Spin texture tunability in Mn${}_{1-x}$Ge${}_x$Bi${}_2$Te${}_4$ through varying Ge Concentration

Abstract

The spin-resolved dispersion dependencies for the topological insulator Mn${}_{1-x}$Ge${}_x$Bi${}_2$Te${}_4$ in the $\bar{\mathrm{K}}\bar{\hat{I}}“{\bar{\mathrm{K}}}^{\prime }$ path of the Brillouin zone were studied by spin- and angle-resolved photoemission spectroscopy using laser radiation (Laser Spin-ARPES) with variation of the concentration of substitutional Ge atoms (x from 0.1 to 0.8) for in-plane ($s_x$) and out-of-plane ($s_z$) spin orientation. The formation of Rashba-like states is shown, which shift to lower energies with increasing Ge concentration. In the region of Ge concentrations from 50% to 75%, the contribution of these states to the formed spin-dependent dispersions becomes predominant. A pronounced in-plane ($s_y$) spin polarization, asymmetric for opposite $\pm k_{\parallel }$ directions, is revealed for the Dirac cone states, while the Rashba-like states exhibit a pronounced asymmetry in both in-plane ($s_y$) and out-of-plane ($s_z$) spin polarizations. Theoretical calculations confirmed the asymmetric polarization of the Rashba-like states formed in the $\bar{\mathrm{K}}\bar{\hat{I}}“{\bar{\mathrm{K}}}^{\prime }$ path of the BZ, simultaneously for in-plane and out-of-plane spin orientation. Constant energy maps for Rashba-like states show a pronounced $s_z$ spin component along the $\bar{\hat{I}}“\bar{\mathrm{K}}$ direction, with a sign change as the contour crosses the $\bar{\hat{I}}“\bar{\mathrm{M}}$ direction. The observed spin polarization can influence the development of spin devices based on magnetic topological insulators.