Magnonic Band Research Articles

Dirac cones and valley topological states of classical spin waves in artificial magnonic crystals with two-dimensional honeycomb lattice

A model of artificial magnonic crystals (AMCs) with a two-dimensional honeycomb lattice of cylindrical ferromagnetic rods embedded in another ferromagnetic material is proposed. Topological properties including Dirac cones, Dirac-like point and valley states of classical spin waves in the above AMCs are theoretically investigated by numerically solving the Landau-Lifshitz equation. It is shown that Dirac cones and valley states at the boundary of the first Brillouin zone can be generated in the dispersion relation. Furthermore, Dirac-like point can also be obtained at the center of the first Brillouin zone due to the accidental degeneracy of the magnonic bands. These discoveries of Dirac cones, Dirac-like point and valley topological states in artificial magnonic crystals not only open a new field in topological condensed matter, but also provide a novel platform for fabricating topological classical spin-wave devices.

Topological magnon band structure of emergent Landau levels in a skyrmion lattice.

The motion of a spin excitation across topologically nontrivial magnetic order exhibits a deflection that is analogous to the effect of the Lorentz force on an electrically charged particle in an orbital magnetic field. We used polarized inelastic neutron scattering to investigate the propagation of magnons (i.e., bosonic collective spin excitations) in a lattice of skyrmion tubes in manganese silicide. For wave vectors perpendicular to the skyrmion tubes, the magnon spectra are consistent with the formation of finely spaced emergent Landau levels that are characteristic of the fictitious magnetic field used to account for the nontrivial topological winding of the skyrmion lattice. This provides evidence of a topological magnon band structure in reciprocal space, which is borne out of the nontrivial real-space topology of a magnetic order.

A perspective on magnon spin Nernst effect in antiferromagnets

Magnon excitations in antiferromagnetic materials and their physical implications have helped to facilitate the emergence of device concepts not presently available in ferromagnets. A unique characteristic of antiferromagnetic magnons is the coexistence of opposite spin polarization, which mimics the electron spin in a variety of transport phenomena. Among them, the most prominent spin-contrasting phenomenon is the magnon spin Nernst effect (SNE), which refers to the generation of a transverse pure magnon spin current through a longitudinal temperature gradient. We introduce selected recent progress in the study of magnon SNE in collinear antiferromagnets with focus on its underlying physical mechanism entailing profound topological features of magnon band structures. By reviewing how the magnon SNE has inspired and enriched the exploration of topological magnons, we offer our perspective on this emerging frontier that holds potential in future spintronic nano-technology.

Spin-space groups and magnon band topology

Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the ten-fold way. Since then, lattice point group and non-symmorphic symmetries have been seen to lead to a vast range of possible topologically nontrivial band structures many of which are realized in materials. In this paper we show that band topology is further enriched in many physically realizable instances where magnetic and lattice degrees of freedom are wholly or partially decoupled. The appropriate symmetry groups to describe general magnetic systems are the spin-space groups. Here we describe cases where spin-space groups are essential to understand the band topology in magnetic materials. We then focus on magnon band topology where the theory of spin-space groups has its simplest realization. We consider magnetic Hamiltonians with various types of coupling including Heisenberg and Kitaev couplings revealing a hierarchy of enhanced magnetic symmetry groups depending on the nature of the lattice and the couplings. We describe, in detail, the associated representation theory and compatibility relations thus characterizing symmetry-enforced constraints on the magnon bands revealing a proliferation of nodal points, lines, planes and volumes.

Topological thermal Hall effect and magnonic edge states in kagome ferromagnets with bond anisotropy

The magnon band topology due to the Dzyaloshinskii–Moriya interaction (DMI) and its relevant topological thermal Hall effect has been extensively studied in kagome lattice magnets. In this theoretical investigation, we report a new mechanism for phase transitions between topological phases of magnons in kagome ferromagnets by tuning the anisotropic nearest-neighbor ferromagnetic interaction and DMI. Using the linear spin-wave theory, we calculate the Chern number and thermal Hall conductivity of magnons in low temperature regime. We show the magnon band structures and magnonic edge states in each topological phase. From the topological phase diagram, we find a sign reversal of the thermal Hall conductivity upon tuning the modulation factors. We explicitly demonstrate the correspondence of thermal Hall conductivity with the propagation direction of the magnonic edge states. Finally, we discuss candidate materials as experimental realizations of our theoretical model.

Magnon band structure of skyrmion crystals and stereographic projection approach

Using semiclassical method combined with stereographic projection approach, we investigate the magnetic dynamics of the skyrmion crystal (SkX), formed in planar ferromagnet with both Dzyaloshinskii-Moriya interaction and uniform magnetic field. The topologically non-trivial ground state of SkX is described in stereographic projection by the complex valued function with simple poles at skyrmions' positions. We use the earlier proposed ansatz for this ground state function in the form of the sum of individual skyrmions. The dynamics follows from the second variation of the classical action. Numerical analysis yields the magnon band structure of tight-binding form in accordance with previously known results. There are two sets of bands, one set with a flat dispersion, topologically trivial and rapidly evolving with magnetic field. Another set is robust to magnetic field, characterized by pronounced dispersion and with the Berry curvature which may be sign-reversal in the Brillouin zone. The developed theory can be straightforwardly generalized for the analysis of magnetic dynamics in topological spin structures of other types.

From the Spin Eigenmodes of Isolated Néel Skyrmions to the Magnonic Bands of Skyrmionic Crystals: A Micromagnetic Study as a Function of the Interfacial Dzyaloshinskii-Moriya Interaction and the Exchange Constants

The presence of interfacial Dzyaloshinskii-Moriya interaction (DMI) may lead to the appearance of Néel skyrmions in ferromagnetic films. These topologically protected structures, whose diameter is as small as a few nanometers, can be nowadays stabilized at room temperature and have been proposed for the realization of artificial magnonic crystals and new spintronic devices, such as racetrack memories. In this perspective, it is of utmost importance to analyze their dynamical properties in the gigahertz range, i.e., in the operation range of current communication devices. In this letter, we exploited the software MuMax3 to calculate the dynamics of Néel skyrmions in the range between 1 and 30 GHz, considering first the eigenmodes of an isolated skyrmion, then the case of two interacting skyrmions, and finally a linear chain, representing a one-dimensional magnonic crystal, whose magnonic band structure has been calculated as a function of the strength of both the DMI- and the exchange-constants, namely <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> . The magnonic bands can be interpreted as derived from the eigenmodes of isolated skyrmions, even if hybridization and anticrossing phenomena occur for specific ranges of values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> . Therefore, varying the latter parameters, for instance, by a proper choice of the materials and thicknesses, may enable one to fine-tune the permitted and forbidden frequency interval of the corresponding magnonic crystal.

Topological Magnon Band Crossing in Y2Ir2O7

Topological magnonic materials have attracted much interest because of the potential for dissipationless spintronic applications. Pyrochlore iridates are theoretically regarded as good candidates for designing topological magnon bands. However, experimental identification of topological magnon bands in pyrochlore iridates remains elusive. We explored this possibility in Y_{2}Ir_{2}O_{7} using Raman spectroscopy to measure both the single-magnon excitations and anomalous phonon shifts. From the single-magnon energies and tight-binding model calculations concerning the phonons, we determined the key parameters in the spin Hamiltonian. These confirm that Y_{2}Ir_{2}O_{7} hosts a nontrivial magnon band topology distinct from other pyrochlore iridate compounds. Our work demonstrates that pyrochlore iridates constitute a system in which the magnon band topology can be tailored and that Raman spectroscopy is a powerful technique to explore magnon band topology.

Data set of article entitled: " From the spin eigenmodes of isolated Néel skyrmions to the magnonic bands of a skyrmionic crystal: a micromagnetic study as a function of the strength of both the interfacial Dzyaloshinskii-Moriya and the exchange constants"

Data set of article entitled: " From the spin eigenmodes of isolated Néel skyrmions to the magnonic bands of a skyrmionic crystal: a micromagnetic study as a function of the strength of both the interfacial Dzyaloshinskii-Moriya and the exchange constants"

Coexisting ferromagnetic-antiferromagnetic state in twisted bilayer CrI3.

Moiré engineering1-3 of van der Waals magnetic materials4-9 can yield new magnetic ground states via competing interactions in moiré superlattices10-13. Theory predicts a suite of interesting phenomena, including multiflavour magnetic states10, non-collinear magnetic states10-13, moiré magnon bands and magnon networks14 in twisted bilayer magnetic crystals, but so far such non-trivial magnetic ground states have not emerged experimentally. Here, by utilizing the stacking-dependent interlayer exchange interactions in two-dimensional magnetic materials15-18, we demonstrate a coexisting ferromagnetic (FM) and antiferromagnetic (AF) ground state in small-twist-angle CrI3 bilayers. The FM-AF state transitions to a collinear FM ground state above a critical twist angle of about 3°. The coexisting FM and AF domains result from a competition between the interlayer AF coupling, which emerges in the monoclinic stacking regions of the moiré superlattice, and the energy cost for forming FM-AF domain walls. Our observations are consistent with the emergence of a non-collinear magnetic ground state with FM and AF domains on the moiré length scale10-13. We further employ the doping dependence of the interlayer AF interaction to control the FM-AF state by electrically gating a bilayer sample. These experiments highlight the potential to create complex magnetic ground states in twisted bilayer magnetic crystals, and may find application in future gate-voltage-controllable high-density magnetic memory storage.

Magnonic bands in periodic arrays of vertically-stacked cylindrical magnetic nanoelements

The spin-wave spectra are studied theoretically in periodic magnonic crystals (MCs) of vertically-stacked cylindrical nickel nanodisks or nanorings separated by nonmagnetic spacers, resulting in infinitely long segmented nanowire or nanotube MC arrays, respectively. A microscopic or Hamiltonian-based approach is employed for the magnetization dynamics, in which an external magnetic field is applied along the cylinder axis and the periodic length is varied by changing the length of the spacers. The results show a broadening and shift of the spin-wave frequency bands at smaller spacer length due to the strong dipolar inter-element coupling, which also modifies the spatially-inhomogeneous equilibrium magnetization in the finite-length cylindrical elements. The effects are found to be more pronounced in a nanotube MC than in a nanowire MC, mainly because the absence of the core in a nanotube favours vortex states.

Topological Phase Transitions of Dirac Magnons in Honeycomb Ferromagnets.

The study of the magnonic thermal Hall effect in magnets with Dzyaloshinskii-Moriya interaction (DMI) has recently drawn attention because of the underlying topology. Topological phase transitions may arise when there exist two or more distinct topological phases, and they are often revealed by a gap-closing phenomenon. In this work, we consider the magnons in honeycomb ferromagnets described by a Heisenberg Hamiltonian containing both an out-of-plane DMI and a Zeeman interaction. We demonstrate that the magnonic system exhibits temperature (or magnetic field) driven topological phase transitions due to magnon-magnon interactions. Specifically, when the temperature increases, the magnonic energy gap at Dirac points closes and reopens at a critical temperature, T_{c}. By showing that the Chern numbers of the magnonic bands are distinct above and below T_{c}, we confirm that the gap-closing phenomenon is indeed a signature for the topological phase transitions. Furthermore, our analysis indicates that the thermal Hall conductivity in the magnonic system exhibits a sign reversal at T_{c}, which can serve as an experimental probe of its topological nature. Our theory predicts that in CrI_{3} such a phenomenon exists and is experimentally accessible.

Intrinsic magnon Nernst effect in pyrochlore iridate thin films

We theoretically study the magnon spin thermal transport using a strong coupling approach in pyrochlore iridate trilayer thin films grown along the [111] direction. As a result of the Dzyaloshinskii-Moriya interaction (DMI), the spin configuration of the ground state is an all-in/all-out ordering on neighboring tetrahedra of the pyrochlore lattice. In such a state, the system has an inversion symmetry and a Nernst-type thermal spin current response is well defined. We calculate the temperature dependence of the magnon Nernst response with respect to the magnon band topology controlled by the spin-orbit coupling parameters and observe topologically protected chiral edge modes over a range of parameters. Our study complements prior work on the magnon thermal Hall effect in thin-film pyrochlore iridates and suggests that the [111] grown thin-film pyrochlore iridates are a promising candidate for thermal spin transport and spin caloritronic devices.

Topological Magnons: A Review

At sufficiently low temperatures, magnetic materials often enter correlated phases hosting collective, coherent magnetic excitations such as magnons or triplons. Drawing on the enormous progress on topological materials of the past few years, recent research has led to new insights into the geometry and topology of these magnetic excitations. Berry phases associated with magnetic dynamics can lead to observable consequences in heat and spin transport, whereas analogs of topological insulators and semimetals can arise within magnon band structures from natural magnetic couplings. Magnetic excitations offer a platform to explore the interplay of magnetic symmetries and topology, drive topological transitions using magnetic fields, examine the effects of interactions on topological bands, and generate topologically protected spin currents at interfaces. In this review, we survey progress on all these topics, highlighting aspects of topological matter that are unique to magnon systems and the avenues yet to be fully investigated.

Interplay of topological electrons and magnons in the Kagome magnet CoCu3(OH)6Cl2

Spin and charge are two interrelated properties of electrons. Most of previous works on topological phases of matter tend to study the topological electronic bands and topological magnon excitations separately. In this work, by combining density functional theory and the Schwinger boson method, we determine the topological electronic band structure and topological magnon spectrum simultaneously in the ferromagnetic phase of CoCu3(OH)6Cl2. This Herbertsmithite material has an ABC-stacking Kagome-lattice structure with fractional occupancies on the Cu sites. We find that the hopping parameters of the electronic and magnonic bands can mutually influence each other and predict in further model studies the possibility of magnetically driven topological phase transitions in the electronic bands. Our study also provides a useful method to deal with correlated topological magnetic systems with narrow band gaps self-consistently.

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.

Photonic Signatures of Spin-Driven Ferroelectricity in Multiferroic Dielectric Oxides.

We study the dispersion and scattering properties of electromagnetic modes coupled to a helically ordered spin lattice hosted by a dielectric oxide with a ferroelectric polarization driven by vector spin chirality. Quasianalytical approaches and full-fledged numerics evidence the formation of a chiral magnonic photonic band gap and the presence of gate-voltage dependent circular dichroism in the scattering of electromagnetic waves from the lattice. Gating couples to the emergent ferroelectric polarization and hence, to the underlying vector-spin chirality. The theory relies on solving simultaneously Maxwell's equations coupled to the driven localized spins taking into account their spatial topology and spatial anisotropic interactions. The developed approach is applicable to various settings involving noncollinear spins and multiferroic systems with potential applications in noncollinear magnetophotonics.

Skyrmion based magnonic crystals

Magnonics is now an attractive field which focuses on the dynamic characteristics of magnons, a kind of quasiparticles in magnetic media, and attempts to apply magnons for functional devices. In order to construct magnon-based devices, it is necessary to fabricate materials with specific and tunable magnon bands and bandgaps. Skyrmion-based magnonic crystal is one of the most suitable materials which possess periodical skyrmion structure and show applicative magnon bands and bandgaps. In this review, we provide an overview over recent theoretical and experimental research on skyrmion-based magnonic crystals. We will first provide an introduction of magnonic crystals and magnetic skyrmion. Then, we will show the theoretical and experimental progress on skyrmion-based magnonic crystals and their magnon band characteristics. At the end, we will give an outlook and perspectives of new fascinating fields on topological nontrivial magnon modes, as well as hybrid and quantum magnonic phenomena of skyrmion-based magnonic crystals.

Magnetic interactions and spin excitations in van der Waals ferromagnet

Using a combination of density functional theory (DFT) and spin-wave theory methods, we investigate the magnetic interactions and spin excitations in semiconducting VI3. Exchange parameters of monolayer, bilayer, and bulk forms are evaluated by mapping the magnetic energies of various spin configurations, calculated using DFT+U, onto the Heisenberg model. The intralayer couplings remain largely unchanged in three forms of VI3, while the interlayer couplings show stronger dependence on the dimensionality of the materials. We calculate the spin-wave spectra within a linear spin-wave theory and discuss how various exchange parameters affect the magnon bands. The magnon–magnon interaction is further incorporated, and the Curie temperature is estimated using a self-consistently renormalized spin-wave theory. To understand the roles of constituent atoms on magnetocrystalline anisotropy energy (MAE), we resolve MAE into sublattices and find that a strong negative V-I inter-sublattice contribution is responsible for the relatively small easy-axis MAE in VI3.

Magnon-driven skyrmion dynamics in antiferromagnets: Effect of magnon polarization

The controllable magnetic skyrmion motion represents a highly concerned issue in preparing advanced skyrmion-based spintronic devices. Specifically, magnon-driven skyrmion motion can be easily accessible in both metallic and insulating magnets, and thus is highly preferred over electric current control further for the ultra-low energy consumption. In this work, we investigate extensively the dynamics of skyrmion motion driven by magnon in an antiferromagnet using the collective coordinate theory, focusing on the effect of magnon polarization. It is revealed that the skyrmion Hall motion driven by circularly polarized magnon becomes inevitable generally, consistent with earlier report. Furthermore, the elastic scattering theory and numerical results unveil the strong inter-dependence between the linearly polarized magnon and skyrmion motion, suggesting the complicated dependence of the skyrmion motion on the polarization nature of driving magnon. On the reversal, the scattering from the moving skyrmion may lead to decomposition of the linearly polarized magnon into two elliptically polarized magnon bands. Consequently, a net transverse force acting on skyrmion is generated owing to the broken mirror symmetry, which in turn drives a skyrmion Hall motion. The Hall motion can be completely suppressed only in some specific condition where the mirror symmetry is preserved. The present work unveils non-trivial skyrmion-magnon scattering behavior in antiferromagnets, advancing the antiferromagnetic spintronics and benefiting to high-performance devices.