Weyl Magnons Research Articles

An efficient material search for room-temperature topological magnons.

Topologically protected magnon surface states are highly desirable as an ideal platform to engineer low-dissipation spintronics devices. However, theoretical prediction of topological magnons in strongly correlated materials proves to be challenging because the ab initio density functional theory calculations fail to reliably predict magnetic interactions in correlated materials. Here, we present a symmetry-based approach, which predicts topological magnons in magnetically ordered crystals, upon applying external perturbations such as magnetic/electric fields and/or mechanical strains. We apply this approach to carry out an efficient search for magnetic materials in the Bilbao Crystallographic Server, where, among 198 compounds with an over 300-K transition temperature, we identify 12 magnetic insulators that support room-temperature topological magnons. They feature Weyl magnons with surface magnon arcs and magnon axion insulators with either chiral surface or hinge magnon modes, offering a route to realize energy-efficient devices based on protected surface magnons.

Type-II Weyl Excitation in Vortex Arrays

Weyl-like magnon excitations in ordered magnets have attracted significant recent attention. Despite the tantalizing physics and application prospects, the experimental observation of Weyl magnons is still challenging owing to their extraordinarily high frequency that is not accessible to the microstrip antenna technique. Here we predict gigahertz Weyl excitations in the collective dynamics of dipolar-coupled magnetic vortices arranged in a three-dimensional stacked honeycomb lattice. It is found that inversion symmetry breaking leads to the emergence of the type-II Weyl semimetal (WSM) state with tilted dispersion. We derive the full phase diagram of the vortex arrays that support WSMs with both single and double pairs of Weyl nodes, and the topological insulator phase. We observe robust arc surface states in a dual-segment fashion due to the tilted nature of type-II WSMs. Our findings uncover the low-frequency WSM phase in magnetic-texture-based crystals that are indispensable for future Weyltronic applications.

Topological Weyl magnons and thermal Hall effect in layered honeycomb ferromagnets

In this work, we study the topological properties and magnon Hall effect of a three-dimensional ferromagnet in the ABC stacking honeycomb lattice, motivated by the recent inelastic neutron scattering study of $\mathrm{Cr}{\mathrm{I}}_{3}$. We show that the magnon band structure and Chern numbers of the magnon branches are significantly affected by the interlayer coupling ${J}_{c}$, which moreover has a qualitatively different effect in the ABC stacking compared to the AA stacking adopted by other authors. The nontrivial Chern number of the lowest magnon band is stabilized by the next-nearest-neighbor Dzyaloshinskii-Moriya interaction in each honeycomb layer, resulting in the hopping term similar to that in the electronic Haldane model for graphene. However, we also find several gapless Weyl points, separating the nonequivalent Chern insulating phases, tuned by the ratio of the interlayer coupling ${J}_{c}$ and the third-neighbor Heisenberg interaction ${J}_{3}$. We further show that the topological character of magnon bands results in nonzero thermal Hall conductivity, whose sign and magnitude depend on ${J}_{c}$ and the intralayer couplings. Since the interlayer coupling strength ${J}_{c}$ can be easily tuned by applying pressure to the quasi-2D material such as $\mathrm{Cr}{\mathrm{I}}_{3}$, this provides a potential route to tuning the magnon thermal Hall effect in an experiment.

Topological transitions of spin-excitations in insulating chiral antiferromagnets

We present a comprehensive study of strain-induced topological magnon phase transitions in insulating three-dimensional (3D) topological chiral antiferromagnets on the kagome-lattice. We show that by applying (100) uniaxial strain, 3D insulating antiferromagnetic Weyl magnons (WMs) manifest as an intermediate phase between a strain-induced 3D magnon Chern insulator (MCI) with integer Chern numbers and a 3D trivial magnon insulator with zero Chern number. In addition, we show that strain suppresses the topological thermal Hall conductivity of magnons in these systems. Due to the similarity between 3D insulating and metallic kagome chiral antiferromagnets, we envision that the current results could also manifest in the 3D antiferromagnetic topological Weyl semimetals Mn3Sn/Ge.

Spin dynamics of a magnetic Weyl semimetal Sr1−xMn1−ySb2

Dirac matters provide a platform for exploring the interplay of their carriers with other quantum phenomena. Sr$_{1-x}$Mn$_{1-y}$Sb$_2$ has been proposed to be a magnetic Weyl semimetal and provides an excellent platform to study the coupling between Weyl fermions and magnons. Here, we report comprehensive inelastic neutron scattering (INS) measurements on single crystals of Sr$_{1-x}$Mn$_{1-y}$Sb$_2$, which have been well characterized by magnetization and magnetotransport measurements, both of which demonstrate that the material is a topologically nontrivial semimetal. The INS spectra clearly show a spin gap of $\sim6$ meV. The dispersion in the magnetic Mn layer extends up to about 76 meV, while that between the layers has a narrow band width of 6 meV. We find that the linear spin-wave theory using a Heisenberg spin Hamiltonian can reproduce the experimental spectra with the following parameters: a nearest-neighbor ($SJ_1\sim28.0$ meV) and next-nearest-neighbor in-plane exchange interaction ($SJ_2\sim9.3$ meV) , interlayer exchange coupling ($SJ_c\sim-0.1$ meV), and spin anisotropy constant ($SD\sim-0.07$ meV). Despite the coexistence of Weyl fermions and magnons, we find no clear evidence that the magnetic dynamics are influenced by the Weyl fermions in Sr$_{1-x}$Mn$_{1-y}$Sb$_2$, possibly because that the Weyl fermions and magnons reside in the Sb and Mn layers separately, and the interlayer coupling is weak due to the quasi-two-dimensional nature of the material, as also evident from the small $SJ_c$ of -0.1 meV.

Magnonic Weyl states in Cu2OSeO3

The multiferroic ferrimagnet Cu$_2$OSeO$_3$ with a chiral crystal structure attracted a lot of recent attention due to the emergence of magnetic skyrmion order in this material. Here, the topological properties of its magnon excitations are systematically investigated by linear spin-wave theory and inelastic neutron scattering. When considering Heisenberg exchange interactions only, two degenerate Weyl magnon nodes with topological charges $\pm$2 are observed at high-symmetry points. Each Weyl point splits into two as the symmetry of the system is further reduced by including into consideration the nearest-neighbor Dzyaloshinsky-Moriya interaction, crucial for obtaining an accurate fit to the experimental spin-wave spectrum. The predicted topological properties are verified by surface state and Chern number analysis. Additionally, we predict that a measurable thermal Hall conductivity can be associated with the emergence of the Weyl points, the position of which can be tuned by changing the crystal symmetry of the material.

Photo-induced Floquet Weyl magnons in noncollinear antiferromagnets

We study periodically driven insulating noncollinear stacked kagome antiferromagnets with a conventional symmetry-protected three-dimensional (3D) in-plane 120° spin structure, with either positive or negative vector chirality. We show that the symmetry protection of the in-plane 120° spin structure can be broken in the presence of an off-resonant circularly or linearly polarized electric field propagating parallel to the in-plane 120° spin structure (say along the x direction). Consequently, topological Floquet Weyl magnon nodes with opposite chirality are photoinduced along the kx momentum direction. They manifest as the monopoles of the photoinduced Berry curvature. We also show that the system exhibits a photoinduced magnon thermal Hall effect for circularly polarized electric field. Furthermore, we show that the photoinduced chiral spin structure is a canted 3D in-plane 120° spin structure, which was recently observed in the equilibrium noncollinear antiferromagnetic Weyl semimetals Mn3Sn/Ge. Our result not only paves the way towards the experimental realization of Weyl magnons and photoinduced thermal Hall effects, but also provides a powerful mechanism for manipulating the intrinsic properties of 3D topological antiferromagnets.

Topological thermal Hall effect due to Weyl magnons

We present the first theoretical evidence of zero magnetic field topological (anomalous) thermal Hall effect due to Weyl magnons in stacked noncoplanar frustrated kagomé antiferromagnets. The Weyl magnons in this system result from macroscopically broken time-reversal symmetry by the scalar spin chirality of noncoplanar chiral spin textures. Most importantly, they come from the lowest excitation, therefore they can be easily observed experimentally at low temperatures due to the population effect. Similar to electronic Weyl nodes close to the Fermi energy, Weyl magnon nodes at the lowest excitation are the most important. Indeed, we show that the topological (anomalous) thermal Hall effect in this system arises from nonvanishing Berry curvature due to Weyl magnon nodes at the lowest excitation, and it depends on their distribution (distance) in momentum space. The present result paves the way to directly probe low excitation Weyl magnons and macroscopically broken time-reversal symmetry in three-dimensional frustrated magnets with the anomalous thermal Hall effect.

Floquet Weyl Magnons in Three-Dimensional Quantum Magnets

In three-dimensional (3D) quantum magnets, magnonic Weyl points (WPs) featuring linear band crossing of two non-degenerate magnon branches can emerge in certain lattice geometry when time-reversal symmetry is broken macroscopically. Unfortunately, there are very limited 3D quantum magnets that host magnonic WPs, and they are yet to be observed experimentally because the intrinsic perturbative interactions that break time-reversal symmetry macroscopically can be very negligible. Here, we present an alternative means via photo-irradiation, in which magnonic WPs can emerge in 3D quantum magnets without relying on intrinsic perturbative interactions to break time-reversal symmetry. By utilizing the magnonic Floquet-Bloch theory, we put forward the general theory of magnonic Floquet WPs in 3D quantum magnets. We show that periodically driven 3D magnonic Dirac nodal-line (DNL) and 3D magnonic gapped trivial insulators can generate 3D magnonic Floquet WPs, which can be tuned by the incident circularly-polarized light. We demonstrate the existence of magnonic Floquet WPs by combining the study of the magnon dispersions, Berry curvatures, and the anomalous thermal Hall effect. The general theoretical formalism can be applied to different magnetic insulators, and thus extending the concept of magnonic WPs to a broader class of 3D magnetically ordered systems.

Chiral topological insulator of magnons

We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to opening of the gap. Finally, we show that by changing certain parameters the system can be tuned between the chiral topological insulator (mcTI), three dimensional magnon anomalous Hall (3D-mAH), and Weyl magnon phases.

Spin Hall and Nernst effects of Weyl magnons

In this paper, we present a simple model of a three-dimensional insulating magnetic structure which represents a magnonic analog of the layered electronic system described in [Phys. Rev. Lett. {\bf 107}, 127205 (2011)]. In particular, our model realizes Weyl magnons as well as surface states with a Dirac spectrum. In this model, the Dzyaloshinskii-Moriya interaction is responsible for the separation of opposite Weyl points in momentum space. We calculate the intrinsic (due to the Berry curvature) transport properties of Weyl and so-called anomalous Hall effect (AHE) magnons. The results are compared with fermionic analogs.

Weyl magnons in pyrochlore antiferromagnets with an all-in-all-out order

We investigate novel topological magnon band crossings of pyrochlore antiferromagnets with all-in-all-out (AIAO) magnetic order. By general symmetry analysis and spin-wave theory, we show that pyrochlore materials with AIAO orders can host Weyl magnons under external magnetic fields or uniaxial strains. Under a small magnetic field, the magnon bands of the pyrochlore with AIAO background can feature two opposite-charged Weyl points, which is the minimal number of Weyl points realizable in quantum materials and has not be experimentally observed so far. We further show that breathing pyrochlores with AIAO orders can exhibit Weyl magnons upon uniaxial strains. These findings apply to any pyrochlore material supporting AIAO orders, irrespective of the forms of interactions. Specifically, we show that the Weyl magnons are robust against direct (positive) Dzyaloshinskii-Moriya interactions. Because of the ubiquitous AIAO orders in pyrochlore magnets including R$_2$Ir$_2$O$_7$, and experimentally achievable external strain and magnetic field, our predictions provide promising arena to witness the Weyl magnons in quantum magnets.

Weyl magnons in noncoplanar stacked kagome antiferromagnets

Weyl nodes have been experimentally realized in photonic, electronic, and phononic crystals. However, magnonic Weyl nodes are yet to be seen experimentally. In this paper, we propose Weyl magnon nodes in noncoplanar stacked frustrated kagome antiferromagnets, naturally available in various real materials. Most crucially, the Weyl nodes in the current system occur at the lowest excitation and possess a topological (anomalous) thermal Hall effect, therefore they are experimentally accessible at low temperatures due to the population effect of bosonic quasiparticles. In stark contrast to other magnetic systems, the current Weyl nodes do not rely on time-reversal symmetry breaking by the magnetic order. Rather, they result from explicit macroscopically broken time reversal symmetry by the scalar spin chirality of noncoplanar spin textures, and can be generalized to chiral spin liquid states. Moreover, the scalar spin chirality gives a real space Berry curvature which is not available in previously studied magnetic Weyl systems. We show the existence of magnon arc surface states connecting projected Weyl magnon nodes on the surface Brillouin zone. We also uncover the first realization of triply-degenerate nodal magnon point in the non-collinear regime with zero scalar spin chirality.

Chiral anomaly of Weyl magnons in stacked honeycomb ferromagnets

Chiral anomaly of Weyl magnons (WMs), featured by nontrivial band crossings at paired Weyl nodes (WNs) of opposite chirality, is investigated. It is shown that WMs can be realized in stacked honeycomb ferromagnets. Using the Aharonov-Casher effect that is about the interaction between magnetic moments and electric fields, the magnon motion in honeycomb layers can be quantized into magnonic Landau levels (MLLs). The zeroth MLL is chiral so that unidirectional WMs propagate in the perpendicular (to the layer) direction for a given WN under a magnetic field gradient from one WN to the other and change their chiralities, resulting in the magnonic chiral anomaly (MCA). A net magnon current carrying spin and heat through the zeroth MLL depends linearly on the magnetic field gradient and the electric field gradient in the ballistic transport.

Floquet topological magnons

We introduce the concept of Floquet topological magnons—a mechanism by which a synthetic tunable Dzyaloshinskii–Moriya interaction (DMI) can be generated in quantum magnets using circularly polarized electric (laser) field. The resulting effect is that Dirac magnons and nodal-line magnons in two-dimensional and three-dimensional quantum magnets can be tuned to magnon Chern insulators and Weyl magnons respectively under circularly polarized laser field. The Floquet formalism also yields a tunable intrinsic DMI in insulating quantum magnets without an inversion center. We demonstrate that the Floquet topological magnons possess a finite thermal Hall conductivity tunable by the laser field.

Weyl and Nodal Ring Magnons in Three-Dimensional Honeycomb Lattices**Supported by the National Basic Research Program of China under Grant No 2015CB921300, the National Natural Science Foundation of China under Grant No 11334012, and the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No XDB07000000.

We study the topological properties of magnon excitations in a wide class of three-dimensional (3D) honeycomb lattices with ferromagnetic ground states. It is found that they host nodal ring magnon excitations. These rings locate on the same plane in the momentum space. The nodal ring degeneracy can be lifted by the Dzyaloshinskii–Moriya interactions to form two Weyl points with opposite charges. We explicitly discuss these physics in the simplest 3D honeycomb lattice and the hyperhoneycomb lattice, and show drumhead and arc surface states in the nodal ring and Weyl phases, respectively, due to the bulk-boundary correspondence.

Kitaev materials beyond iridates: Order by quantum disorder and Weyl magnons in rare-earth double perovskites

Motivated by the experiments on the rare-earth double perovskites, we propose a generalized Kitaev-Heisenberg model to describe the generic interaction between the spin-orbit-entangled Kramers' doublets of the rare-earth moments. We carry out a systematic analysis of the mean-field phase diagram of this new model. In the phase diagram, there exist large regions with a continuous U(1) or O(3) degeneracy. Since no symmetry of the model protects such a continuous degeneracy, we predict that the quantum fluctuation lifts the continuous degeneracy and favors various magnetic orders in the phase diagram. From this order by quantum disorder mechanism, we further predict that the magnetic excitations of the resulting ordered phases are characterized by nearly gapless pseudo-Goldstone modes. We find that there exist Weyl magnon excitations for certain magnetic orders. We expect our prediction to inspire further study of Kitaev physics, the order by quantum disorder phenomenon and topological spin wave modes in the rare-earth magnets and the systems alike.

Tunable Magnon Weyl Points in Ferromagnetic Pyrochlores.

The dispersion relations of magnons in ferromagnetic pyrochlores with Dzyaloshinskii-Moriya interaction are shown to possess Weyl points, i. e., pairs of topologically nontrivial crossings of two magnon branches with opposite topological charge. As a consequence of their topological nature, their projections onto a surface are connected by magnon arcs, thereby resembling closely Fermi arcs of electronic Weyl semimetals. On top of this, the positions of the Weyl points in reciprocal space can be tuned widely by an external magnetic field: rotated within the surface plane, the Weyl points and magnon arcs are rotated as well; tilting the magnetic field out of plane shifts the Weyl points toward the center Γ[over ¯] of the surface Brillouin zone. The theory is valid for the class of ferromagnetic pyrochlores, i. e., three-dimensional extensions of topological magnon insulators on kagome lattices. In this Letter, we focus on the (111) surface, identify candidates of established ferromagnetic pyrochlores which apply to the considered spin model, and suggest experiments for the detection of the topological features.

Weyl magnons in breathing pyrochlore antiferromagnets.

Frustrated quantum magnets not only provide exotic ground states and unusual magnetic structures, but also support unconventional excitations in many cases. Using a physically relevant spin model for a breathing pyrochlore lattice, we discuss the presence of topological linear band crossings of magnons in antiferromagnets. These are the analogues of Weyl fermions in electronic systems, which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral magnon surface states forming arcs at finite energy. We argue that such antiferromagnets present a unique example, in which Weyl points can be manipulated in situ in the laboratory by applied fields. We discuss their appearance specifically in the breathing pyrochlore lattice, and give some general discussion of conditions to find Weyl magnons, and how they may be probed experimentally. Our work may inspire a re-examination of the magnetic excitations in many magnetically ordered systems.