Using density functional theory and Monte Carlo calculations, we study the thickness dependence of the magnetic and electronic properties of a van der Waals interlayer antiferromagnet in the twodimensional limit. Considering MnBi2Te4 as a model material, we find it to demonstrate a remarkable set of thickness-dependent magnetic and topological transitions. While a single septuple layer block of MnBi2Te4 is a topologically trivial ferromagnet, the thicker films made of an odd (even) number of blocks are uncompensated (compensated) interlayer antiferromagnets, which show wide bandgap quantum anomalous Hall (zero plateau quantum anomalous Hall) states. Thus, MnBi2Te4 is the first stoichiometric material predicted to realize the zero plateau quantum anomalous Hall state intrinsically. This state has been theoretically shown to host the exotic axion insulator phase.After the isolation of graphene, the field of twodimensional (2D) van der Waals (vdW) materials has experienced an explosive growth and new families of 2D systems and block-layered bulk materials, such as tetradymite-like topological insulators (TIs) [1, 2], transition metal dichalcogenides [3], and others [4-6] have been discovered. The remarkable electronic properties, along with the possibility of their tuning via thickness control, doping, intercalation, proximity effects, etc., make the layered vdW materials attractive from both practical and fundamental points of view. The relative simplicity of fabrication with a number of techniques has greatly facilitated a comprehensive study of these systems. However, the important step towards magnetic functionalization of the inherently nonmagnetic layered vdW materials and a controllable fabrication of the resulting hybrid systems has proven challenging. Therefore, aiming at exploring magnetism of layered vdW materials in the 2D limit, new possibilities have been considered. One of them is the ultrathin laminae exfoliation from intrinsically ferromagnetic (FM) vdW crystals, such as Cr 2 Ge 2 Te 6 and CrI 3 , whose magnetic behaviour has been studied down to a few layers thickness [7,8]. An alternative fabrication strategy is epitaxial growth [9,10]. With this technique, a 2D FM septuple layer (SL) block of MnBi 2 Se 4 has been grown on top of the Bi 2 Se 3 TI surface [9]. Similar systems have been theoretically proposed as a promising platform for achieving the quantized anomalous Hall (QAH) and magnetoelectric effects at elevated temperatures [11,12]. Later, epitaxial growth of the Bi 2 Se 3 /MnBi 2 Se 4 multilayer heterostructure has been reported [10].The field of 2D vdW magnets is in its infancy and many more materials with new properties are to be explored. In particular, vdW antiferromagnets are expected to be of great interest. Indeed, recently it has been reported that the layered vdW compound MnBi 2 Te 4 is the first ever antiferromagnetic (AFM) TI [13]. This state of matter is predicted to give rise to exotic phenomena such as quantized magnetoelectric effect [14], axion electrodynamics [15], and Maj...

An interplay of spin-orbit coupling and intrinsic magnetism is known to give rise to the quantum anomalous Hall and topological magnetoelectric effects under certain conditions. Their realization could open access to low power consumption electronics as well as many fundamental phenomena like image magnetic monopoles, Majorana fermions and others. Unfortunately, being realized very recently, these effects are only accessible at extremely low temperatures and the lack of appropriate materials that would enable the temperature increase is a most severe challenge. Here, we propose a novel material platform with unique combination of properties making it perfectly suitable for the realization of both effects at elevated temperatures. The key element of the computational material design is an extension of a topological insulator (TI) surface by a thin film of ferromagnetic insulator, which is both structurally and compositionally compatible with the TI. Following this proposal we suggest a variety of specific systems and discuss their numerous advantages, in particular wide band gaps with the Fermi level located in the gap.

Feasibility of many emergent phenomena that intrinsic magnetic topological insulators (TIs) may host depends crucially on our ability to engineer and efficiently tune their electronic and magnetic structures. Here we report on a large family of intrinsic magnetic TIs in the homologous series of the van der Waals compounds (MnBi2Te4)(Bi2Te3)m with m = 0, ⋯, 6. Magnetic, electronic and, consequently, topological properties of these materials depend strongly on the m value and are thus highly tunable. The antiferromagnetic (AFM) coupling between the neighboring Mn layers strongly weakens on moving from MnBi2Te4 (m = 0) to MnBi4Te7 (m = 1) and MnBi6Te10 (m = 2). Further increase in m leads to change of the overall magnetic behavior to ferromagnetic (FM) one for (m = 3), while the interlayer coupling almost disappears. In this way, the AFM and FM TI states are, respectively, realized in the m = 0, 1, 2 and m = 3 cases. For large m numbers a hitherto-unknown topologically nontrivial phase can be created, in which below the corresponding critical temperature the magnetizations of the non-interacting 2D ferromagnets, formed by the MnBi2Te4 building blocks, are disordered along the third direction. The variety of intrinsic magnetic TI phases in (MnBi2Te4)(Bi2Te3)m allows efficient engineering of functional van der Waals heterostructures for topological quantum computation, as well as antiferromagnetic and 2D spintronics.