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.
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 magnons in two-dimensional (2D) and three-dimensional (3D) 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 th…
We study irradiated two-dimensional insulating bilayer honeycomb ferromagnets and antiferromagnets coupled antiferromagnetically with a zero net magnetization. The former is realized in the recently synthesized bilayer honeycomb chromium triiodide CrI$_{\bf 3}$. In both systems, we show that circularly-polarized electric field breaks time-reversal symmetry and induces a dynamical Dzyaloshinskii-Moriya interaction in each honeycomb layer. However, the resulting bilayer antiferromagnetic system still preserves a combination of time-reversal and space-inversion ($\mathcal{PT}$) symmetry. We show …
We introduce the magnonic Floquet Hofstadter butterfly in the two-dimensional insulating honeycomb ferromagnet. We show that when the insulating honeycomb ferromagnet is irradiated by an oscillating space- and time-dependent electric field, the hopping magnetic dipole moment (i.e. magnon quasiparticles) accumulate the Aharonov-Casher phase. In the case of only space-dependent electric field, we realize the magnonic Hofstadter spectrum with similar fractal structure as graphene subject to a perpendicular magnetic field, but with no spin degeneracy due to broken time-reversal symmetry by the fer…
We study periodically driven pure Kitaev model and ferromagnetic phase of the Kitaev-Heisenberg model on the honeycomb lattice by off-resonant linearly and circularly-polarized lights at zero magnetic field. Using a combination of linear spin wave and Floquet theories, we show that the effective time-independent Hamiltonians in the off-resonant regime map onto the corresponding anisotropic static spin model, plus a tunable photoinduced magnetic field along the $[111]$ direction, which precipitates Floquet topological magnons and chiral magnon edge modes. They are tunable by the light amplitude…
We study periodically driven insulating noncollinear stacked kagome antiferromagnets with a conventional symmetry-protected three-dimensional (3D) in-plane $120^\circ$ spin structure, with either positive or negative vector chirality. We show that the symmetry protection of the in-plane $120^\circ$ spin structure can be broken in the presence of an off-resonant circularly or linearly polarized electric field propagating parallel to the in-plane $120^\circ$ spin structure (say along the $x$ direction). Consequently, topological Floquet Weyl magnon nodes with opposite chirality are photoinduced …
Floquet-Weyl states at one-photon resonances in three-dimensional topological insulators
The University of Tokyo（东京大学）；Tokyo University of Science（东京理科大学）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所 物质创造科学研究中心）；Hiroshima University（广岛大学）
We present the first theoretical evidence of zero magnetic field topological (anomalous) thermal Hall effect due to Weyl magnons. Here, we consider Weyl magnons in stacked noncoplanar frustrated kagomé antiferromagnets recently proposed by Owerre, [arXiv:1708.04240]. 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 electr…
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 analogs 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…
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 ma…
When irradiated via high frequency circularly polarized light, the stroboscopic dynamics in a Heisenberg spin system on a honeycomb lattice develops a next nearest neighbor (NNN) Dzyaloshinskii-Moriya (DM) type term\cite{owerre}, making it a magnonic Floquet topological insulator. We investigate the entanglement generation and its evolution on such systems - particularly an irradiated ferromagnetic XXZ spin-$\frac{1}{2}$ model in a honeycomb lattice as the system parameters are optically tuned. In the high frequency limit, we compute the lowest quasi-energy state entanglement in terms of the c…
A saddle point plus fluctuations analysis of the periodically driven half-filled two-dimensional Hubbard model is performed. For drive frequencies below the equilibrium gap, we find discontinuous transitions to time-dependent solutions. A highly excited, generically non-thermal distribution of magnons occurs even for drive frequencies far above the gap. Above a critical drive amplitude, the low-energy magnon distribution diverges as the frequency tends to zero and antiferromagnetism is destroyed, revealing the generic importance of collective mode excitations arising from a non-equilibrium dri…
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 CrI$_3$. 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-neighbour Dzyaloshinsky-Mor…
The periodic driving of a quantum system can enable new topological phases without analogs in static systems. This provides a route towards preparing non-equilibrium quantum phases rooted into the non-equilibrium nature by periodic driving engineering. Motivated by the ongoing considerable interest in topological semimetals, we are interested in the novel topological phases in the periodically driven topological semimetals without a static counterpart. We propose to design non-equilibrium topological semimetals in the regime of weakly driving field where the spectrum width of shares the same m…
When a Dirac semimetal is subject to a circularly polarized laser, it is predicted that the Dirac cone splits into two Weyl nodes and a nonequilibrium transient state called the Floquet Weyl semimetal is realized. We focus on the previously unexplored low-frequency regime, where the upper and lower Dirac bands resonantly couple with each other through multi-photon processes, which is a realistic situation in solid state ultrafast pump-probe experiments. We find a series of new Weyl nodes emerging in pairs when the Floquet replica bands hybridize with each other. The nature of the Floquet Weyl …
The dispersion relations of magnons in ferromagnetic pyrochlores with Dzyaloshinskii-Moriya interaction is shown to possess Weyl points, i.\,e., pairs of topological 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 magn…
We study the inelastic neutron scattering cross section in the vicinity of touching points in magnon bands. Among the possible touching points are magnon Weyl points in three dimensional ordered magnets with significant spin-orbit coupling that are characterized by a linear dispersion in their vicinity. A Weyl point is topologically protected by its net chirality and here we show that this leads to a characteristic form for the dynamical structure factor. To address this question, we show that scattering intensities in the vicinity of arbitrary magnon two-band touching points are identical to …
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 pyrochlore…
Towards the First Realization of Weyl Magnons in the Non-Coplanar Antiferromagnet MnTe$_2$
The Ohio State University（俄亥俄州立大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Oak Ridge National Laboratory（橡树岭国家实验室）；Duke University（杜克大学）
It is generally believed that non-Hermiticity can transform Weyl semimetals into Weyl-exceptional-ring semimetals. However, this belief is from the systems without skin effect. We investigate the non-Hermitian Weyl semimental and its Floquet engineering in a system with skin effect, which breaks the bulk-boundary correspondence in its Hermitian counterpart. It is found in both the static and periodically driven cases that the skin effect makes this general belief no longer valid. We discover that exotic non-Hermitian topological matters, e.g., a composite phase of Weyl semimetal and topologica…
Weyl fermions, which are fermions with definite chiralities, can give rise to anomalous breaking of the symmetry of the physical system which they are a part of. In their (3+1)-dimensional realizations in condensed matter systems, i.e., the so-called Weyl semimetals, this anomaly gives rise to topological electromagnetic response of magnetic fluctuations, which takes the form of non-local interaction between magnetic fluctuations and electromagnetic fields. We study the physical consequences of this non-local interaction, including electric field assisted magnetization dynamics, an extra gaple…
Weyl points with monopole charge $\pm 1$ have been extensively studied, however, real materials of multi-Weyl points, whose monopole charges are higher than $1$, have yet to be found. In this Rapid Communication, we show that nodal-line semimetals with nontrivial line connectivity provide natural platforms for realizing Floquet multi-Weyl points. In particular, we show that driving crossing nodal lines by circularly polarized light generates double-Weyl points. Furthermore, we show that monopole combination and annihilation can be observed in crossing-nodal-line semimetals and nodal-chain semi…
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 consideratio…
The compound GdPtBi is known as a material where the non-trivial topology of electronic bands interplays with an antiferromagnetic order, which leads to the emergence of many interesting magnetotransport phenomena. Although the magnetic structure of the compound has previously been reliably determined, the magnetic interactions responsible for this type of order remained controversial. In the present study, we employed time-of-flight inelastic neutron scattering to map out the low-temperature spectrum of spin excitations in single-crystalline GdPtBi. The observed spectra reveal two spectrally …
We study the photoinduced magnetic transition in an itinerant magnet described by the double-exchange model, in which conduction electrons couple with localized spins through the ferromagnetic (FM) Hund coupling. It is shown that intense light applied to the FM ground state induces an antiferromagnetic (AFM) order, in contrast to the AFM-to-FM transition due to the photocarrier injection. In particular, we focus on the mechanism for instability of the FM structure by the light irradiation. The magnon spectrum in the Floquet state is formulated on the basis of the pertrubative expansion of the …
In this paper, we theoretically investigate how laser fields change the nature of topological Kondo insulators(TKIs). By employing a prototypical model of TKIs, we treat the effect of the laser fields with Floquet theory, which gives effective description under high frequency laser fields. We derive the effective model of TKIs under the laser irradiation and discuss its topological properties. We demonstrate a possible realization of Floquet Chern insulators specified by various values of Chern number and reveal how the topological phase changes with increasing the laser light intensity. Furth…
Ultracold two-level atoms in optical lattices offer an excellent experimental platform to explore magnon excitations [Fukuhara et al 2013 Nat. Phys. 9, 235; Fukuhara et al 2013 Nature 502, 76]. Here, we investigate how gradient magnetic field and periodically modulated tunneling strength affect the two-magnon excitations in these ultracold atomic systems. In the resonant condition where the driving frequency matches and smooths the potential bias, the system gains translational invariance in both space and time in the rotating frame, and thus we can develop a Floquet-Bloch band theory for two …
Floquet states can be realized in quantum systems driven by continuous time-periodic perturbations. It is known that a state known as the Floquet Weyl semimetal can be realized when free Dirac fermions are placed in a rotating electric field. What will happen if strong interaction is introduced to this system? Will the interaction wash out the characteristic features of Weyl semimetals such as the Hall response? Is there a steady state and what is its thermodynamic behavior? We answer these questions using AdS/CFT correspondence in the $\mathcal{N}=2$ supersymmetric massless QCD in a rotating …
We study the laser control of magnon topological phases induced by the Aharonov-Casher effect in insulating antiferromagnets (AFs). Since the laser electric field can be considered as a time-periodic perturbation, we apply the Floquet theory and perform the inverse frequency expansion by focusing on the high frequency region. Using the obtained effective Floquet Hamiltonian, we study nonequilibrium magnon dynamics away from the adiabatic limit and its effect on topological phenomena. We show that a linearly polarized laser can generate helical edge magnon states and induce the magnonic spin Ne…
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 dia…
Nonequilibrium many-body dynamics is becoming one of the central topics of modern condensed matter physics. Floquet topological states were suggested to emerge in photodressed band structures in the presence of periodic laser driving. Here we propose a viable nonequilibrium route without requiring coherent Floquet states to reach the elusive magnetic Weyl semimetallic phase in pyrochlore iridates by ultrafast modification of the effective electron-electron interaction with short laser pulses. Combining \textit{ab initio} calculations for a time-dependent self-consistent reduced Hubbard $U$ con…
Nonequilibrium steady states in driven holographic Weyl semi-metals
Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington（华盛顿大学物理学部量子模拟创新中心）；Department of Mathematics, University of Michigan（密歇根大学数学系）
Spontaneous magnon decay is a generic feature of the magnetic excitations of anisotropic magnets and isotropic magnets with non-collinear order. In this paper, we argue that the effect of interactions on one-magnon states can, under many circumstances, be treated in terms of an effective, energy independent, non-Hermitian Hamiltonian for the magnons. In the vicinity of Dirac or Weyl touching points, we show that the spectral function has a characteristic anisotropy arising from topologically protected exceptional points or lines in the non-Hermitian spectrum. Such features can, in principle, b…
A single Weyl fermion, which is prohibited in static lattice systems by the Nielsen-Ninomiya theorem, is shown to be realized in a periodically driven three-dimensional lattice system with a topologically nontrivial Floquet unitary operator, manifesting the chiral magnetic effect. We give a topological classification of Floquet unitary operators in the Altland-Zirnbauer symmetry classes for all dimensions, and use it to predict that all gapless surface states of topological insulators and superconductors can emerge in bulk quasienergy spectra in Floquet systems.
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 clearl…
The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons above an Ising-like ferromagnetic ground state in a two-dimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI$_3$, and in a 3D Heisenberg magnet Cu$_3$TeO$_6$. Here we report on our inelastic neutron scattering investigation on large single crystals of a stacked honeycomb lattice magnet CoTiO$_3$, which is part of a broad family of ilm…
Driving a two-dimensional Mott insulator with circularly polarized light breaks time-reversal and inversion symmetry, which induces an optically-tunable synthetic scalar spin chirality interaction in the effective low-energy spin Hamiltonian. Here, we show that this mechanism can stabilize topological magnon excitations in honeycomb ferromagnets and in optical lattices. We find that the irradiated quantum magnet is described by a Haldane model for magnons that hosts topologically-protected edge modes. We study the evolution of the magnon spectrum in the Floquet regime and via time propagation …
Topological magnons are emergent quantum spin excitations featured by magnon bands crossing linearly at the points dubbed nodes, analogous to fermions in topological electronic systems. Experimental realization of topological magnons in three dimensions has not been reported so far. Here, by measuring spin excitations (magnons) of a three-dimensional antiferromagnet Cu$_{3}$TeO$_{6}$ with inelastic neutron scattering, we provide direct spectroscopic evidence for the coexistence of symmetry-protected Dirac and triply degenerate nodes, the latter involving three-component magnons beyond the Dira…
Optical pump-probe experiments carried out in the time domain reveal both the intrinsic low energy dynamics and its connections to higher energy excitations in correlated electron systems. In this work, we propose two microscopic mechanisms for the optical generation of coherent magnetic modes in van der Waals magnets, and derive the corresponding effective light-spin interactions: either through pumping atomic orbital excitations resonantly or via a light-induced Floquet spin Hamiltonian, the ground state of the system is driven out of equilibrium. The subsequent long-time relaxational dynami…
