Magnetic Dirac semimetal state of (Mn,Ge)Bi${}_2$Te${}_4$

Abstract

For quantum electronics, the possibility to finely tune the properties of magnetic topological insulators (TIs) is a key issue. We studied solid solutions between two isostructural Z${}_2$ TIs, magnetic MnBi${}_2$Te${}_4$ and nonmagnetic GeBi${}_2$Te${}_4$, with Z${}_2$ invariants of 1;000 and 1;001, respectively. For high-quality, large mixed crystals of Ge${}_x$Mn${}_{1-x}$Bi${}_2$Te${}_4$, we observed linear x-dependent magnetic properties, composition-independent pairwise exchange interactions along with an easy magnetization axis. The bulk band gap gradually decreases to zero for $x$ from 0 to 0.4, before reopening for $x>0.6$, evidencing topological phase transitions (TPTs) between topologically nontrivial phases and the semimetal state. The TPTs are driven purely by the variation of orbital contributions. By tracing the x-dependent $6p$ contribution to the states near the fundamental gap, the effective spin-orbit coupling variation is extracted. As $x$ varies, the maximum of this contribution switches from the valence to the conduction band, thereby driving two TPTs. The gapless state observed at $x=0.42$ closely resembles a Dirac semimetal above the Neel temperature and shows a magnetic gap below, which is clearly visible in raw photoemission data. The observed behavior of the Ge${}_x$Mn${}_{1-x}$Bi${}_2$Te${}_4$ system thereby demonstrates an ability to precisely control topological and magnetic properties of TIs.