Quite recently, magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. Thermal Hall conductivity $κ^{xy}$, changes sign as a function of magnetic field or temperature on the kagome lattice, and $κ^{xy}$ changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the breaking of inversion symmetry of the lattice, however, by a next-nearest-neighbour Dzyaloshinsky-Moriya (DM) interaction. We find that $κ^{xy}$ has a fixed sign for all parameter regimes considered. These results are in contrast to the Lieb, kagome and pyrochlore lattices. We further show that the low-temperature dependence on the magnon Hall conductivity follows a $T^{2}$ law, as opposed to the kagome and pyrochlore lattices. These results suggest an experimental procedure to measure thermal Hall conductivity within a class of 2D honeycomb quantum magnets and ultracold atoms trapped in honeycomb optical lattice.
It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon-magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion …
We investigate a microscopic origin of nonreciprocal magnon that is distinct from the Dzyaloshinskii-Moriya interaction in a honeycomb antiferromagnet. The key ingredient is a symmetric anisotropic exchange interaction depending on the bond direction, which results in a valley-type nonreciprocal magnon excitations under the staggered antiferromagnetic ordering. Furthermore, we find this type of nonreciprocal magnon exhibits a peculiar magnetic-field response; the nonreciprocal direction can be manipulated by the in-plane rotating magnetic field. The obtained results can be accounted for the em…
Magnons and phonons are two fundamental neutral excitations of magnetically ordered materials which can significantly dominate the low-energy thermal properties. In this work we study the interplay of magnons and phonons in honeycomb and Kagome lattices. When the mirror reflection with respect to the magnetic ordering direction is broken, the symmetry-allowed in-plane Dzyaloshinskii-Moriya (DM) interaction will couple the magnons to the phonons and the magnon-polaron states are formed. Besides, both lattice structures also allow for an out-of-plane DM interaction rendering the uncoupled magnon…
Motivated by the fact that many bilayer quantum magnets occur in nature, we generalize the study of thermal Hall transports of spin excitations to bilayer magnetic systems. It is shown that bilayer magnetic systems can be coupled either ferromagnetically or antiferromagnetically. We study both scenarios on the honeycomb lattice and show that the system realizes topologically nontrivial magnon bands induced by alternating next-nearest-neighbour Dzyaloshinsky-Moriya interaction (DMI). As a result, the bilayer system realizes both magnon Hall effect and magnon spin Nernst effect. We show that ant…
We propose the existence of a symmetry-protected topological Dirac nodal line (DNL) magnonic phase in layered honeycomb collinear antiferromagnets even in the presence of spin-orbit Dzyaloshinskii-Moriya interaction. We show that the magnon spin Nernst effect, predicted to occur in strictly two-dimensional (2D) honeycomb collinear antiferromagnets cancels out in the layered honeycomb collinear antiferromagnets. In other words, the magnon spin Nernst effect in each 2D antiferromagnetic layer cancels out the succeeding layer. Hence, the Berry curvature vanish in the entire Brillouin zone due to …
We study the magnon bands of twisted bilayer honeycomb quantum magnets using linear spin wave theory. Although the interlayer coupling can be ferromagnetic or antiferromagnetic, we keep the intralayer one ferromagnetic to avoid possible frustration. For the interlayer ferromagnetic case, we find the magnon bands have similar features with the corresponding electronic energy spectrums. Although the linear dispersions near the Dirac points are preserved in the magnon bands of twisted bilayer magnets, their slopes are graduately reduced with the decrease of the twist angles. On the other hand, th…
We calculate the two-magnon Raman scattering spectra in antiferromagnetic phases of several frustrated spin models defined on the honeycomb lattice. These include the Néel antiferromagnetic phase of a $J_1$-$J_2$-$J_3$ model and the stripe phase of the Heisenberg-Kitaev model. We show that both the magnetic frustration and the anisotropy of interactions may significantly affect the Raman spectra. We further discuss the implications of our results to the magnetic excitations of the iron-based compound BaFe$_2$Se$_2$O and show how the magnetic interactions can be extracted from fit to the Raman …
CrBr$_3$ is an excellent realization of the two-dimensional honeycomb ferromagnet, which offers a bosonic equivalent of graphene with Dirac magnons and topological character. We perform inelastic neutron scattering (INS) measurements using state-of-the-art instrumentation to update 50-year-old data, thereby enabling a definitive comparison both with recent experimental claims of a significant gap at the Dirac point and with theoretical predictions for thermal magnon renormalization. We demonstrate that CrBr$_3$ has next-neighbor $J_2$ and $J_3$ interactions approximately 5\% of $J_1$, an ideal…
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…
Two dimensional van der Waals ferromagnets with honeycomb structures are expected to host the bosonic version of Dirac particles in their magnon excitation spectra. Using inelastic neutron scattering, we study spin wave excitations in polycrystalline CrCl$_3$, which exhibits ferromagnetic honeycomb layers with antiferromagnetic stackings along the $c$-axis. For comparison, polycrystal samples of CrI$_3$ with different grain sizes are also studied. We find that the powder-averaged spin wave spectrum of CrCl$_3$ at $T$ = 2 K can be adequately explained by the two dimensional spin Hamiltonian inc…
In the conventional ferromagnetic systems, topological magnon bands and thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In principle, however, the DMI is either negligible or it is not allowed by symmetry in some quantum magnets. Therefore, we expect that topological magnon features will not be present in those systems. In addition, quantum magnets on the triangular-lattice are not expected to possess topological features as the DMI or spin-chirality cancels out due to equal and opposite contributions from adjacent triangles. Here, however, we predict that the isomo…
The topological properties of massive and massless fermionic quasiparticles have been intensively investigated over the past decade in topological materials without magnetism. Recently, the bosonic analogs of such quasiparticles arising from spin waves have been reported in the two-dimensional (2D) honeycomb lattice ferromagnet/antiferromagnet and the 3D antiferromagnet. Here we use time-of-flight inelastic neutron scattering to study spin waves of the S = 1 honeycomb lattice antiferromagnet BaNi2(AsO4)2, which has a zig-zag antiferromagnetic (AF) ground state identical to that of the Kitaev q…
The pseudo-magnetic field created by a non-uniform unaxial strain is introduced into the antiferromagnetic honeycomb nanoribbons. The formation of magnon pseudo-Landau levels, which appear from the upper end of the spectrum and whose level spacings are proportional to the square root of the level index, is revealed by the linear spin-wave theory. The antiferromagnetic order is gradually weakened along the $y$-direction by the strain. At large enough strength, the system is decoupled into isolated zigzag chains near the upper boundary, and demonstrates one-dimensional magnetic property there. W…
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…
Ferromagnetic honeycomb systems are known to exhibit a magnonic topological phase under the existence of the next-nearest neighbor Dzyaloshinskii-Moriya interaction (DMI). Motivated by the recent progress in the sublattice-specific control of magnetic anisotropy, we study the topological phase of magnon bands of honeycomb ferromagnetic monolayer and bilayer with the sublattice symmetry breaking due to the different anisotropy energy in the presence of the DMI. We show that there is a topological phase transition between the topological magnon insulator and the topologically trivial magnon phas…
We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $Γ$ and isotropic third-nearest-neighbor interaction $J_3$ on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides $α$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$, and Ru-based materials such as $α$-RuCl$_3$. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate hermitian operators. This approach gives us an advantage over the conventional one in identifying paramet…
We have used resonant inelastic x-ray scattering to reveal optical magnons in a honeycomb lattice iridate $α$-Li$_{2}$IrO$_{3}$. The spectrum in the energy region 20-25 meV exhibits momentum dependence, of which energy is highest at the location of the magnetic Bragg peak, ($\textit{h}, \textit{k}$) = ($\pm$0.32, 0), and lowered toward (0, 0) and ($\pm$1, 0). We compare our data with a linear spin-wave theory based on a generic nearest-neighbor spin model. We find that a dominant bond-directional Kitaev interaction of order 20 meV is required to explain the energy scale observed in our study. …
In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling $J$ and interlayer coupling $J_L$, which is realizable in the honeycomb chromium compounds CrX$_3$ (X $\equiv$ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for…
In this Letter, we study the magnetic transport in AA-stacked bilayer honeycomb chiral magnets coupled either ferromagnetically or antiferromagnetically. For both couplings, we observe chirality-induced gaps, chiral protected edge states, magnon Hall and magnon spin Nernst effects of magnetic spin excitations. For ferromagnetically coupled layers, thermal Hall and spin Nernst conductivities do not change sign as function of magnetic field or temperature similar to single-layer honeycomb ferromagnetic insulator. In contrast, for antiferromagnetically coupled layers, we observe a sign change in …
Quantum information storage using charge-neutral quasiparticles are expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-$1/2$ XYZ Heisenberg model on the honeycomb lattice with discrete Z$_2$ symmetry and a Dzyaloshinskii-Moriya interaction. We show that the s…
We propose that non-collinear magnetic order in quantum magnets can harbor a novel higher-order topological magnon phase with non-Hermitian topology and hinge magnon modes. We consider a three-dimensional system of interacting local moments on stacked-layers of honeycomb lattice. It initially favors a collinear magnetic order along an in-plane direction, which turns into a non-collinear order upon applying an external magnetic field perpendicular to the easy axis. We exploit the non-Hermitian nature of the magnon Hamiltonian to show that this field-induced transition corresponds to the transfo…
Recently, a SU(4) $π$-flux Hubbard model on the honeycomb lattice has been proposed to study the spin-orbit excitations of $α$-ZrCl$_3$ [Phys.~Rev.~Lett. 121.097201~(2017)]. Based on this model with a zigzag edge, we show the edge defects can induce edge flat bands that result in a SU(4) edge ferromagnetism. We develop an effective one-dimensional interaction Hamiltonian to study the corresponding SU(4) spin excitations. Remarkably, SU(4) spin excitations of the edge ferromagnet appear as a continuum covering the entire energy region rather than usual magnons. Through further entanglement entr…
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 report the neutron scattering results on magnetic orderings and excitations in $\mathrm{Ba}_2\mathrm{CoTeO}_6$ composed of two almost isolated subsystems A and B, which are described as an $S\,{=}\,1/2$ triangular Heisenberg-like antiferromagnet and a frustrated honeycomb Ising-like antiferromagnet, respectively. Stripy ordering of subsystem B was confirmed below $T_{\rm N1}\,{=}\,12.0$ K, whereas sharp streaks were observed along $(1/3, 1/3, L)$ and $(2/3, 2/3, L)$ at 0.3 K (${\ll}\,T_{\rm N2}\,{=}\,3.0$ K). This indicates the two-dimensional nature of ordering in subsystem A. It was found…
The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as $α$-RuCl$_3$. Currently, two competing scenarios exist for the intermediate field phase of this compound ($B=7-10$ T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian natu…
Search for higher-order topological insulators, characterized by topologically protected gapless boundary states of codimension higher than one, in bosonic systems has attracted growing interest. Here, we establish twisted bilayer honeycomb magnets as a new platform for hosting second-order topological magnon insulators (SOTMIs) without fine-tuning. We employ a simple, minimal Heisenberg spin model to describe misaligned bilayer sheets of honeycomb ferromagnetic magnets with a large commensurate twist angle. We found that the higher-order topology in this bilayer system shows a significant dep…
Temperature and field dependence of collective spin excitations or magnon in monolayer honeycomb spin lattices is investigated using an anisotropic exchange XZ-Heisenberg model in an external field. Magnetic phase transition in the presence of the transverse field is the spin reorientation (SR) transition with magnon intensity existing above the SR temperature. The transverse field either decreases or sustains the spin-wave intensity in the temperature region below or above the SR temperature, respectively. The gap of the zero-momentum low-energy magnon branch closes at the SR transverse field…
We theoretically propose a second-order topological magnon insulator by stacking the van der Waals honeycomb ferromagnets with antiferromagnetic interlayer coupling. The system exhibits Z$_{2}$ topological phase, protected by pseudo-time-reversal symmetry (PTRS). An easy-plane anisotropy term breaks PTRS and destroys the topological phase. Nevertheless, it respects a magnetic two-fold rotational symmetry which protects a second-order topological phase with corner modes in bilayer and hinge modes along stacking direction. Moreover, an introduced staggered interlayer coupling establishes a Z$_{2…
We present a comprehensive $1/S$ study of the field-induced dynamical properties of the nearest-neighbor $XXZ$ antiferromagnet on a honeycomb lattice using the formalism of the nonlinear spin-wave theory developed for this model. The external magnetic field controls spin frustration in the system and induces non-collinearity of the spin structure, which is essential for the two-magnon decay processes. Our results include an intriguing field-evolution of the regions of the Brillouin zone wherein decays of spin excitations are prominent, a detailed classification of the decay channels involving …
Thermal conductivity κis measured at very low temperatures down to 0.28 K for pure and Mg-doped CuGeO_3 single crystals. The doped samples carry larger amount of heat than the pure sample at the lowest temperature. This is because antiferromagnetic magnons appear in the doped samples and are responsible for the additional heat conductivity, while κof the pure sample represents phonon conductivity at such low temperatures. The maximum energy of the magnon is estimated to be much lower than the spin-Peierls-gap energy. The result presents the first example that κat very low temperatures probes t…
We study geometrical responses of magnons driven by a temperature gradient in frustrated spin systems. While Dzyaloshinskii-Moriya (DM) interactions are usually incorporated to obtain geometrically nontrivial magnon bands, here we investigate thermal Hall responses of magnons that do no rely on the DM interactions. Specifically, we focus on frustrated spin systems with sublattice degrees of freedom and show that a nonzero Berry curvature requires breaking of an effective $PT$ symmetry. According to this symmetry consideration, we study the $J_1$-$J_2$-$J_2^\prime$ Heisenberg models on a honeyc…
Based on a symmetry analysis of the microscopic Hubbard and t-J models, a systematic low-energy effective field theory is constructed for hole-doped antiferromagnets on the honeycomb lattice. In the antiferromagnetic phase, doped holes are massive due to the spontaneous breakdown of the $SU(2)_s$ symmetry, just as nucleons in QCD pick up their mass from spontaneous chiral symmetry breaking. In the broken phase the effective action contains a single-derivative term, similar to the Shraiman-Siggia term in the square lattice case. Interestingly, an accidental continuous spatial rotation symmetry …
The specific heat and thermal conductivity of the insulating ferrimagnet Y$_3$Fe$_5$O$_{12}$ (Yttrium Iron Garnet, YIG) single crystal were measured down to 50 mK. The ferromagnetic magnon specific heat $C$$_m$ shows a characteristic $T^{1.5}$ dependence down to 0.77 K. Below 0.77 K, a downward deviation is observed, which is attributed to the magnetic dipole-dipole interaction with typical magnitude of 10$^{-4}$ eV. The ferromagnetic magnon thermal conductivity $κ_m$ does not show the characteristic $T^2$ dependence below 0.8 K. To fit the $κ_m$ data, both magnetic defect scattering effect an…
This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-$1/2$ quantum XY model with a next-nearest-neighbour Dzyaloshinsky-Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, thermal and spin Nernst conductivities. Due to the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological pr…
Novel magnetic ordering on the honeycomb lattice due to emergent weak anisotropic interactions generated by the mixing between the $J=1/2$ sector and the magnetically inactive 3/2 sector is investigated in a three-orbital interacting electron model in the absence of Hund's coupling. Self-consistent determination of magnetic order yields anisotropic Néel and zigzag orders for different parameter regimes, highlighting the effect of the emergent single-ion anisotropy. Study of magnon excitations shows extremely small magnon energy scale compared to the hopping energy scale, and enhancement of ani…
We provide an exact study of dynamical correlations for the quantum spin-orbital liquid phases of an SU(2)-symmetric Kitaev honeycomb lattice model. We show that the spin dynamics in this Kugel-Khomskii type model is exactly the density-density correlation function of S=1 fermionic magnons, which could be probed in resonant inelastic x-ray scattering experiments. We predict the characteristic signatures of spin-orbital fractionalization in inelastic scattering experiments and compare them to the ones of the spin-anisotropic Kitaev honeycomb spin liquid. In particular, the resonant inelastic x-…
We report on the unusual behavior of the in-plane thermal conductivity ($κ$) and torque ($τ$) response in the Kitaev-Heisenberg material $α$-RuCl$_3$. $κ$ shows a striking enhancement with linear growth beyond H = 7 T, where magnetic order disappears, while $τ$ for both of the in-plane symmetry directions shows an anomaly at the same field. The temperature- and field-dependence of $κ$ are far more complex than conventional phonon and magnon contributions, and require us to invoke the presence of unconventional spin excitations whose properties are characteristic of a field-induced spin-liquid …
We present results of the thermal conductivity of $\rm La_2CuO_4$ and $\rm La_{1.8}Eu_{0.2}CuO_4$ single-crystals which represent model systems for the two-dimensional spin-1/2 Heisenberg antiferromagnet on a square lattice. We find large anisotropies of the thermal conductivity, which are explained in terms of two-dimensional heat conduction by magnons within the CuO$_2$ planes. Non-magnetic Zn substituted for Cu gradually suppresses this magnon thermal conductivity $κ_{\mathrm{mag}}$. A semiclassical analysis of $κ_{\mathrm{mag}}$ is shown to yield a magnon mean free path which scales linear…
Spin-1/2 Heisenberg diamond-like decorated honeycomb lattice in a magnetic field from the perspective of localized magnons and exact diagonalization
Faculty of Science, P. J. Šafárik University（帕·约·沙法里克大学理学院）；Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université（CY塞尔吉巴黎大学，CNRS UMR 8089理论物理与建模实验室）
In two-dimensional (2D) insulating magnets, the thermal Hall effect of magnons is believed to be a consequence of topological magnon insulator with separated magnon bands and a well-defined Chern number. Due to broken time-reversal symmetry the thermal Hall effect vanishes in Dirac magnons. In this paper, we show that periodically driven semi-Dirac magnon in 2D insulating honeycomb ferromagnet results in a photoinduced Dirac magnon at the topological phase transition between a photoinduced topological and trivial magnon insulator. Remarkably, the photoinduced Dirac magnon and the photoinduced …
Motivated by recent terahertz absorption measurements in $α$-RuCl$_3$, we develop a theory for the electromagnetic absorption of materials described by the Kitaev model on the honeycomb lattice. We derive a mechanism for the polarization operator at second order in the nearest-neighbor hopping Hamiltonian. Using the exact results of the Kitaev honeycomb model, we then calculate the polarization dynamical correlation function corresponding to electric dipole transitions, in addition to the spin dynamical correlation function corresponding to magnetic dipole transitions.
We study the orbital angular momentum of magnons for collinear ferromagnet (FM) and antiferromagnetic (AF) systems with nontrivial networks of exchange interactions. The orbital angular momentum of magnons for AF and FM zig-zag and honeycomb lattices becomes nonzero when the lattice contains two inequivalent sites and is largest at the avoided-crossing points or extremum of the frequency bands. Hence, the arrangement of exchange interactions may play a more important role at producing the orbital angular momentum of magnons than the spin-orbit coupling energy and the resulting non-collinear ar…
The Kitaev quantum spin liquid (KSL) is a theoretically predicted state of matter whose fractionalized quasiparticles are distinct from bosonic magnons, the fundamental excitation in ordered magnets. The layered honeycomb antiferromagnet $α$-RuCl$_3$ is a KSL candidate material, as it can be driven to a magnetically disordered phase by application of an in-plane magnetic field, with $H_c \sim 7$ T. Here we report a detailed characterization of the magnetic excitation spectrum of this material by high-resolution time-domain terahertz (THz) spectroscopy. We observe two sharp magnon resonances wh…
