Engineering magnetic topological insulators in ${\mathrm{Eu}}_5{M}_2{X}_6$ Zintl compounds

Magnetic topological insulators provide a prominent material platform for quantum anomalous Hall physics and axion electrodynamics. However, the lack of material realizations with cleanly gapped surfaces hinders technological utilization of these exotic quantum phenomena. Here, using the Zintl concept and the properties of nonsymmorphic space groups, we computationally engineer magnetic topological insulators. Specifically, we explore ${\mathrm{Eu}}_5{M}_2{X}_6$ (M=metal, X=pnictide) Zintl compounds and find that ${\mathrm{Eu}}_5{\mathrm{Ga}}_2{\mathrm{Sb}}_6$, ${\mathrm{Eu}}_5{\mathrm{Tl}}_2{\mathrm{Sb}}_6$, and ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{Bi}}_6$ form stable structures with nontrivial ${\mathbb{Z}}_2$ indices. We also show that epitaxial and uniaxial strain can be used to control the ${\mathbb{Z}}_2$ index and the bulk energy gap. Finally, we discuss experimental progress towards the synthesis of the proposed candidates and provide insights that can be used in the search for robust magnetic topological insulators in Zintl compounds.

Figure 1

Atomic and electronic structure of ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{Sb}}_6$. (a) The polyanions ${\left[{\mathrm{In}}_2{\mathrm{Sb}}_6\right]}^{-10}$ are comprised of pairs of approximate tetrahedra formed by Sb atoms and an In atom at their center. (b) Along the $c$ axis, the corner-sharing tetrahedra form a quasi-1D chain. Eu and ${\mathrm{Sb}}_1$ are located at integer layers while ${\mathrm{Sb}}_2$, ${\mathrm{Sb}}_3$, and In atoms are located at half-integer layers. Arrows indicate the direction along which the In atoms were displaced. (c) Electronic band structure of nonmagnetic (Eu $f$ electrons in the core) ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{Sb}}_6$ in the presence of SOC. Inset shows the reproduced band structure from Rosa et al. [20], in which case the displacement of the In atoms causes the ${\mathbb{Z}}_2$ index to change.

Figure 2

The ${\mathbb{Z}}_2$ index of ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{Sb}}_6$ as a function of epitaxial and uniaxial strain. The ${\mathbb{Z}}_2$ index becomes nontrivial by either applying compressive uniaxial strain along $c$ or expansive epitaxial strain in the $ab$ plane. Strains of this magnitude are impractical but nevertheless provide insight into the mechanisms that drive Zintl compounds into topological phases.

Figure 3

Band structures (a)–(d) without magnetism and without SOC, (e)–(h) without magnetism and with SOC, and (i)–(l) with an A-type AFM configuration and SOC for the four compounds obtained by isoelectronic substitution of ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{Sb}}_6$. ${\mathrm{Eu}}_5{\mathrm{Ga}}_2{\mathrm{Sb}}_6$, ${\mathrm{Eu}}_5{\mathrm{Tl}}_2{\mathrm{Sb}}_6$, and ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{Bi}}_6$ are topologically nontrivial while ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{As}}_6$ is trivial.

Figure 4

Effect of uniaxial strain on (a) direct and (b) indirect gaps. (e) Comparison between band structures with ${\lambda }_{\text{uni}}^c=1.00$ and ${\lambda }_{\text{uni}}^c=0.95$.

Figure 5

The $c$ axis and $b/a$ ratio of polycrystalline ${\mathrm{Eu}}_5{\mathrm{In}}_{2-x}{\mathrm{Ga}}_x{\mathrm{Sb}}_6$ show a systematic evolution with Ga substitution up to $x\approx 0.4$, the apparent solid solubility limit. Contraction of the $c$ lattice constant with increased Ga concentration indicates movement away from the CET limit, in agreement with the DFT prediction.