Magnonic Band Research Articles

Symmetry enhanced spin-Nernst effect in honeycomb antiferromagnetic transition metal trichalcogenide monolayers

We investigate systematically the spin-Nernst effect in N\'eel and zigzag ordered honeycomb antiferromagnets. Monolayers of transition-metal trichalcogenides, $\mathrm{Mn}\mathrm{P}{\mathrm{Se}}_{3}$, $\mathrm{Mn}{\mathrm{PS}}_{3}$, and ${\text{VPS}}_{3}$ show an antiferromagnetic N\'eel order while $\mathrm{Cr}\mathrm{Si}{\mathrm{Te}}_{3}$, $\mathrm{Ni}{\mathrm{PS}}_{3}$, and $\mathrm{Ni}\mathrm{P}{\mathrm{Se}}_{3}$ show an antiferromagnetic zigzag order. We extract the exchange and Dzyaloshinskii-Moriya interaction parameters from ab initio calculations. Using these parameters, we predict that the spin-Nernst coefficient is at least two orders of magnitude larger in zigzag compared to the N\'eel ordered antiferromagnets. We find that this enhancement relies on the large band splitting due to the symmetry of magnetic configuration in the zigzag order. Our calculations indicate that the Dzyaloshinskii-Moriya interaction is the underlying factor for the spin-Nernst effect in both cases, although with different microscopic mechanisms. In the case of N\'eel antiferromagnets, magnon bands already possess a Berry curvature and introducing the Dzyaloshinskii-Moriya interaction splits the magnon bands with the opposite helicity throughout the Brillouin zone which results in an unbalanced population of magnons carrying opposite spins. In the case of zigzag antiferromagnets, magnon bands do not possess the Berry curvature but they are split for opposite helicity magnons due to symmetry of the system. In this case, introducing the Dzyaloshinskii-Moriya interaction induces the Berry curvature and results in the spin-Nernst effect. Due to large magnon band splitting, the spin-Nernst effect in zigzag antiferromagnets is stronger than N\'eel antiferromagnets.

Frequency Filtering with a Magnonic Crystal Based on Nanometer-Thick Yttrium Iron Garnet Films

Magnonics rely on the wave nature of the magnetic excitations to process information, an approach that is common to many fields such as photonics, phononics, and plasmonics. Nevertheless, magnons, the quanta of spin-wave excitations, have the unique advantage to be at frequencies that are lying between a few GHz to tens of GHz, that is, in the technologically relevant radio-frequency bands for 4G and 5G telecommunications. Furthermore, their typical wavelengths are compatible with on-chip integration. Here, we demonstrate radio-frequency signal filtering by a micron-scale magnonic crystal (MC) based on a nanopatterned 20 nm-thick film of yttrium iron garnet with a minimum feature size of 100 nm where the Bragg vector is set to be kB = 2.1 μm–1. We map the intensity and the phase of spin waves (SWs) propagating in the periodic magnetic structure using phase-resolved microfocus Brillouin light-scattering spectroscopy. Based on these maps, we obtain the SW dispersion and the attenuation characteristics. Efficient filtering is obtained with a frequency selectivity of 20 MHz at an operating frequency of 4.9 GHz. The results are analyzed by performing time- and frequency-resolved full-scale micromagnetic simulations of the MC that reproduce quantitatively the complexity of the harmonic response across the magnonic band gap and allow the identification of the relevant SW-quantized modes, thereby providing an in-depth insight into the physics of SW propagation in periodically modulated nanoscale structures.

Magnonic Su-Schrieffer-Heeger model in honeycomb ferromagnets

Topological electronics has extended its richness to non-electronic systems where phonons and magnons can play the role of electrons. In particular, topological phases of magnons can be enabled by the Dzyaloshinskii-Moriya interaction (DMI) which acts as an effective spin-orbit coupling. We show that besides DMI, an alternating arrangement of Heisenberg exchange interactions critically determines the magnon band topology, realizing a magnonic analog of the Su-Schrieffer-Heeger model. On a honeycomb ferromagnet with perpendicular anisotropy, we calculate the topological phase diagram, the chiral edge states, and the associated magnon Hall effect by allowing the relative strength of exchange interactions on different links to be tunable. Including weak phonon-magnon hybridization does not change the result. Candidate materials are discussed.

2D Surface Spin Waves in Dynamic Magnonic Crystals Created by a Surface Acoustic Wave in YIG Films

Some results of the study of 2D propagation of surface magnetostatic spin waves (SMSW) in dynamic magnonic crystals (DMC) created by a surface acoustic wave (SAW) in a structure with a yttrium-iron garnet (YIG) film are presented. Such studies are interesting from the practical point of view of creating real relatively complex devices on spin waves when they propagate in different directions, and not only in the 1D case. The methods of experimental research are presented, in particular, the features of the method of excitation of SAW in the structure that do not lead to the appearance of additional magnetic anisotropy in it, a method for measuring the angular dependencies of SMSW using mobile antenna–probes is presented. The angular dependences of the magnonic band gap frequencies are measured. It is established that the transmission bands with the transformation of the reflected SMSW into other types of magnetostatic waves (MSW) exist at any angle values, while the intervals in which there are no SMSW transformations during reflections occur in a certain narrower range of angles. The angles of the directions of the wave vectors and the Poynting vector of the reflected SMSW were also measured. A satisfactory agreement was obtained with the calculation performed using the method of isofrequency curves and the laws of inelastic scattering SMSW on SAW.

Magnonic Bending, Phase Shifting and Interferometry in a 2D Reconfigurable Nanodisk Crystal.

Strongly interacting nanomagnetic systems are pivotal across next-generation technologies including reconfigurable magnonics and neuromorphic computation. Controlling magnetization states and local coupling between neighboring nanoelements allows vast reconfigurability and a host of associated functionalities. However, existing designs typically suffer from an inability to tailor interelement coupling post-fabrication and nanoelements restricted to a pair of Ising-like magnetization states. Here, we propose a class of reconfigurable magnonic crystals incorporating nanodisks as the functional element. Ferromagnetic nanodisks are crucially bistable in macrospin and vortex states, allowing interelement coupling to be selectively activated (macrospin) or deactivated (vortex). Through microstate engineering, we leverage the distinct coupling behaviors and magnonic band structures of bistable nanodisks to achieve reprogrammable magnonic waveguiding, bending, gating, and phase-shifting across a 2D network. The potential of nanodisk-based magnonics for wave-based computation is demonstrated via an all-magnon interferometer exhibiting XNOR logic functionality. Local microstate control is achieved here via topological magnetic writing using a magnetic force microscope tip.

Finite-temperature dynamics and the role of disorder in nearly critical Ni(Cl1−xBrx)2·4SC(NH2)2

Inelastic neutron scattering is used to investigate the temperature dependence of spin correlations in the 3-dimensional XY antiferromagnet Ni(Cl$_{1-x}$Br$_x$)$_2$$\cdot$4SC(NH$_2$)$_2$, $ x = 0.14(1)$, tuned close to the chemical-composition-induced soft-mode transition. The local dynamic structure factor shows $\hbar\omega/T$ scaling behavior characteristic of a quantum critical point. The deviation of the measured critical exponent from spin wave theoretical expectations are attributed to disorder. Another effect of disorder is local excitations above the magnon band. Their energy, structure factor and temperature dependence are well explained by simple strong-bond dimers associated with Br-impurity sites.

Magnon magic angles and tunable Hall conductivity in 2D twisted ferromagnetic bilayers

Twistronics is currently one of the most active research fields in condensed matter physics, following the discovery of correlated insulating and superconducting phases in twisted bilayer graphene (tBLG). Here, we present a magnonic analogue of tBLG. We study magnons in twisted ferromagnetic bilayers (tFBL) with collinear magnetic order, including exchange and weak Dzyaloshinskii-Moriya interactions (DMI). For negligible DMI, tFBL presents discrete magnon magic angles and flat moiré minibands analogous to tBLG. The DMI, however, changes the picture and renders the system much more exotic. The DMI in tFBL induces a rich topological magnon band structure for any twist angle. The twist angle turns to a control knob for the magnon valley Hall and Nernst conductivities. Gapped flat bands appear in a continuum of magic angles in tFBL with DMI. In the lower limit of the continuum, the band structure reconstructs to form several topological flat bands. The luxury of twist-angle control over band gaps, topological properties, number of flat bands, and valley Hall and Nernst conductivities renders tFBL a novel device from fundamental and applied perspectives.

Moiré magnons in twisted bilayer magnets with collinear order

We explore the moir\'e magnon bands in twisted bilayer magnets with next-nearest neighboring Dzyaloshinskii-Moriya interactions, assuming that the out-of-plane collinear magnetic order is preserved under weak interlayer coupling. By calculating the magnonic band structures and the topological Chern numbers for four representative cases, we find that (i) the valley moir\'e bands are extremely flat over a wide range of continuous twist angles; (ii) the topological Chern numbers of the lowest few flat bands vary significantly with the twist angle; and (iii) the lowest few topological flat bands in bilayer antiferromagnets entail nontrivial thermal spin transport in the transverse direction; These properties make twisted bilayer magnets an ideal platform to study the magnonic counterparts of moir\'e electrons, where the statistical distinction between magnons and electrons leads to fundamentally new physical behavior.

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.

Frustrated quantum Heisenberg double-tetrahedral and octahedral chains at high magnetic fields

We consider the spin-1/2 antiferromagnetic Heisenberg model on two one-dimensional frustrated lattices, double-tetrahedral chain and octahedral chain, with almost dispersionless (flat) lowest magnon band in a strong magnetic field. Using the localized magnons picture, we construct an effective description of the one-dimensional chains with triangle and square traps within the strong coupling approximation. We perform extensive exact diagonalization and density matrix renormalization group calculations to check the validity of the obtained effective Hamiltonians by comparison with the initial models with special focus on the magnetization and specific heat at high magnetic fields.

Controlling the propagation of dipole-exchange spin waves using local inhomogeneity of the anisotropy

Spin waves are promising candidates to carry, transport, and process information. Controlling the propagation characteristics of spin waves in magnetic materials is an essential ingredient for designing spin-wave based computing architectures. Here, we study the influence of surface inhomogeneities on the spin-wave signals transmitted through thin films. We use micromagnetic simulations to study the spin-wave dynamics in an in-plane magnetized yttrium iron garnet thin film with a thickness in the nanometre range in the presence of surface defects in the form of locally introduced uniaxial anisotropies. These defects are used to demonstrate that the Backward Volume Magnetostatic Spin Waves (BVMSW) are more responsive to backscattering in comparison to Magnetostatic Surface Spin Waves (MSSWs). For this particular defect type, the reason for this behavior can be quantitatively related to the difference in the magnon band structures for the two types of spin waves. To demonstrate this, we develop a quasi-analytical theory for the scattering process. It shows an excellent agreement with the micromagnetic simulations, sheds light on the backscattering processes and provides a new way to analyze the spin-wave transmission rates in the presence of surface inhomogeneities in sufficiently thin films, for which the role of exchange energy in the spin-wave dynamics is significant. Our study paves the way to designing magnonic logic devices for data processing which rely on a designed control of the spin-wave transmission.

Spin Seebeck effect near the antiferromagnetic spin-flop transition

We develop a low-temperature, long-wavelength theory for the interfacial spin Seebeck effect (SSE) in easy-axis antiferromagnets. The field-induced spin-flop (SF) transition of N\'eel order is associated with a qualitative change in SSE behavior: Below SF, there are two spin carriers with opposite magnetic moments, with the carriers polarized along the field forming a majority magnon band. Above SF, the low-energy, ferromagnetic-like mode has magnetic moment opposite the field. This results in a sign change of the SSE across SF, which agrees with recent measurements on Cr$_2$O$_3$/Pt and Cr$_2$O$_3$/Ta devices [Li $\textit{et al.,}$ $\textit{Nature}$ $\textbf{578,}$ 70 (2020)]. In our theory, SSE is due to a N\'eel spin current below SF and a magnetic spin current above SF. Using the ratio of the associated N\'eel to magnetic spin-mixing conductances as a single constant fitting parameter, we reproduce the field dependence of the experimental data and partially the temperature dependence of the relative SSE jump across SF.

Topological Magnons with Nodal-Line and Triple-Point Degeneracies: Implications for Thermal Hall Effect in Pyrochlore Iridates.

We analyze the magnon excitations in pyrochlore iridates with all-in-all-out (AIAO) antiferromagnetic order, focusing on their topological features. We identify the magnetic point group symmetries that protect the nodal-line band crossings and triple-point degeneracies that dominate the Berry curvature. We find three distinct regimes of magnon band topology, as a function of the ratio of Dzyaloshinskii-Moriya interaction to the antiferromagnetic exchange. We show how the thermal Hall response provides a unique probe of the topological magnon band structure in AIAO systems.

Effect of exchange and dipolar interlayer interactions on the magnonic band structure of dense Fe/Cu/Py nanowires with symmetric and asymmetric layer widths

We present a systematic experimental and theoretical investigation of the magnonic band structure in dense arrays of both asymmetric and symmetric cross-section trilayered Fe(10 nm)/Cu( $t$)/Py(10 nm) nanowires (NWs). The Cu spacer thickness ($t$) is varied in the range between 0 and 10 nm. The frequency dispersion of collective spin-wave excitations in the above trilayered NW arrays has been studied by the Brillouin light-scattering technique while sweeping the wave vector perpendicularly to the nanowire length over four Brillouin zones of the reciprocal space. The experimental results have been quantitatively reproduced by an original numerical model that includes a two-dimensional Green's function description of the dipole field of the dynamic magnetization and exchange coupling between the layers. We found that, depending on $t$, the Py and Fe magnetic layers within the same nanowire are coupled by either the interlayer exchange or dipolar interactions. This has an impact on both the magnetization reversal and the collective dynamical properties of the artificial crystal. In particular, it is possible to stabilize a magnetization configuration where the layer magnetization vectors point in the same or in the opposite direction over a field range that varies with the Cu thickness. In addition, several modes are detected whose propagation properties (i.e., stationary or dispersive) through the array depend on static magnetization configuration as well as on the relative phase (in-phase or out-of-phase) of dynamic magnetizations between the two layers within the same nanowire.

Spin-texture driven reconfigurable magnonics in chains of connectedNi80Fe20submicron dots

Topological magnonics has attracted intense interest for application in energy efficient computational devices. Here, we show reconfigurable magnonic band structure and band gap by a bias-field controlled spin texture in chains of connected ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ submicron dots. Particularly for an identical field value, we achieve both ``$S$'' and shifted-core vortex states based on magnetic history leading to a drastic change in magnonic band structure. A first-order phase transition from the saturation to vortex state drives this change, as opposed to a continuous change from the saturation to $S$ state.

Gradual pressure-induced enhancement of magnon excitations in CeCoSi

CeCoSi is an intermetallic antiferromagnet with a very unusual temperature-pressure phase diagram: at ambient pressure it orders below $T_{\mathrm{N}} = 8.8$ K, while application of hydrostatic pressure induces a new magnetically ordered phase with exceptionally high transition temperature of $\sim40$ K at 1.5 GPa. We studied the magnetic properties and the pressure-induced magnetic phase of CeCoSi by means of elastic and inelastic neutron scattering (INS) and heat capacity measurements. At ambient pressure CeCoSi orders into a simple commensurate AFM structure with a reduced ordered moment of only $m_{\mathrm{Ce}} = 0.37(6)$ $\mu_{\mathrm{B}}$. Specific heat and low-energy INS indicate a significant gap in the low-energy magnon excitation spectrum in the antiferromagnetic phase, with the CEF excitations located above 10 meV. Hydrostatic pressure gradually shifts the energy of the magnon band towards higher energies, and the temperature dependence of the magnons measured at 1.5 GPa is consistent with the phase diagram. Moreover, the CEF excitations are also drastically modified under pressure.

Topological magnon bands in the flux state of Shastry-Sutherland lattice model

We investigate low energy magnon excitations above the non-collinear flux state and non-coplanar canted flux state in a Heisenberg anti-ferromagnet with Dzyaloshinskii-Moriya interaction~(DMI) on a Sashtry-Sutherland lattice.While previous studies have shown the presence of topological magnetic excitation in the dimer and ferromagnetic phases on the Shastry-Sutherland lattice, our results establish the non-trivial topology of magnons in the anti-ferromagnetic flux and canted flux states. Our results uncover the existence of a multitude of topological phase transitions in the magnon sector -- evidenced by the changing Chern numbers of the single magnon bands -- as the Hamiltonian parameters are varied, even when the ground state remains unchanged. The thermal Hall conductivity is calculated and its derivative is shown to exhibit a logarithmic divergence at the phase transitions, independent of the type of band touching involved. This may provide a useful means to identify the energy at which the transition occurs. Finally, we propose the way to realize the studied model in a practical material.

Modulation of magnonic bands of dipole-exchange spin waves in fishbone-like yttrium iron garnet nanostrip magnonic crystal waveguides

We designed a fishbone-like yttrium iron garnet nanostrip magnonic crystal waveguide structure and investigated the modulation of the structural parameters to the propagating characteristics of dipole-exchange spin waves by using the object oriented micromagnetic framework numerical calculation method. The number, position, and width of the allowed bands in the magnonic band maps can be manipulated by changing the tilted angles of the sides branch (θ), the width of the ‘main bone’ (W1), and the separatiion distance between the two side branches (P2). Besides the normal band gaps appearing at the Brillouin zone (BZ) boundaries, extra band gaps emerge at certain values of k in the dispersion curves with a deviation Λ away from the BZ boundaries which can also be controlled by θ, W1, and P2. Compared with other parameters, the tilted angle θ has a greater impact on spin wave propagation.

Antichiral edge states in Heisenberg ferromagnet on a honeycomb lattice

We demonstrate the emergence of anti-chiral edge states in a Heisenberg ferromagnet with Dzyaloshinskii-Moriya interaction(DMI) on a honeycomb lattice with in-equivalent sub-lattices. The DMI, which acts between atoms of the same species, differs in magnitude for the two sub-lattices, resulting in a shifting of the energy of the magnon bands in opposite directions at the two Dirac points. The chiral symmetry is broken and for sufficiently strong asymmetry, the band shifting leads to anti-chiral edge states (in addition to the normal chiral edge states) in a rectangular strip where the magnon current propagates in the same direction along the two edges. This is compensated by a counter-propagating bulk current that is enabled by the broken chiral symmetry. We analyze the resulting magnon current profile across the width of the system in details and suggest realistic experimental probes to detect them. Finally, we propose a material that can potentially exhibit such anti-chiral edge states.

SU(3) Topology of Magnon-Phonon Hybridization in 2D Antiferromagnets.

Magnon-phonon hybrid excitations are studied theoretically in a two-dimensional antiferromagnet with an easy axis normal to the plane. We show that two magnon bands and one phonon band are intertwined by the magnetoelastic coupling through a nontrivial SU(3) topology, which can be intuitively perceived by identifying a skyrmion structure in the momentum space. Our results are insensitive to lattice details and generally applicable to two-dimensional antiferromagnets. We show this by developing a continuum theory as the long-wavelength approximation to the tight-binding model. The theoretical results can be probed by measuring the thermal Hall conductance as a function of the temperature and the magnetic field. We envision that the magnetoelastic coupling in antiferromagnets can be a promising venue in search of various topological excitations, which cannot be found in magnetic or elastic models alone.