In this Letter we present a comprehensive study of topological magnon bands and thermal Hall effect in non-collinear antiferromagnetic systems on the honeycomb lattice with an intrinsic Dzyaloshinskii-Moriya interaction. We theoretically show that the system possesses topological magnon bands with Chern number protected edge modes accompanied by a nonzero thermal magnon Hall effect. These features result from non-collinearity of the magnetic moments due to an applied out-of-plane magnetic field. Our results provide an experimental clue towards the realization of topological magnon transports in honeycomb antiferromagnetic compounds such as XPS$_3$ (X=Mn,Fe) and $α$-Cu$_2$V$_2$O$_7$.
Our joint theoretical and computer experimental study of heat-to-spin conversion reveals that noncollinear antiferromagnetic insulators are promising materials for generating magnon spin currents upon application of a temperature gradient: they exhibit spin Seebeck and spin Nernst effects. Using Kubo theory and spin dynamics simulations, we explicitly evaluate these effects in a single kagome sheet of potassium iron jarosite, KFe$_3$(OH)$_6$(SO$_4$)$_2$, and predict a spin Seebeck conversion factor of $0.2 μ\mathrm{V}/\mathrm{K}$ at a temperature of $20 \mathrm{K}$.
In the absence of an external magnetic field and a spin-polarized charge current, an antiferromagnetic system supports two degenerate magnon modes. An applied thermal bias activates the magnetic dynamics, leading to a magnon flow from the hot to the cold edge (magnonic spin Seebeck current). Both degenerate bands contribute to the magnon current but the orientations of the magnetic moments underlying the magnons are opposite in different bands. Therefore, while the magnon current is nonzero, the net spin current is zero.
A noncollinear magnet consists of the magnetic moments forming a noncollinear spin structure. Because of this structure, the Hamiltonian of magnons acquires the cubic terms. Although the cubic terms are the magnon-magnon interactions characteristic of noncollinear magnets, their effects on magnon transport have not been clarified yet. Here we show that in a canted antiferromagnet the cubic terms cause a magnon drag that magnons drag magnon spin current and heat current, which can be used to enhance these currents by tuning a magnetic field. For a strong magnetic field, we find that the cubic t…
We investigate the intrinsic magnon spin current in a noncollinear antiferromagnetic insulator. We introduce a definition of the magnon spin current in a noncollinear antiferromagnet and find that it is in general non-conserved, but for certain symmetries and spin polarizations the averaged effect of non-conserving terms can vanish. We formulate a general linear response theory for magnons in noncollinear antiferromagnets subject to a temperature gradient and analyze the effect of symmetries on the response tensor. We apply this theory to single-layer potassium iron jarosite KFe$_3$(OH)$_6$(SO…
We study magnon-magnon interactions and their effects in a spiral magnet induced by combination of an antiferromagnetic Heisenberg interaction and a Dzyaloshinsky-Moriya interaction. We show that the main effect of magnon-magnon interactions on low-energy magnons is to renormalize the coefficient of energy dispersion. This could explain why some experiments are consistent with the noninteracting theory. We also show that although the magnon-magnon interactions induce the pair amplitude for low-energy magnons, its effect on the excitation energy is negligible. This suggests that for magnons the…
We investigate the nonequilibrium spin polarization due to a temperature gradient in antiferromagnetic insulators, which is the magnonic analogue of the inverse spin-galvanic effect of electrons. We derive a linear response theory of a temperature-gradient-induced spin polarization for collinear and noncollinear antiferromagnets, which comprises both extrinsic and intrinsic contributions. We apply our theory to several noncentrosymmetric antiferromagnetic insulators, i.e., to a one-dimensional antiferromagnetic spin chain, a single layer of kagome noncollinear antiferromagnet, e.g., $\text{KFe…
We generalize the concept of the spin-momentum locking to magnonic systems and derive the formula to calculate the spin expectation value for one-magnon states of general two-body spin Hamiltonians. We give no-go conditions for magnon spin to be independent of momentum. As examples of the magnon spin-momentum locking, we analyze a one-dimensional antiferromagnet with the Néel order and two-dimensional kagome lattice antiferromagnets with the 120$^\circ$ structure. We find that the magnon spin depends on its momentum even when the Hamiltonian has the $z$-axis spin rotational symmetry, which can…
The richness in both the dispersion and energy of antiferromagnetic magnons has spurred the magnetism community to consider antiferromagnets for future spintronic/magnonic applications. However, the excitation and control of antiferromagnetic magnons remains challenging, especially when compared to ferromagnetic counterparts. A middle ground is found with synthetic antiferromagnet metamaterials, where acoustic and optical magnons exist at GHz frequencies. In these materials, the magnon energy spectrum can be tuned by static symmetry-breaking external fields or dipolar interactions hybridizing …
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 a spin Hamiltonian for spin-orbit-coupled ferromagnets on the honeycomb lattice. We find that the effective Hamiltonian for magnons, a quanta of spin-wave excitations from ordered states, is equivalent to the Haldane model for electrons in the honeycomb lattice, which indicates the nontrivial topology of the magnon bands and the existence of the associated edge state. We also take the Schwinger boson (or bosonic spinon) representations of spins that are applicable both to ordered and disordered phases. We show that the spinon bands within the mean-field treatment are top…
Spin waves in antiferromagnetic materials have great potential for next-generation magnonic technologies. However, their properties and their dependence on the type of ground-state antiferromagnetic structure are still open questions. Here, we investigate theoretically spin waves in one- and two-dimensional model systems with a focus on noncollinear antiferromagnetic textures such as spin spirals and skyrmions of opposite topological charges. We address in particular the nonreciprocal spin excitations recently measured in bulk antiferromagnet $α$--$\text{Cu}_2\text{V}_2\text{O}_7$ utilizing in…
The discovery of spontaneous magnetism in van der Waal (vdW) magnetic monolayers has opened up an unprecedented platform for investigating magnetism in purely two-dimensional systems. Recently, it has been shown that the magnetic properties of vdW magnets can be easily tuned by adjusting the relative composition of halides. Motivated by these experimental advances, here we derive a model for a trihalide CrClBrI monolayer from symmetry principles and we find that, in contrast to its single-halide counterparts, it can display highly anisotropic nearest- and next-to-nearest neighbor Dzyaloshinski…
We investigate the properties of magnon edge states in a ferromagnetic honeycomb spin lattice with a Dzyaloshinskii-Moriya interaction (DMI). We derive analytical expressions for the energy spectra and wavefunctions of the edge states localized on the boundaries. By introducing an external on-site potential at the outermost sites, we show that the bosonic band structure is similar to that of the fermionic graphene. We investigate the region in the momentum space where the bosonic edge states are well defined and we analyze the width of the edge state and their dependence with DMI strength. Our…
When the crystalline symmetries that protect a higher-order topological phase are not preserved at the boundaries of the sample, gapless hinge modes or in-gap corner states cannot be stabilized. Therefore, careful engineering of the sample termination is required. Similarly, magnetic textures, whose quantum fluctuations determine the supported magnonic excitations, tend to relax to new configurations that may also break crystalline symmetries when boundaries are introduced. Here we uncover that antiskyrmion crystals provide an experimentally accessible platform to realize a magnonic topologica…
Pursuing topological phases in natural and artificial materials is one of the central topics in modern physical science and engineering. In classical magnetic systems, spin waves (or magnons) and magnetic solitons (such as domain wall, vortex, skyrmion, etc) represent two important excitations. Recently, the topological insulator and semimetal states in magnon- and soliton-based crystals (or metamaterials) have attracted growing attention owing to their interesting dynamics and promising applications for designing robust spintronic devices. Here, we give an overview of current progress of topo…
Symmetric Mode Ansatz: Theory of Magnon Collective Modes in Chern Insulators
Princeton Center for Theoretical Science, Princeton University（普林斯顿大学理论科学中心）；Department of Physics, Princeton University（普林斯顿大学物理系）；Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ctd.qmat, Julius-Maximilians-Universität Würzburg（维尔茨堡大学理论与天体物理研究所及维尔茨堡-德累斯顿卓越集群ctd.qmat）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊卡巴斯科，巴斯克科学基金会）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究院计算量子物理中心）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎第七大学，索邦巴黎城）
