Topological Electronic Structure and Intrinsic Magnetization in ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$: A ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ Derivative with a Periodic Mn Sublattice

Combinations of nontrivial band topology and long-range magnetic order hold promise for realizations of novel spintronic phenomena, such as the quantum anomalous Hall effect and the topological magnetoelectric effect. Following theoretical advances, material candidates are emerging. Yet, so far a compound that combines a band-inverted electronic structure with an intrinsic net magnetization remains unrealized. ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ has been established as the first antiferromagnetic topological insulator and constitutes the progenitor of a modular $({\mathrm{Bi}}_2{\mathrm{Te}}_3{)}_n({\mathrm{MnBi}}_2{\mathrm{Te}}_4)$ series. Here, for $n=1$, we confirm a nonstoichiometric composition proximate to ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$. We establish an antiferromagnetic state below 13 K followed by a state with a net magnetization and ferromagnetic-like hysteresis below 5 K. Angle-resolved photoemission experiments and density-functional calculations reveal a topologically nontrivial surface state on the ${\mathrm{MnBi}}_4{\mathrm{Te}}_7(0001)$ surface, analogous to the nonmagnetic parent compound ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. Our results establish ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ as the first band-inverted compound with intrinsic net magnetization providing a versatile platform for the realization of magnetic topological states of matter.

Popular Summary

Topological insulators, novel materials that conduct electricity on their surfaces yet behave as insulators in their interiors, derive their peculiar properties from an effect known as a band inversion, where the normal conduction and valence bands swap places. It is thought that magnetization might control this band inversion, offering a potential way to manipulate topological behavior in new and exciting ways. But researchers have yet to find a suitable material that contains a band inversion and an intrinsic net magnetization—until now. Here, we report on the first realization of such a material.

We study high-quality single crystals of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$, part of a family of compounds known to exhibit some aspects of magnetization and topological behavior. Using a variety of experimental techniques, we uncover a complex magnetic behavior with competing magnetic states as a function of temperature. We also use advanced spectroscopy and theoretical calculations to confirm the presence of an inverted band structure. By cooling the crystals to a few degrees above absolute zero, we identify a regime where a net magnetization of the sample coincides with the presence of a topological surface state, a phase that has not been previously realized in a stoichiometric material (one whose elemental proportions are ratios of natural numbers).

These results are a major advance in the search for new classes of topological materials. Thanks to its versatile magnetic and electronic properties, ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ is a unique material platform for the realization of tunable topological quantum phenomena. This provides fascinating perspectives for the realization of quantum effects in bulk materials under normal conditions.

Figure 1

(a) Crystal structure of ${\mathrm{Mn}}_{1-x}{\mathrm{Bi}}_{4+2x/3}{\mathrm{Te}}_7$ (${\mathrm{GeBi}}_4{\mathrm{Te}}_7$ structure type) with alternating (${\mathrm{Bi}}_2{\mathrm{Te}}_3$) and (${\mathrm{Mn}}_{1-x}{\square }_{x/3}{\mathrm{Bi}}_{2+2x/3}{\mathrm{Te}}_4$) blocks. Mn atoms are shown in green; Bi in blue; Te in orange. (b) As-grown crystals with the experimental composition (EDX) ${\mathrm{Mn}}_{0.8(1)}{\mathrm{Bi}}_{4.3(1)}{\mathrm{Te}}_7$.

Figure 2

Magnetic and transport properties of Mn147. (a) In-plane electrical resistivity as a function of the temperature. (b),(c) Normalized magnetization as a function of temperature for fields applied both perpendicular and parallel to the $ab$ directions. Open and filled symbols correspond to ZFC and FC protocols, respectively. (d),(e) Hall resistivity and magnetization as a function of the field applied perpendicular to the $ab$ planes. (f) Magnetization as a function of the field applied parallel to the $ab$ planes. The hysteretic behavior for temperatures $T\le 5\mathrm{K}$ indicates ferromagnetic (intraplane) interactions.

Figure 3

Spectroscopy of magnetic properties in Mn147. (a) Typical ESR spectra measured at $T=4\mathrm{K}$ and $T=30\mathrm{K}$. (b) Frequency dependence of the resonance field of the ESR signal measured at temperatures of 4, 15, and 30 K. (c) The anisotropy gap $\mathrm{\Delta }$ as a function of temperature extracted from (a) by fitting $\nu =\mathrm{\Delta }+g{\mu }_B{\mu }_0{H}_0/h$. (d) XMCD and (e) XMLD data for Mn147(0001) obtained at the Mn $L_{2,3}$ absorption edge with circularly polarized (RCP and LCP) and linearly polarized (LV and LH) light, respectively. Measurements are performed in normal (NI) and grazing (GI) light incidence geometries, as sketched in the inset of (d). XMCD signals are shown for an external field (${\mu }_{0}H=6\mathrm{T}$) along the light incidence direction and for remnant conditions (${\mu }_{0}H=0\hspace{0.17em}\hspace{0.17em}\mathrm{T}$) at $T=2\mathrm{K}$. (e) XMLD data without external field are reported for different temperatures.

Figure 4

Band inversion phenomena in Mn147 ($\mathrm{GGA}+U+\mathrm{SOC}$). (a) Band structure in the ferromagnetic configuration. The symbol size in each $k$ point and band is proportional to the overlap between the corresponding Bloch state and the Te and Bi $p$ orbitals, respectively, depicted in different colors. Filled (empty) dots correspond to spin-down (spin-up). The black arrow indicates the energy of the Weyl node of lowest energy in the conduction band. (b) Band structure for the antiferromagnetic AFM1 configuration. (c) Wannier center evolution in the $k_z=0$ plane. $k_x$ is the crystal momentum along the primitive lattice vector ${\overline{b}}_1$ and ${\overline{b}}_2$ is the second primitive vector in the $k_z=0$ plane. (d) Mn147(0001) surface spectral density along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction for a quintuple layer termination.

Figure 5

Electronic structure of the Mn147(0001) surface as measured by ARPES. (a) Overview data set of the valence band structure obtained at $T=8\mathrm{K}$ showing characteristic surface states SS1 and SS2 and a feature related to Mn $3d$ states (cf. Figs. S9–S12 [32]). (b),(c),(f) High-resolution data sets of the electronic structure near $E_F$ obtained at different photon energies and a temperature of $T=8\mathrm{K}$, showing a topological surface state (TSS) in the gap between conduction and valence-band derived states (BCB and BVB). (d) Photon-energy dependence of the ARPES intensity at $E_F$ ($T=8\mathrm{K}$). (e) Same as in (f), but for $T=80\mathrm{K}$. (g) Same as in (f), but for a septuple layer (SL) termination. All other data sets in Fig. 4 are assigned to a quintuple layer (QL) termination. The ARPES data sets in Fig. 5 are measured along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ high-symmetry direction.

Figure 6

Schematic topological phase diagram of ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$. The scheme follows the experimentally observed trends: a correlated paramagnetic state above $T_N$, followed by an antiferromagnetic phase that at lower temperatures evolves to a magnetic state with a strong ferromagnetic component. The text in red highlights possible nontrivial topology (see text for details).