{\mathcal{z}}\mathcal{U}t$, ${\mathcal{M}}_{\mathcal{z}}$ and ${\mathcal{M}}_{L}$ symmetries in AM multilayers can be significantly modulated by magnetic orders, crystal symmetry, and external perpendicular gate field (${E}_{\mathcal{z}}$). Due to the spin-compensated bands of sublayers linked by overall ${\mathcal{M}}_{\mathcal{z}}$ and interlayers ${\mathcal{M}}_{L}$ symmetries, the $\mathrm{C}{\mathrm{r}}_{2}{\mathrm{S}}_{2}$ odd-layer exhibits the unique coexistence of spin splitting and spin degeneracy at high symmetry paths and in the X or Y valley, respectively. Furthermore, owing to the higher priority of overall ${\mathcal{M}}_{L}$ symmetry compared to interlayers ${\mathcal{M}}_{L}$ symmetry in AM even layers, the spin-layer coupling of AM multilayers shows strong odd- and even-layer dependence. Our work not only offers a new direction for manipulating spin splitting but also greatly enriches the research on AM monolayer and multilayer.