  The metastable layered compound MnBi2Te4 is the first experimentally realized
intrinsic antiferromagnetic topological insulator, predicted to host the
quantum anomalous Hall effect at high temperatures upon exfoliation to
atomically thin layers. While its magnetic ordering and topological properties
have generated intensive interest, the mechanism behind its metastability and
the ideal crystal synthesis conditions have remained elusive. 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. We identify a narrow temperature range (767 K to 873 K) in which the
compound is stable with respect to the competing binary phases and successfully
synthesize high-quality MnBi2Te4 single crystals using the Bi-Te flux method
within this range. We also predict the various contributions to the total
specific heat, which is consistent with our experimental measurements. Our
findings indicate that the degrees of freedom responsible for the van der Waals
interaction, magnetic coupling, and nontrivial band topology in layered
materials not only enable emergent phenomena but also determine thermodynamic
stability. This conclusion lays the foundation for future computational
material synthesis of novel layered systems.
