Prediction and observation of the first antiferromagnetic topological insulator

Abstract: Magnetic topological insulators (MTIs) are narrow gap semiconductor materials that combine non-trivial band topology and magnetic order. Unlike their nonmagnetic counterparts, MTIs may have some of the surfaces gapped due to breaking the time-reversal symmetry, which enables a number of exotic phenomena having potential applications in spintronics. So far, MTIs have only been created by means of doping nonmagnetic TIs with 3d transition metal elements, however, such an approach leads to strongly inhomogeneous magnetic and electronic properties of these materials, restricting the observation of important effects to very low temperatures. Finding intrinsic MTI, i.e. a stoichiometric well-ordered magnetic compound, could be an ideal solution to these problems, but no such material was observed to date. Here, using density functional theory we predict and further confirm by means of structural, transport, magnetic, angle- and spin-resolved photoemission spectroscopy measurements the realization of the antiferromagnetic (AFM) TI phase, that is hosted by the van der Waals layered compound MnBi$2$Te$_4$. An interlayer AFM ordering makes MnBi$_2$Te$_4$ invariant with respect to the combination of the time-reversal ($\Theta$) and primitive-lattice translation ($T{1/2}$) symmetries, $S = \Theta T_{1/2}$, giving rise to the $Z_2$ topological classification of AFM insulators. We find $Z_2 = 1$ for MnBi$_2$Te$_4$, which confirms its topologically nontrivial nature. The $S$-breaking (0001) surface of MnBi$_2$Te$_4$ exhibits a giant bandgap in the topological surface state as evidenced by ab initio calculations and photoemission measurements. These results culminate almost a decade-long search of an AFMTI, predicted in 2010. Furthermore, MnBi$_2$Te$_4$ is the first intrinsic magnetic TI realized experimentally.

• The paper demonstrates that MnBi₂Te₄ hosts an AFMTI phase using DFT and Monte Carlo simulations to reveal interlayer antiferromagnetic ordering and a 200 meV inverted band gap.
• The experimental work confirms a gapped Dirac cone via ARPES and a Néel temperature of about 24.2 K, validating the predicted topological characteristics.
• This breakthrough offers a promising platform for future spintronic and quantum device applications by linking antiferromagnetism with topological electronic properties.

Prediction and Observation of the First Antiferromagnetic Topological Insulator

The paper presents a significant advancement in the understanding of topological materials by addressing the antiferromagnetic topological insulator (AFMTI) phase, which had been theorized but not experimentally observed until this study. The authors predict and confirm the existence of the AFMTI state in the van der Waals compound MnBi$_2$Te$_4$, utilizing a combination of theoretical calculations and experimental validation.

Theoretical Framework

Using density functional theory (DFT) and Monte Carlo simulations, the paper predicts that MnBi$_2$Te$_4$ hosts an AFMTI phase. The theoretical exploration reveals that this compound exhibits interlayer antiferromagnetic ordering, making it invariant under the combined symmetries of time reversal and a half-lattice translation, denoted as $S=\Theta T_{1/2}$. As a result, MnBi$_2$Te$_4$ is classified as a $Z_2$ AFMTI, which fundamentally changes its electronic structure, including the opening of a substantial bandgap at its surface.

The phase exhibits a $Z_2$ invariant of 1, confirming its topological nature. The calculations demonstrate that the strong spin-orbit coupling (SOC) associated with Bi and Te elements contributes to an inverted band gap of approximately 200 meV, classifying MnBi$_2$Te$_4$ as a three-dimensional (3D) AFMTI.

Experimental Validation

The paper describes comprehensive experimental efforts to validate the AFMTI phase in MnBi$_2$Te$_4$. Structural, transport, magnetic, and angle-resolved photoemission spectroscopy (ARPES) measurements are employed.

1. Structural Analysis: Single crystals of MnBi$_2$Te$_4$ are synthesized and characterized using x-ray diffraction techniques to confirm its $R\bar 3m$ lattice symmetry with some degree of cation disorder.
2. Magnetic Properties: Magnetic susceptibility and magnetization measurements indicate a transition to a 3D antiferromagnetic order at a Néel temperature $T_\text{N}$ of about 24.2 K. This corresponds well with the theoretical prediction and confirms the AFM state in bulk.
3. Electronic Properties: ARPES data reveal a gapped Dirac cone on the MnBi$_2$Te$_4$(0001) surface, consistent with the theoretical predictions of a 88-meV bandgap at the Dirac point. The experimental observations confirmed the band inversion necessary for the topological nature.
4. Topological Evidence: The detection of metallic states on the (0001) surface underlines the AFMTI phase’s robustness even above $T_\text{N}$, suggesting potential AFM orders persist.

Implications and Future Directions

The implications of this discovery extend to both practical applications in spintronics and theoretical physics. MnBi$_2$Te$_4$'s AFMTI phase, with its significant bandgap at the surface state, makes it an ideal candidate for realizing the quantized magnetoelectric effect and investigating axion insulator states. These phenomena carry potential applications in quantum computing and advanced electronic devices.

The study points to the possibility of tuning MnBi$_2$Te$_4$ via controlled doping to yield nearly charge-neutral samples. An avenue of exciting research includes investigating layered van der Waals materials and understanding the interactions between SOC and AFM order in such contexts. MnBi$_2$Te$_4$ provides a compelling platform for exploring new physical phenomena and possibly linking the fields of antiferromagnetic spintronics and topological insulators in future studies.

In summary, the paper successfully demonstrates the existence of an AFMTI phase in MnBi$_2$Te$_4$, serving as a breakthrough in the pursuit of these exotic states. This work opens new paths for both fundamental research and technological applications, supporting further exploration into the interactions and potential applications of antiferromagnetic materials in spintronics and quantum devices.