www.nature.com/npjcompumats ARTICLE OPEN Subtle metastability of the layered magnetic topological insulator MnBi2Te4 from weak interactions ✉ Jinliang Ning1, Yanglin Zhu2, Jamin Kidd1, Yingdong Guan2, Yu Wang2, Zhiqiang Mao 2 and Jianwei Sun 1 Layered quantum materials can host interesting properties, including magnetic and topological, for which enormous computational predictions have been done. Their thermodynamic stability is much less visited computationally, which however determines the existence of materials and can be used to guide experimental synthesis. MnBi2Te4 is one of such layered quantum materials that was predicted to be an intrinsic antiferromagnetic topological insulator, and later experimentally realized but in a thermodynamically metastable state. Here, using a combined first-principles-based approach that considers lattice, charge, and spin degrees of freedom, we investigate the metastability of MnBi2Te4 by calculating the Helmholtz free energy for the reaction Bi2Te3 + MnTe → MnBi2Te4.Weidentifyatemperaturerange(~500–873 K) in which the compound is stable with respect to the competing binary phases, consistent with experimental observation. We validate the predictions by comparing the calculated specific heats contributed from different degrees of freedom with experimental results. Our findings indicate that the degrees of freedom responsible for the van der Waals interaction, lattice vibration, magnetic coupling, and nontrivial band topology in MnBi2Te4 not only enable emergent phenomena but also play a crucial role in determining its thermodynamic stability. This conclusion lays the foundation for the future computational material synthesis of novel layered systems. 1234567890():,; npj Computational Materials (2020) 6:157 ; https://doi.org/10.1038/s41524-020-00427-y INTRODUCTION Thermodynamic stability of materials can be predicted from Layered quantum materials, such as graphene and two- chemical reaction free energy based on first-principles density dimensional (2D) semiconductors of transition metal dichalcogen- functional theory (DFT) calculations. Nevertheless, for complex ides, have revolutionized many fields in condensed matter physics layered magnetic quantum materials like MnBi2Te4, such predic- and materials science because of their exotic quantum proper- tions are challenging, due to the increasing importance of various 1 weak interactions (including SOC, magnetic coupling, lattice ties . A new member in this family is MnBi2Te4 that is an intrinsic antiferromagnetic topological insulator (TI) currently under vibrations, and vdW interactions), most of which are also 2–10 responsible for their emergent properties, as illustrated in Fig. 1. intensive study . In MnBi2Te4, the interplay between magnet- ism and topology has been shown to generate exotic quantum Typically, these materials have different kinds of chemical bonds states, including quantum anomalous Hall effect4, axion insula- ranging from strong intralayer covalent bonds to weak interlayer vdW interactions, with interaction strengths across almost 3 orders tor6,7, and high-Chern-number insulator9, upon exfoliation to of magnitude (from ~1 eV for strong bonds to ~1 meV for vdW atomically thin layers. interactions). Both strong chemical bonds and weak interactions MnBi Te is formed by intercalating magnetic MnTe layers into 2 4 are equally important for the thermodynamic stability predictions, the quintuple layers of Bi Te , which is topologically protected due 2 3 demanding a single density functional approximation for simulta- to spin–orbit coupling (SOC)-induced band inversions11,12. The neously accurate descriptions. More importantly, the electronic, experimental synthesis of large, pure, high-quality MnBi Te single 2 4 magnetic, and vibrational thermal excitation energies of these crystals suitable for magnetotransport measurements is however fi fi fi materials at nite temperature can be up to several tens of meV; notoriously dif cult. Different experiments have con rmed that although this scale is typically negligible for stability predictions of MnBi2Te4 is a metastable phase that can only be synthesized bulk solids 21, it is comparable to the thermal energy required to within a narrow temperature range below 873 K3,13–15. Without a stabilize MnBi2Te4. Since DFT is a zero-temperature ground-state fundamental understanding of its metastability, the ideal growth electronic structure method, post-DFT models have to be used to conditions for pure, large crystal synthesis will remain elusive, describe such excitations. Therefore, all these interactions have to ultimately preventing further experimental study of its unique be considered and described accurately for the thermodynamic topological and magnetotransport properties. Furthermore, stability of MnBi2Te4, either at the DFT level or by DFT-based although there have been a significant number of materials models. predicted to host interesting topological properties16–18, using fi – Here, using a set of rst-principles-based approaches that different symmetry indicators16 19, there are only a handful of consider lattice, charge, and spin degrees of freedom to take into – experimental realizations of such predictions16 18,20. Hence, the account the various weak interactions, we calculate the understanding of the metastability of MnBi2Te4 is also highly temperature-dependent reaction free energy of MnBi2Te4 based desirable for the synthesis of other candidate layered topological on the reaction MnTe + Bi2Te3 → MnBi2Te4, which identifies a materials. narrow temperature range for the metastability of MnBi2Te4 1Department of Physics and Engineering Physics, Tulane University, New Orleans, LA 70118, USA. 2Department of Physics, The Pennsylvania State University, University Park, PA ✉ 16802, USA. email: [email protected] Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences J. Ning et al. 2 Fig. 2 Reaction free energy based on Bi2Te3 + MnTe → MnBi2Te4. The energy is calculated at different levels of theory, including the 0 K DFT reaction energy from PBE (EPBE), SCAN + rVV10 (ESCAN+rVV10), + Fig. 1 Schematic of synthesis reaction and various interactions and SCAN rVV10 with SOC (ESCAN+rVV10+SOC, denoted as E0); the electronic excitation (el), lattice vibrational (harmonic approxima- determining metastability in MnBi2Te4.aSchematic of the synthesis reaction of the target ternary layered magnetic material tion, phHA, and quasi-harmonic approximation with Debye model to 1234567890():,; MnBi Te from two competing binary phases: Bi Te + MnTe → include the anharmonic contribution for high temperature starting 2 4 2 3 around 150 K, ph ), and magnetic (mag) contributions. Experi- MnBi2Te4. Note the layered structures of Bi2Te3 and MnBi2Te4, and AHA mental melting temperatures of Bi2Te3 (TmBT) and MnBi2Te4 the localized magnetic moments (illustrated by blue and red arrows 14 (TmMBT) , MnBi2Te4 start decomposition temperature (Tsd) upon on Mn) in MnTe and MnBi2Te4. b Schematic of the weak interactions 14 considered here, found to be critical in determining the metast- heating (dashed blue line) , and uncertainty in MnBi2Te4 formation temperature (shaded area)13,14 are shown. ability of MnBi2Te4. Top left: SOC; top right: magnetic coupling interaction; bottom left: anharmonic nature of lattice vibration in comparison with the harmonic approximation; bottom right: vdW the competing binaries by about 6 meV/atom below the melting interaction. temperature from the calculations. RESULTS AND DISCUSSION consistent with experiments. These approaches are then validated Van der Waals interaction by comparing the predicted specific heat capacities of the It is well known that layered materials are bound by vdW relevant compounds to experimental results. interactions between layers, while the popular Figure 2 shows that MnBi Te is unstable with respect to its 2 4 Perdew–Burke–Ernzerhof (PBE) density functional22 misses most competing binary phases (MnTe and Bi2Te3) for low temperatures, vdW interactions and barely binds layered materials23,24. Mean- and becomes stable above 500 K, indicated by the calculated while, it has been shown that the strongly constrained and reaction free energy (blue solid line) with contributions from all appropriately-normed (SCAN) density functional25,26 combined considered degrees of freedom. The predicted thermodynamic with the revised Vydrov-Van Voorhis (rVV10) nonlocal correlation = equilibrium temperature T 500 K is close to the experimentally density functional27,28 is effective in accurately describing 14 estimated formation temperature range between 673 and structural and energetic properties of layered materials24.As 13 808 K and above ~423 K, at which MnBi2Te4 was observed to expected, Fig. 2 shows that PBE destabilizes MnBi Te with respect 13 2 4 start decomposing during heating . Since the melting points are to the competing binaries by about 11 meV/atom in comparison 14 ~853 and ~873 K for Bi2Te3 and MnBi2Te4, respectively , the with SCAN + rVV10 for the 0 K ground-state energies. Since quenching required for single crystal synthesis of MnBi2Te4 11 meV/atom is comparable to the finite temperature contribu- without the minor Bi2Te3 phase must occur between ~853 and tions to the reaction free energy from the electronic, magnetic, ~873 K. This narrow temperature window, in addition to the fact and vibrational degrees of freedom, PBE will falsely predict that that MnBi2Te4 is only more stable than the competing binaries by MnBi2Te4 cannot