Magnon Edge Research Articles

Electrical activity of topological chiral edge magnons

Electrical activity of topological chiral edge magnons

Coupled Electronic and Magnonic Topological States in Two-Dimensional Ferromagnets.

Magnetic materials offer a fertile playground for fundamental physics discovery, with not only electronic but also magnonic topological states intensively explored. However, one natural material with both electronic and magnonic nontrivial topologies is still unknown. Here, we demonstrate the coexistence of first-order topological magnon insulators (TMIs) and electronic second-order topological insulators (SOTIs) in 2D honeycomb ferromagnets, giving rise to the nontrivial corner states being connected by the charge-free magnonic edge states. We show that, with symmetry, the phase factor ± ϕ caused by the next nearest-neighbor Dzyaloshinskii-Moriya interaction breaks the pseudo-spin time-reversal symmetry , which leads to the split of magnon bands, i.e., the emergence of TMIs with a nonzero Chern number of , in experimentally feasible candidates of MoI3, CrSiTe3, and CrGeTe3 monolayers. Moreover, protected by the symmetry, the electronic SOTIs characterized by nontrivial corner states are obtained, bridging the topological aspect of fermions and bosons with a high possibility of innovative applications in spintronics devices.

Zero-Frequency Chiral Magnonic Edge States Protected by Nonequilibrium Topology.

Topological bosonic excitations must, in contrast to their fermionic counterparts, appear at finite energies. This is a key challenge for magnons, as it prevents straightforward excitation and detection of topologically protected magnonic edge states and their use in magnonic devices. In this Letter, we show that in a nonequilibrium state, in which the magnetization is pointing against the external magnetic field, the topologically protected chiral edge states in a magnon Chern insulator can be lowered to zero frequency, making them directly accessible by existing experimental techniques. We discuss the spin-orbit torque required to stabilize this nonequilibrium state, and show explicitly using numerical Landau-Lifshitz-Gilbert simulations that the edge states can be excited with a microwave field. Finally, we consider a propagating spin wave spectroscopy experiment, and demonstrate that the edge states can be directly detected.

Discrete time crystal made of topological edge magnons

Discrete time crystal made of topological edge magnons

Topological magnons on the triangular kagome lattice

We present the topology of magnons on the triangular kagome lattice (TKL) by calculating its Berry curvature, Chern number, and edge states. In addition to the ferromagnetic state, the TKL hosts ferrimagnetic ground state as its two sublattices can couple with each other either ferromagnetically or antiferromagnetically. Using Holstein-Primakoff (HP) boson theory and Green's function approach, we find that the TKL has a rich topological band structure with added high Chern numbers compared with the kagome and honeycomb lattices. The magnon edge current allows a convenient calculation of thermal Hall coefficients and the orbital angular momentum gives correlation to the Einstein--de Haas effect. We apply the calculations to the TKL and derive the topological gyromagnetic ratio showing a nonzero Einstein--de Haas effect in the zero-temperature limit. Our results render the TKL as a potential platform for quantum magnonics applications including high-precision mechanical sensors and information transmission.

Long-distance coupling of spin qubits via topological magnons

We consider two distant spin qubits in quantum dots, both coupled to a two-dimensional topological ferromagnet hosting chiral magnon edge states at the boundary. The chiral magnon is used to mediate entanglement between the spin qubits, realizing a fundamental building block of scalable quantum computing architectures: a long-distance two-qubit gate. Previous proposals for long-distance coupling with magnons involved off-resonant coupling, where the detuning of the spin-qubit frequency from the magnonic band edge provides protection against spontaneous relaxation. The topological magnon mode, on the other hand, lies in between two magnonic bands far away from any bulk magnon resonances, facilitating strong and highly tuneable coupling between the two spin qubits. Even though the coupling between the qubit and the chiral magnon is resonant for a wide range of qubit splittings, we find that the magnon-induced qubit relaxation is vastly suppressed if the coupling between the qubit and the ferromagnet is antiferromagnetic. A fast and high-fidelity long-distance coupling protocol is presented capable of achieving spin-qubit entanglement over micrometer distances with $1\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$ gate speed and up to $99.9%$ fidelities. The resulting spin-qubit entanglement may be used as a probe for the long-sought detection of topological edge magnons.

Spin Waves and Magnetic Exchange Hamiltonian in CrSBr.

CrSBr is an air‐stable two‐dimensional (2D) van der Waals semiconducting magnet with great technological promise, but its atomic‐scale magnetic interactions—crucial information for high‐frequency switching—are poorly understood. An experimental study is presented to determine the CrSBr magnetic exchange Hamiltonian and bulk magnon spectrum. The A‐type antiferromagnetic order using single crystal neutron diffraction is confirmed here. The magnon dispersions are also measured using inelastic neutron scattering and rigorously fit the excitation modes to a spin wave model. The magnon spectrum is well described by an intra‐plane ferromagnetic Heisenberg exchange model with seven nearest in‐plane exchanges. This fitted exchange Hamiltonian enables theoretical predictions of CrSBr behavior: as one example, the fitted Hamiltonian is used to predict the presence of chiral magnon edge modes with a spin‐orbit enhanced CrSBr heterostructure.

Unified formulation of interfacial magnonic pumping from noncollinear magnets

We establish a general formulation for spin current pumped by magnons at the interface between a normal metal and a magnetic insulator, valid for any noncollinear magnetic configuration in the linear spin wave regime. This current is generated by driving the system in a nonequilibrium state, covering setups such as thermal spin injection (spin Seebeck effect) or spin voltage by irradiation of the insulator (spin pumping). We illustrate the formula in the special case of a honeycomb topological ferromagnet, for simplicity, and cover both the spin Seebeck and spin pumping setups. We show how the topological parameters influence the spin current and propose a way to obtain a contribution mainly from the topological edge magnons in the spin pumping case.

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.

Theoretical realization of rich magnon topology by symmetry-breaking in honeycomb bilayer ferromagnets

We reveal the rich magnon topology in honeycomb bilayer ferromagnets (HBF) induced by the combined effect of interlayer exchange, Dzyaloshinskii-Moriya interaction (DMI), and electrostatic doping (ED). In particular, we present a systematic study of the Hamiltonian non-adiabatic evolution in the HBF parametric space, spanned by the symmetry-breaking terms (DMI and ED) and interlayer exchange. We determine the band closure manifolds which are found to divide the parametric space into six distinct regions, matched with five distinct topological phases and one topologically trivial phase. The characteristic Chern numbers and thermal Hall conductivities are calculated for the topological phases. Edge spectra, dictated by the bulk-edge correspondence, are also analyzed in the nanoribbon version of the model. Both bulk and edge spectra are found to be nonreciprocal as a consequence of ED and edge magnons are observed to counter propagate on opposite edges. The predicted results offer new insights on the manipulation of magnonic Chern numbers and magnon topological transport via experimentally tunable parameters.

Spin interactions and topological magnonics in chromium trihalide CrClBrI

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 Dzyaloshinskii-Moriya and Heisenberg interactions. Depending on the parameters, the DM interactions are responsible for the formation of exotic chiral spin states, such as skyrmions and spin cycloids, as shown by our Monte Carlo simulations. Focusing on a ground state with a two-sublattice unit cell, we find spin-wave bands with nonvanishing Chern numbers. The resulting magnon edge states yield a magnon thermal Hall conductivity that changes sign as function of temperature and magnetic field, suggesting chromium trihalides as a candidate for testing topological magnon transport in two-dimensional noncollinear spin systems.

Magnonic topological insulator realized in 2D magnetic skyrmion crystals

With the concept of topological order of electronic states in crystals being proposed, the pursuit of topological phases in various systems has become an important subject of modern physical science. The existence of antisymmetric Dzyaloshinskii–Moriya interaction caused by spin–orbit coupling in magnetic systems leads to the non-reciprocal propagation of magnons, which is a key factor to realize the magnonic analog of an electronic topological insulator (TI). Here, a two-dimensional magnetic skyrmion crystal (SkX) is introduced as a platform for realizing magnonic TI. It is numerically demonstrated that nonchiral and chiral edge states could exist in different magnonic bandgaps. The nonchiral edge magnons can propagate to both directions simultaneously along the boundary of the SkX with different wavelengths and group velocities. By contrast, chiral edge magnons are topologically protected, resulting in the unidirectional propagation along the boundaries and the robustness against defects or disorders. Furthermore, the chirality and the presence of edge magnons can be manipulated by the polarity of skyrmions and the width of the second magnonic bandgap via the magnetic field. Our findings could provide a skyrmionic paradigm for investigating topological magnonics and even quantum magnonics.

Photoinduced Floquet topological magnons in a ferromagnetic checkerboard lattice

This theoretical work is devoted to investigating laser-irradiated Floquet topological magnon insulators on a two-dimensional checkerboard ferromagnet and corresponding topological phase transitions. It is shown that the checkerboard Floquet topological magnon insulator is able to be transformed from a topological magnon insulator into another one possessing various Berry curvatures and Chern numbers by changing the light intensity. Especially, we also show that both Tamm-like and topologically protected Floquet magnon edge states can exist when a nontrivial gap opens. In addition, our results display that the sign of the Floquet thermal Hall conductivity is also tunable via varying the light intensity of the laser field.

Edge states in quantum spin chains: The interplay among interaction, gradient magnetic field, and Floquet engineering

We explore the edge defects induced by spin-spin interaction in a finite paradigmatic Heisenberg spin chain. By introducing a gradient magnetic field and a periodically modulated spin-exchange strength, the resonance between modulation frequency and magnetic-field gradient can also induce asymmetric defects at the edges, dubbed as Floquet-Wannier-Zeeman edge defects. The interplay between these two types of edge defects allows us to manipulate the magnon edge states from an isolated band into a continuum one. In the high-frequency regime, we analytically derive effective models to interpret the formation mechanisms for edge states by employing the multiscale perturbation analysis. Our study offers insights to understand and control the magnon edge states governed by the interplay between edge defects induced by the spin-spin interaction and the Floquet-Wannier-Zeeman manipulation.

Topological magnons in ferromagnetic Kitaev-Heisenberg model on CaVO lattice

A number of topological phases are found to emerge in the ferromagnetic Kitaev-Heisenberg model on CaVO lattice in the presence of Dzyaloshinskii-Moriya interaction. Heisenberg and Kitaev terms have been considered on nearest and next-nearest neighbor bonds in a variety of ways. Both isotropic and anisotropic couplings are taken into account. Topological phases are characterized by Chern numbers for the distinct magnon bands as well as the number of modes for topologically protected gapless magnon edge states. Band structure, dispersion relation along the high-symmetric points of first Brillouin zone, density of states and thermal Hall conductance have been evaluated for every phase. An extensive Phase diagram has been constructed. Topological phase transition in the parameter space is also studied.

Bosonic Bott Index and Disorder-Induced Topological Transitions of Magnons.

We investigate the role of disorder on the various topological magnonic phases present in deformed honeycomb ferromagnets. To this end, we introduce a bosonic Bott index to characterize the topology of magnon spectra in finite, disordered systems. The consistency between the Bott index and Chern number is numerically established in the clean limit. We demonstrate that topologically protected magnon edge states are robust to moderate disorder and, as anticipated, localized in the strong regime. We predict a disorder-driven topological phase transition, a magnonic analog of the "topological Anderson insulator" in electronic systems, where the disorder is responsible for the emergence of the nontrivial topology. Combining the results for the Bott index and transport properties, we show that bulk-boundary correspondence holds for disordered topological magnons. Our results open the door for research on topological magnonics as well as other bosonic excitations in finite and disordered systems.

Light-induced topological magnons in two-dimensional van der Waals magnets

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 of the magnon Hamiltonian for a slowly varying pulse envelope. Compared to similar but conceptually distinct driving schemes based on the Aharanov-Casher effect, the dimensionless light-matter coupling parameter \lambda = eEa/\hbar\omegaλ=eEa/ℏω at fixed electric field strength is enhanced by a factor \sim 10^5∼105. This increase of the coupling parameter allows to induce a topological gap of the order of \Delta \approx 2Δ≈2 meV with realistic laser pulses, bringing an experimental realization of light-induced topological magnon edge states within reach.

Relativistic exchange interactions in CrX3 ( X=Cl , Br, I) monolayers

It has been predicted theoretically and indirectly confirmed experimentally that single-layer CrX$_3$ (X=Cl, Br, I) might be the prototypes of topological magnetic insulators (TMI). In this work, by using first-principles calculations combined with atomistic spin dynamics we provide a complete picture of the magnetic interactions and magnetic excitations in CrX$_3$. The focus is here on the two most important aspects for the actual realization of TMI, namely the relativistic magnetic interactions and the finite-size (edge) effects. We compute the full interaction tensor, which includes both Kitaev and Dzyaloshinskii-Moriya terms, which are considered as the most likely mechanisms for stabilizing topological magnons. First, we instigate the properties of bulk CrI$_3$ and compare the simulated magnon spectrum with the experimental data [Phys. Rev. X 8, 041028 (2018)]. Our results suggest that a large size of topological gap, seen in experiment ($\approx$ 4 meV), can not be explained by considering pair-wise spin interactions only. We identify several possible reasons for this disagreement and suggest that a pronounced magneto-elastic coupling should be expected in this class of materials. The magnetic interactions in the monolayers of CrX$_3$ are also investigated. The strength of the anisotropic interactions is shown to scale with the position of halide atom in the Periodic Table, the heavier the element the larger is the anisotropy. Comparing the magnons for the bulk and single-layer CrI$_3$, we find that the size of the topological gap becomes smaller in the latter case. Finally, we investigate finite-size effects in monolayers and demonstrate that the anisotropic couplings between Cr atoms close to the edges are much stronger than those in ideal periodic structure. This should have impact on the dynamics of the magnon edge modes in this class of materials.

Dynamically reconfigurable magnonic crystal composed of artificial magnetic skyrmion lattice

Skyrmion-based magnonic crystal (MC) provides the dynamic tunability of manipulating magnonic band structure, and this brings obvious advantages over geometry or material-modulated MCs with a static band. But the existence of stable skyrmion usually requires strong Dzyaloshinskii–Moriya interaction (DMI) in combination with an external magnetic field under specific strength, and all these features limit the experimental realization and practical designing of the skyrmion-based MC. Here, we introduce the concept of artificial magnetic skyrmion-based MC. The artificial skyrmion lattice is realized by patterning an array of magnetic nanodisks on a thin film. The coupling between nanodisks and thin film generates an array of skyrmions possessing the same period as the nanodisk array. Via applying the pulsed magnetic field, one can turn on and off the skyrmion lattice, which allows switching between two very different magnonic band structures. Furthermore, via a honeycomb lattice, we extend this design to the dynamic on and off for chiral magnon edge state. The on and off switching is fast and in the range of nanoseconds. Considering that the coupling from nanodisks can greatly enhance the stability of skyrmions, no matter whether the DMI or magnetic field exists or not, our design points to a simple realization of dynamic skyrmion MC and topological magnonic devices.

Strong coupling between magnons confined in a single magnonic cavity

Strong coupling between magnons and cavity photons was studied extensively for quantum electrodynamics in the past few years. Recently, the strong magnon–magnon coupling between adjacent layers in magnetic multilayers has been reported. However, the strongly coupled magnons confined in a single nanomagnet remains to be revealed. Here, we report the interaction between different magnon modes in a single magnonic cavity. The intermodel coupling between edge and center magnon modes in the strong coupling regime was approached with a maximum coupling strength of 0.494 GHz and cooperativity of 60.1 with a damping of 1 × 10−3. Furthermore, it is found that the coupling strength is highly dependent on the geometric parameters of the magnonic cavity. Our findings could greatly enrich the still evolving field of quantum magnonics.