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Chern insulators are two-dimensional magnetic topological materials that conduct electricity along their edges via the one-dimensional chiral modes. The number of these modes is a topological invariant called the first Chern number C that defines the quantized Hall conductance as Sxy = Ce2/h. Increasing C is pivotal for the realization of low-power-consumption topological electronics, but there has been no clear-cut solution to this problem so far, with the majority of existing Chern insulators showing C = 1. Here, by using state-of-the-art theoretical methods, we propose an efficient approach for the realization of the high-C state in MnBi2Te4/hBN van der Waals multilayer heterostructures. We show that a stack of n MnBi2Te4 films with C = 1 intercalated by hBN monolayers gives rise to a high Chern number state with C = n, characterized by n chiral edge modes. This state can be achieved both under the external magnetic field and without it, both cases leading to the quantized Hall conductance Sxy = Ce2/h. Our results, therefore, pave the way to practical high-C quantized Hall systems.

Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics.

Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics.

Using density functional theory, we propose the (MnSb2Te4)·(Sb2Te3)n family of stoichiometric van der Waals compounds that harbor multiple topologically nontrivial magnetic phases. In the ground state, the first three members of the family (n = 0, 1, 2) are 3D antiferromagnetic topological insulators, while for n ≥ 3 a special phase is formed, in which a nontrivial topological order coexists with a partial magnetic disorder in the system of the decoupled 2D ferromagnets, whose magnetizations point randomly along the third direction. Furthermore, due to a weak interlayer exchange coupling, these materials can be field-driven into the FM Weyl semimetal (n = 0) or FM axion insulator states (n ≥ 1). Finally, in two dimensions, we reveal these systems to show intrinsic quantum anomalous Hall and AFM axion insulator states, as well as quantum Hall state, achieved under external magnetic field. Our results demonstrate that MnSb2Te4 is not topologically trivial as was previously believed that opens possibilities of realization of a wealth of topologically nontrivial states in the (MnSb2Te4)·(Sb2Te3)n family.

We present a combined experimental and theoretical study of the two-dimensional electron states at the iridium-silicide surface of the antiferromagnet GdIr2Si2 above and below the Néel temperature. Using angle-resolved photoemission spectroscopy (ARPES) we find a significant spin-orbit splitting of the surface states in the paramagnetic phase. By means of ab initio density-functional-theory (DFT) calculations we establish that the surface electron states that reside in the projected band gap around the ¯¯¯¯M point exhibit very different spin structures which are governed by the conventional and the cubic Rashba effect. The latter is reflected in a triple spin winding, i.e., the surface electron spin reveals three complete rotations upon moving once around the constant energy contours. Below the Néel temperature, our ARPES measurements show an intricate photoemission intensity picture characteristic of a complex magnetic domain structure. The orientation of the domains, however, can be clarified from a comparative analysis of the ARPES data and their DFT modeling. To characterize a single magnetic domain picture, we resort to the calculations and scrutinize the interplay of the Rashba spin-orbit coupling field with the in-plane exchange field, provided by the ferromagnetically ordered 4f moments of the near-surface Gd layer.

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 EuIr2Si2, 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.

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order. Unlike their nonmagnetic counterparts, magnetic topological insulators may have some of the surfaces gapped, which enables a number of exotic phenomena that have potential applications in spintronics, such as the quantum anomalous Hall effect and chiral Majorana fermions. So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators 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. An intrinsic magnetic topological insulator—a stoichiometric well ordered magnetic compound—could be an ideal solution to these problems, but no such material has been observed so far. Here we predict by ab initio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBiTe. The antiferromagnetic ordering that MnBiTe shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to a ℤ topological classification; ℤ = 1 for MnBiTe, confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBiTe exhibits a large bandgap in the topological surface state. We expect this property to eventually enable the observation of a number of fundamental phenomena, among them quantized magnetoelectric coupling and axion electrodynamics. Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect and chiral Majorana fermions.

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 two-dimensional 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 band gap 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.

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 EuIrSi, where in contrast to its non-magnetic 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.