The long fascination antiferromagnetic materials have exerted on the scientific community over about a century has been entirely renewed recently with the discovery of several unexpected phenomena including various classes of anomalous spin and charge Hall effects and unconventional magnonic transport, but also homochiral magnetic entities such as skyrmions. With these breakthroughs, antiferromagnets standout as a rich playground for the investigation of novel topological behaviors, and as promising candidate materials for disruptive low-power microelectronic applications. Remarkably, the newly discovered phenomena are all related to the topology of the magnetic, electronic or magnonic ground state of the antiferromagnets. This review exposes how non-trivial topology emerges at different levels in antiferromagnets and explores the novel mechanisms that have been discovered recently. We also discuss how novel classes of quantum magnets could enrich the currently expanding field of antiferromagnetic spintronics and how spin transport can in turn favor a better understanding of exotic quantum excitations.
The recent discovery of antiferromagnetic (AFM) topological insulator (TI) MnBi$_2$Te$_4$ has triggered great research efforts on exploring novel magnetic topological physics. Based on first-principles calculations, we find that the manipulation of magnetic orientation and order not only significantly affects material symmetries and orbital hybridizations, but also results in variant new magnetic topological phases in MnBi$_2$Te$_4$. We thus predict a series of unusual topological quantum phase transitions that are magnetically controllable in the material, including phase transitions from AFM…
We consider antiferromagnets breaking both time-reversal (Theta) and a primitive lattice translational symmetry (T) of a crystal but preserving the combination S = Theta T. The S symmetry leads to a Z_2 topological classification of insulators, separating the ordinary insulator phase from the "antiferromagnetic topological insulator" (AFTI) phase. This state is similar to the "strong" topological insulator with time-reversal symmetry, and shares with it such properties as a quantized magnetoelectric effect. However, for certain surfaces the surface states are intrinsically gapped with a half-q…
We propose to use ferromagnetic insulator MnBi2Se4/Bi2Se3/antiferromagnetic insulator Mn2Bi2Se5 heterostructures for the realization of the axion insulator state. Importantly, the axion insulator state in such heterostructures only depends on the magnetization of the ferromagnetic insulator and hence can be observed in a wide range of external magnetic field. Using density functional calculations and model Hamiltonian simulations, we find that the top and bottom surfaces have opposite half-quantum Hall conductance, with a sizable global spin gap of 5.1 meV opened for the topological surface st…
A topological state with simultaneous nonzero Chern number and spin Chern number is possible for electrons on honeycomb lattice based on band engineering by staggered electric potential and antiferromagnetic exchange field in presence of intrinsic spin-orbit coupling. With first principles calculation we confirm that the scheme can be realized by material modification in perovskite G-type antiferromagnetic insulators grown along [111] direction, where d electrons hop on a single buckled honeycomb lattice. This material is ideal for spintronics applications, since it provides a spin-polarized q…
The magnetic properties of the van der Waals magnetic topological insulators MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$ are investigated by magneto-transport measurements. We evidence that the relative strength of the inter-layer exchange coupling J to the uniaxial anisotropy K controls a transition from an A-type antiferromagnetic order to a ferromagnetic-like metamagnetic state. A bi-layer Stoner-Wohlfarth model allows us to describe this evolution, as well as the typical angular dependence of specific signatures, such as the spin-flop transition of the uniaxial antiferromagnet and the switching fiel…
The second-order magneto-optical effects, represented by Voigt and Schäfer-Hubert effects, are effective methods to detect the spin textures in antiferromagnets, whereas the previous studies are usually limited to collinear antiferromagnets. In noncollinear antiferromagnets, the spin textures characterized by spin chirality have been revealed to play a critical role in many exciting physics. In particular, the first-order topological magneto-optical effects originated from scalar spin chirality have been discovered recently. In this work, using the first-principles calculations and group theor…
The dynamical axion field is a new state of quantum matter where the magnetoelectric response couples strongly to its low-energy magnetic fluctuations. It is fundamentally different from an axion insulator with a static quantized magnetoelectric response. The dynamical axion field exhibits many exotic phenomena such as axionic polariton and axion instability. However, these effects have not been experimentally confirmed due to the lack of proper topological magnetic materials. Here by combining analytic models and first-principles calculations, we predict a series of van der Waal layered Mn$_2…
In this work, we studied time-reversal-breaking topological phases as a result of the interplay between antiferromagnetism and inverted band structures in thin films of antiferromagnetic double perovskite transition-metal Sr$_2$FeOsO$_6$. By combining the first-principles calculations and analytical models, we demonstrate that the quantum anomalous Hall phase and chiral topological superconducting phase can be realized in this system. We find that to achieve time-reversal-breaking topological phases in antiferromagnetic materials, it is essential to break the combined symmetry of time reversal…
We experimentally study the structure and dynamics of magnetic domains in synthetic antiferromagnets based on Co/Ru/Co films. Dramatic effects arise from the interaction among the topological defects comprising the dual domain walls in these structures. Under applied magnetic fields, the dual domain walls propagate following the dynamics of bi-meronic (bi-vortex/bi-antivortex) topological defects built in the walls. Application of an external field triggers a rich dynamical response: The propagation depends on mutual orientation and chirality of bi-vortices and bi-antivortices in the domain wa…
Recently, MnBi2Te4 has been discovered as the first intrinsic antiferromagnetic topological insulator (AFM TI), and will become a promising material to discover exotic topological quantum phenomena. In this work, we have realized the successful synthesis of high-quality MnBi2Te4 single crystals by solid-state reactions. The as-grown MnBi2Te4 single crystal exhibits a van der Waals layered structure, which is composed of septuple Te-Bi-Te-Mn-Te-Bi-Te sequences as determined by powder X-ray diffraction (PXRD) and high-resolution high-angle annular dark field scanning transmission electron micros…
Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which exploits the Néel vector to control the topological electronic states and the associated spin-dependent transport properties. A recently discovered Néel spin-orbit torque has been proposed to electrically manipulate Dirac band crossings in antiferromagnets; however, a reliable AFM material to realize these properties in practice is missing. Here, we predict that room temperature AFM metal MnPd$_{2}$ allows the electrical control of the Dirac nodal line by the Néel spin-orbit torque. Based on first-principle…
The abstract notion of topology has led to profound insights into real materials. Notably, the surface and edges of topological materials can host physics, such as unidirectional charge or spin transport, that is unavailable in isolated one- and two-dimensional systems. However, to fully control the mixing and interference of edge-state wave functions, one needs robust and tunable junctions. We propose to achieve this control using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels on its surface, one from antiferromagnetic domain wal…
The topological states of matters arising from the nontrivial magnetic configuration provide a better understanding of physical properties and functionalities of solid materials. Such studies benefit from the active control of spin orientation in any solid, which is yet known to rarely take place in the two-dimensional (2D) limit. Here we demonstrate by the first-principles calculations that spin-orientation dependent topological states can appear in the geometrically frustrated monolayer antiferromagnet. Different topological states including quantum anomalous Hall (QAH) effect and time-rever…
The recent demonstrations of electrical manipulation and detection of antiferromagnetic spins have opened up a chapter in the spintronics story. In this article, we review the emerging research field that is exploring synergies between antiferromagnetic spintronics and topological structures in real and momentum space. Active topics include proposals to realize Majorana fermions in an antiferromagnetic topological superconductors, to control topological protection of Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topological Hall effects of ze…
We theoretically study the interplay between bulk Weyl electrons and magnetic topological defects, including magnetic domains, domain walls, and $\mathbb{Z}_6$ vortex lines, in the antiferromagnetic Weyl semimetals \mnsn\ and Mn$_3$Ge with negative vector chirality. We argue that these materials possess a hierarchy of energies scales which allows a description of the spin structure and spin dynamics using a XY model with $\mathbb{Z}_6$ anisotropy. We propose a dynamical equation of motion for the XY order parameter, which implies the presence of $\mathbb{Z}_6$ vortex lines, the double-domain p…
The topological electronic structure plays a central role in the non-trivial physical properties in topological quantum materials. A minimal, hydrogen-atom-like topological electronic structure is desired for researches. In this work, we demonstrate an effort towards the realization of such a system in the intrinsic magnetic topological insulator MnBi2Te4, by manipulating the topological surface state (TSS) via surface modification. Using high resolution laser- and synchrotron-based angle-resolved photoemission spectroscopy (ARPES), we found the TSS in MnBi2Te4 is heavily hybridized with a tri…
We theoretically study the effect of low-frequency light pulses in resonance with phonons in the topological and magnetically ordered two septuple-layer (2-SL) MnBi2Te4 (MBT) and MnSb2Te4 (MST). These materials share symmetry properties and an antiferromagnetic ground state in pristine form but present different magnetic exchange interactions. In both materials, shear and breathing Raman phonons can be excited via non-linear interactions with photo-excited infrared phonons using intense laser pulses attainable in current experimental setups. The light-induced transient lattice distortions lead…
The manipulation of antiferromagnetic order by means of spin-orbit torques opens unprecedented opportunities to exploit the dynamics of antiferromagnets in spintronic devices. In this work, we investigate the current-induced switching of the magnetic octupole vector in the Weyl antiferromagnet Mn$_3$Sn as a function of pulse shape, field, temperature, and time. We find that the switching behavior can be either bistable or tristable depending on the temporal structure of the current pulses. Time-resolved Hall effect measurements reveal that Mn$_3$Sn switching proceeds via a two-step demagnetiza…
Antiferromagnetic skyrmion crystals are magnetic phases predicted to exist in antiferromagnets with Dzyaloshinskii-Moriya interactions. Their spatially periodic noncollinear magnetic texture gives rise to topological bulk magnon bands characterized by nonzero Chern numbers. We find topologically-protected chiral magnonic edge states over a wide range of magnetic fields and Dzyaloshinskii-Moriya interaction values. Moreover, and of particular importance for experimental realizations, edge states appear at the lowest possible energies, namely, within the first bulk magnon gap. Thus, antiferromag…
We theoretically study magnon-phonon hybrid excitations (magnon-polarons) in two-dimensional antiferromagnets on a honeycomb lattice. With an in-plane Dzyaloshinskii-Moriya interaction (DMI) allowed from mirror symmetry breaking from phonons, we find non-trivial Berry curvature around the anti-crossing rings among magnon and both optical and acoustic phonon bands, which gives rise to finite Chern numbers. We show that the Chern numbers of the magnon-polaron bands can be manipulated by changing the magnetic field direction or strength. We evaluate the thermal Hall conductivity reflecting the no…
We study three-dimensional nodal line semimetals (NLSMs) with magnetic ordering and strong spin-orbit interaction. Two distinct classes of magnetic NLSMs are proposed. The first class is band-inversion NLSM where the accidental line node is induced by band inversion and locally protected by glide mirror plane and the combined time-reversal and inversion symmetries. This can be viewed as a trivial stacking of the two-dimensional antiferromagnetic Dirac semimetals. The second class is essential NLSM where the nodal features are filling-enforced by specific magnetic symmetry group. We further pro…
A flat band in fermionic system is a dispersionless single-particle state with a diverging effective mass and nearly zero group velocity. These flat bands are expected to support exotic properties in the ground state, which might be important for a wide range of promising physical phenomena. For many applications it is highly desirable to have such states in Dirac materials, but so far they have been reported only in non-magnetic Dirac systems. In this work we propose a realization of topologically protected spin-polarized flat bands generated by domain walls in planar magnetic topological ins…
By means of the first-principles calculations and magnetic topological quantum chemistry, we demonstrate that the low energy physics in the checkerboard antiferromagnetic (AFM) monolayer FeSe, very close to an AFM topological insulator that hosts robust edge states, can be well captured by a double-degenerate fragile topologically flat band just below the Fermi level. The Wilson loop calculations identify that such fragile topology is protected by the $S_{4z}$ symmetry, which gives rise to an AFM higher-order topological insulator that support the bound state with fractional charge $e/2$ at th…
Using an electric field instead of an electric current (or a magnetic field) to tailor the electronic properties of magnetic materials is promising for realizing ultralow energy-consuming memory devices because of the suppression of Joule heating, especially when the devices are scaled to the nanoscale. In the review, we summarize recent results on the giant magnetization and resistivity modulation in a metamagnetic intermetallic alloy - FeRh, which is achieved by electric-field-controlled magnetic phase transitions in multiferroic heterostructures. Furthermore, the approach is extended to top…
Antiferromagnetic topological insulators harbor topological in-gap surface states protected by an anti-unitary $S$ symmetry, which is broken by the inevitable presence of domain walls. Whether an antiferromagnetic topological insulator with domain walls is gapless and metallic on its topological surfaces remains to be elucidated. We show that a single non-statistical index characterizing the magnetic order of domain wall-decorated antiferromagnetic topological insulator, referred to as the Ising moment, determines the topological surface gap, which can be zero even when the $S$ symmetry is man…
We propose a realization of chiral Majorana modes propagating on the hinges of a 3D antiferromagnetic topological insulator, which was recently theoretically predicted and experimentally confirmed in the tetradymite-type $\mathrm{MnBi_2Te_4}$-related ternary chalgogenides. These materials consist of ferromagnetically ordered 2D layers, whose magnetization direction alternates between neighboring layers, forming an antiferromagnetic order. Besides surfaces with a magnetic gap, there also exsist gapless surfaces with a single Dirac cone, which can be gapped out when proximity coupled to an $s$-w…
We investigate spin transport in two dimensional ferromagnetic (FTI) and antiferromagnetic (AFTI) topological insulators. In presence of an in plane magnetization AFTI supports zero energy modes, which enables topologically protected edge conduction at low energy. We address the nature of current-driven spin torque in these structures and study the impact of spin-independent disorder. Interestingly, upon strong disorder the spin torque develops an antidamping component (i.e. {\em even} upon magnetization reversal) along the edges, which could enable current-driven manipulation of the antiferro…
Coexistence of Superconductivity and Antiferromagnetism in Topological Magnet MnBi2Te4 Films
The Pennsylvania State University（宾夕法尼亚州立大学）；Paul Scherrer Institute（保罗谢尔研究所）；National Institute of Standards and Technology（美国国家标准与技术研究院）；National High Magnetic Field Laboratory（国家高磁场实验室）
Magnetic solitons offer functionalities as information carriers in multiple spintronic and magnonic applications. However, their potential for nanoscale energy transport has not been revealed. Here we demonstrate that antiferromagnetic solitons, e.g. domain walls, can uptake, transport and release energy. The key for this functionality resides in their relativistic kinematics; their self-energy increases with velocity due to Lorentz contraction of the soliton and their dynamics can be accelerated up to the effective speed of light of the magnetic medium. Furthermore, their classification in ro…
We study the behavior of non-equilibrium spin density and spin-orbit torque in a topological insulator - antiferromagnet heterostructure. Unlike ferromagnetic heterostructures where Dirac cone is gapped due to time-reversal symmetry breaking, here the Dirac cone is preserved. We demonstrate the existence of a staggered spin density corresponding to a damping like torque, which is quite robust against the scalar impurity, when the transport energy is in the topological insulator surface energy regime. We show the contribution to the non-equilibrium spin density due to both surface and bulk topo…
The existence of the magnetostatic surface spin waves in ferromagnets, known as Damon-Eshbach mode, was recently demonstrated to originate from the topology of the dipole-dipole interaction. In this work, we study the topological characteristics of magnons in easy-axis antiferromagnets with uniaxial anisotropy. The dipolar spin waves are found to be, driven by the dipole-dipole interaction, in a topological nodal-line semimetal phase, which hosts Damon-Eshbach-type surface modes due to the bulk-edge correspondence. The long wavelength character of dipolar spin waves makes our proposal valid fo…
A rich variety of specific multidomain textures recently observed in antiferromagnetically coupled multilayers with perpendicular anisotropy include regular (equilibrium) multidomain states as well as different types of topological magnetic defects. Within a phenomenological theory we have classified and analyzed the possible magnetic defects in the antiferromagnetic ground state and determine their structures. We have derived the optimal sizes of the defects as functions of the antiferromagnetic exchange, the applied magnetic field, and geometrical parameters of the multilayer. The calculated…
Topological quantum matter and spintronics research have been developed to a large extent independently. In this Review we discuss a new role that the antiferromagnetic order has taken in combining topological matter and spintronics. This occurs due to the complex microscopic symmetries present in antiferromagnets that allow, e.g., for topological relativistic quasiparticles and the newly discovered Néel spin-orbit torques to coexist. We first introduce the concepts of topological semimetals and spin-orbitronics. Secondly, we explain the antiferromagnetic symmetries on a minimal Dirac semimeta…
We investigated the topological property of magnon bands in the collinear magnetic orders of zigzag and stripy phases for the antiferromagnetic honeycomb lattice and identified Berry curvature and symmetry constraints on the magnon band structure. Different symmetries of both zigzag and stripy phases lead to different topological properties, in particular, the magnon bands of the stripy phase being disentangled with a finite Dzyaloshinskii-Moriya (DM) term with non-zero spin Chern number. This is corroborated by calculating the spin Nernst effect. Our study establishes the existence of the non…
The antiferromagnetic topological insulator MnBi2Te4 (MBT) exhibits an ideal platform to study exotic topological phenomena and magnetic properties. The transport signatures of magnetic phase transitions in the MBT family materials have been well-studied. However, their mechanical properties and magneto-mechanical coupling have not been well-explored. We use nanoelectromechanical systems to study the intrinsic magnetism in MBT thin flakes via their magnetostrictive coupling. We investigate mechanical resonance signatures of magnetic phase transitions from antiferromagnetic (AFM) to canted anti…
We propose a spintronics-based hardware implementation of neuromorphic computing, specifically, the spiking neural network, using topological winding textures in one-dimensional antiferromagnets. The consistency of such a network is emphasized in light of the conservation of topological charges, and the natural spatiotemporal interconversions of magnetic winding. We discuss the realization of the leaky integrate-and-fire behavior of neurons and the spike-timing-dependent plasticity of synapses. Our proposal opens the possibility for an all-spin neuromorphic platform based on antiferromagnetic …
We study the effect of electrostatic disorder on the conductivity of a three-dimensional antiferromagnetic insulator (a stack of quantum anomalous Hall layers with staggered magnetization). The phase diagram contains regions where the increase of disorder first causes the appearance of surface conduction (via a topological phase transition), followed by the appearance of bulk conduction (via a metal-insulator transition). The conducting surface states are stabilized by an effective time-reversal symmetry that is broken locally by the disorder but restored on long length scales. A simple self-c…
We predict that junctions between an antiferromagnetic insulator and a superconductor provide a robust platform to create a one-dimensional topological superconducting state. Its emergence does not require the presence of intrinsic spin-orbit coupling nor non-collinear magnetism, but arises solely from repulsive electronic interactions on interfacial solitonic states. We demonstrate that a topological superconducting state is generated by repulsive interactions at arbitrarily small coupling strength, and that the size of the topological gap rapidly saturates to the one of the parent trivial su…
Two-dimensional topological superconductivity has attracted great interest due to the emergence of Majorana modes bound to vortices and propagating along edges. However, due to its rare appearance in natural compounds, experimental realizations rely on a delicate artificial engineering involving materials with helical states, magnetic fields and conventional superconductors. Here we introduce an alternative path using a class of three-dimensional antiferromagnet to engineer a two- dimensional topological superconductor. Our proposal exploits the appearance of solitonic states at the interface …
CrSb is an attractive material for room-temperature antiferromagnetic spintronic applications because of its high Néel temperature $\sim$700 K and semi-metallic character. We study the magnetic properties of CrSb bilayers on few-layer topological insulator thin films using \emph{ab initio} density functional theory. We find that the intrinsic parts of the total anomalous Hall conductivities of the thin films are non-zero, and approximately quantized. The Néel temperature of CrSb bilayers on few-layer topological insulator thin films is found to be approximately two times larger than that of an…
Recently, the magnetic domain walls have been experimentally observed in antiferromagnetic topological insulators MnBi$_2$Te$_4$, where we find that the topological zero-line modes (ZLMs) appear along the domain walls. Here, we theoretically demonstrate that these ZLMs are layer-dependent in MnBi$_2$Te$_4$ multilayers. For domain walls with out-of-plane ferromagnetism, we find that ZLMs are equally distributed in the odd-number layers. When domain walls possess in-plane magnetization, the ZLMs can also exist in even-number layers due to in-plane mirror-symmetry breaking. Moreover, the conducti…
The two dimensional square lattice antiferromagnet with spin-orbit coupling and nonsymmorphic symmetry is recently found to be topological insulator (TI). We theoretically studied the Floquet states of the antiferromagnetic crystal with optical irradiation, which could be applicable in opto-spintronic. An optical irradiation with circular polarization induces topological phase transition into quantum Anomalous Hall (QAH) phase with varying Chern number. At the phase boundaries, the Floquet systems could be semimetal with one, two or three band valleys. A linear polarized optical field induces …
We report on the formation of topological defects emerging from the cycloidal antiferromagnetic order at the surface of bulk BiFeO$_3$ crystals. Combining reciprocal and real-space magnetic imaging techniques, we first observe, in a single ferroelectric domain, the coexistence of antiferromagnetic domains in which the antiferromagnetic cycloid propagates along different wavevectors. We then show that the direction of these wavevectors is not strictly locked to the preferred crystallographic axes as continuous rotations bridge different wavevectors. At the junctions between the magnetic domains…
The gapless surface Dirac cone of time reversal invariant topological insulators is protected by time reversal symmetry due to the Kramers' theorem. Spin degree of freedom is usually required since Kramers' theorem only guarantees double degeneracy for spinful fermions, but not for spinless fermions. In this paper, we present an antiferromagnetic spinless model, which breaks time reversal symmetry. Similar to time reversal invariant topological insulators, this model possesses a topologically non-trivial phase with a single surface Dirac cone, which is protected by the combination of time reve…
We demonstrate theoretically that the thermal Hall effect of magnons in collinear antiferromagnetic insulators is an indicator of magnetic and topological phase transitions in the magnon spectrum. The transversal heat current of magnons caused by a thermal gradient is calculated for an antiferromagnet on a honeycomb lattice. An applied magnetic field drives the system from the antiferromagnetic phase via a spin-flop phase into the field-polarized phase. Besides these magnetic phase transitions we find topological phase transitions within the spin-flop phase. Both types of transitions manifest …
