¦ van der Waals gap Septuple layer J § J || T 1/2 J 0,1 || J 0,2 || J 0,3 || J 0,4 ||

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.

The development of materials that are non-magnetic in the bulk but exhibit two-dimensional (2D) magnetism at the surface is at the core of spintronics applications. Here, we present the valence-fluctuating material EuIr 2 Si 2 , where in contrast to its nonmagnetic bulk, the Si-terminated surface reveals controllable 2D ferromagnetism. Close to the surface the Eu ions prefer a magnetic divalent configuration and their large 4f moments order below 48 K. The emerging exchange interaction modifies the spin polarization of the 2D surface electrons originally induced by the strong Rashba effect. The temperature-dependent mixed valence of the bulk allows to tune the energy and momentum size of the projected band gaps to which the 2D electrons are confined. This gives an additional degree of freedom to handle spin-polarized electrons at the surface. Our findings disclose valence-fluctuating rare-earth based materials as a very promising basis for the development of systems with controllable 2D magnetic properties which is of interest both for fundamental science and applications.