Linear Spin Wave Research Articles

Spin-wave resonance frequency and quantum fluctuation of the (anti)ferri-(anti)ferrimagnetic double-layer superlattice

The Hamiltonian of a four-sublattice simple cubic superlattice was solved by applying the linear spin-wave theory and the retarded Green's function technique. This study focused on the spin-wave resonance frequency, energy gap, sublattice magnetization, and quantum fluctuations of the system. The results show that the spin quantum number, interlayer (intralayer) exchange couplings, and intralayer anisotropy have a significant influence. In the ground state, the magnetizations of the sublattices are smaller than their spin quantum numbers, indicating the existence of quantum zero-point vibrations in the (anti)ferrimagnetic-(anti)ferrimagnetic bilayer system.

Rich magnon topology in triangular lattice magnets

The two-dimensional magnet has been an emerging and rapidly growing field. The nontrivial topological phenomenon in these materials is an attracting subject. Yet, the realization of such magnets exhibiting topological magnons remains a challenge. Here, employing the linear spin-wave theory and the first-principles calculations, we propose that variety of topological phases exist in the triangular ferromagnet. These include magnon Chern insulators and high-order topological insulators. Interestingly, these topological states can coexist within a certain parameter space, leading to a hybrid topological state. We propose that these topological phases can be realized via atomic substitutions inMnSe2orMnTe2single-layers. The following detailed analysis suggests that non-uniform Dzyaloshinsky-Moriya interactions are crucial in achieving topological magnons. Our work unveil a unique approach to obtaining non-trivial topological magnons in two-dimensional materials.

Bright and Dark ILSM in a bilinear and biquadratic antiferromagnetic spin lattice

In the semiclassical limit, we investigate the intrinsic localized spin-wave modes (ILSM) in an antiferromagnetic spin system with bilinear, biquadratic and D-M interactions. Derivation of the nonlinear Schrödinger equation for the coherent-state amplitude involves the introduction of the multiple scale approximation paired with a quasi discreteness approximation. Consequently, we discover that the oscillatory frequency of the Bright–Dark stationary type ILSM’s can appear below the linear spin wave spectrum and the Bright–Dark type kink lies below the upper of the linear spin-wave spectrum. The effect of the interaction parameters in the system is also examined.

Spin waves in antiferromagnetically coupled bilayers of transition-metal dichalcogenides with Dzyaloshinskii–Moriya interaction

In this paper we analyse quantized spin waves (also referred to as magnons) in bilayers of two-dimensional van der Waals materials, like Vanadium-based dichalcogenides, VX2 (X = S, Se, Te) and other materials of similar symmetry. We assume that the materials exhibit Dzyaloshinskii–Moriya interaction and in-plane easy-axis magnetic anisotropy due to symmetry breaking induced externally (e.g. by strain, gate voltage, proximity effects to an appropriate substrate/oberlayer, etc.). The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong in-plane magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein–Primakoff–Bogoliubov transformation. Accordingly, the description takes into account quantum antiferromagnetic fluctuations. However, it is limited to linear spinwave modes. The Dzyaloshinskii–Moriya interaction is shown to modify the spin wave spectrum of the bilayers, making its low energy part qualitatively similar to the electronic spectrum of the Rashba spin–orbit model.

Magnon bands and transverse transport in a proposed two-dimensional [formula omitted] ferrimagnet

The copper fluoride Cu2F5 is a proposed stable compound that can be seen as a layered lattice of S=1 and S=1/2 sites, corresponding to copper ions. Intending to cast light on the transport properties of ferrimagnetic magnons, we use the linear spin wave approach to study the magnon band structure of the 2D lattice in a ferrimagnetic off-plane order, as well as the transverse transport of magnons in the crystal bulk. A magnetic field or temperature gradient can induce transverse (Hall-like) transport within the linear response theory generated by the Berry curvature of the eigenstates. As in most cases involving magnons, the Berry curvature is related to Dzyaloshinskii–Moriya interactions between next-near-neighbors The band structure of the system is non-degenerate and the transport coefficients are non-null. The novel and interesting feature of the system is that, within certain conditions, the transport coefficients versus temperature curves are non-monotonic and present a sign change, opening the exciting possibility of controlling the transverse magnon flow direction and magnitude with the temperature change.

Spin wave resonance frequency in bilayer ferromagnetic films with the biquadratic exchange interaction

Abstract The dependences of spin wave resonance (SWR) frequency on the surface anisotropy field, interface exchange coupling, symmetry, biquadratic exchange (BQE) interaction, film thickness, and the external magnetic field in bilayer ferromagnetic films are theoretically analyzed by employing the linear spin wave approximation and Green’s function method. A remarkable increase of SWR frequency, except for energetically lower two modes, can be obtained in our model that takes the BQE interaction into account. Again, the effect of the external magnetic field on SWR frequency can be increased by increasing the biquadratic to interlayer exchange ratio. It has been identified that the BQE interaction is of utmost importance in improving the SWR frequency of the bilayer ferromagnetic films. In addition, for bilayer ferromagnetic films, the frequency gap between the energetically highest mode and lowest mode is found to increase by increasing the biquadratic to interlayer exchange ratio and film thickness and destroying the symmetry of the system. These results can be used to improve the understanding of magnetic properties in bilayer ferromagnetic films and thus may have prominent implications for future magnetic devices.

Topological magnons in a non-coplanar magnetic order on the triangular lattice

The bond-dependent Kitaev interaction K is familiar in the effective spin model of transition metal compounds with octahedral ligands. In this work, we find a peculiar non-coplanar magnetic order can be formed with the help of K and next-nearest neighbor Heisenberg coupling J 2 on the triangular lattice. It can be seen as a miniature version of skyrmion crystal, since it has nine spins and an integer topological number in a magnetic unit cell. The magnon excitations in such an order are studied by the linear spin-wave theory. Of note is that the change in the relative size of J 2 and K produces topological magnon phase transitions although the topological number remains unchanged. We also calculated the experimentally observable thermal Hall conductivity, and found that the signs of thermal Hall conductivity will change with topological phase transitions or temperature changes in certain regions.

Topological band engineering and tunable thermal Hall effect in trimerized Lieb lattice ferromagnets

We theoretically study the topological properties of magnons and the relevant magnon thermal Hall effect in trimerized Lieb lattice ferromagnets in the presence of next-nearest-neighbor Dzyaloshinskii-Moriya interactions. By calculating the magnon band structures and their Chern numbers with the linear spin-wave theory, we show that the system can undergo a phase transition between a magnonic topological insulator phase and a magnonic trivial insulator phase. The main results are presented in the form of topological phase diagrams, where the Chern numbers or magnon thermal Hall conductivity are shown as a function of the two lattice trimerization parameters. We find a sharp change of the thermal Hall conductivity across the critical point of phase transformations associated with topological nontrivial edge states. The behaviors reflect that the existence of trimerizations breaks the C4 rotational symmetry of the Lieb lattice. Finally, we show that our theoretical predictions could be experimentally realized in high-temperature cuprate superconductors or organic magnetic materials. Published by the American Physical Society 2024

Systematic determination of a material’s magnetic ground state from first principles

We present a self-consistent method based on first-principles calculations to determine the magnetic ground state of materials, regardless of their dimensionality. Our methodology is founded on satisfying the stability conditions derived from the linear spin wave theory (LSWT) by optimizing the magnetic structure iteratively. We demonstrate the effectiveness of our method by successfully predicting the experimental magnetic structures of NiO, FePS3, FeP, MnF2, FeCl2, and CuO. In each case, we compared our results with available experimental data and existing theoretical calculations reported in the literature. Finally, we discuss the validity of the method and the possible extensions.

Magnon thermal Hall effect via emergent SU(3) flux on the antiferromagnetic skyrmion lattice

Complexity of quantum phases of matter is often understood theoretically by using gauge structures, as is recognized by the Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} and U(1) gauge theory description of spin liquids in frustrated magnets. Anomalous Hall effect of conducting electrons can intrinsically arise from a U(1) gauge expressing the spatial modulation of ferromagnetic moments or from an SU(2) gauge representing the spin-orbit coupling effect. Similarly, in insulating ferro and antiferromagnets, the magnon contribution to anomalous transports is explained in terms of U(1) and SU(2) fluxes present in the ordered magnetic structure. Here, we report thermal Hall measurements of MnSc2S4 in an applied field up to 14 T, for which we consider an emergent higher rank SU(3) flux, controlling the magnon transport. The thermal Hall coefficient takes a substantial value when the material enters a three-sublattice antiferromagnetic skyrmion phase, which is in agreement with the linear spin-wave theory. In our description, magnons are dressed with SU(3) gauge field, which is a mixture of three species of U(1) gauge fields originating from the slowly varying magnetic moments on these sublattices.

Effect of interlayer exchange coupling interaction on topological phase of a bilayer honeycomb Heisenberg ferromagnet

Layered magnetic topological materials are material systems that exhibit both magnetic ordering and topological properties in their smallest two-dimensional units. Studying these systems may lead to the observation of new physical properties and phenomena, which has attracted considerable attention from researchers. The effect of interlayer exchange coupling interactions on bilayer honeycomb Heisenberg ferromagnets with interlayer coupled topological phase is investigated by using linear spin wave theory. The influence of introducing two additional types of interactions, i.e. interlayer exchange coupling interaction and interlayer easy-axis anisotropy interaction, on the topological phase transition are also explored in this work. By calculating the magnon dispersion relations at various interlayer exchange coupling interaction intensities, it is found that the band gaps of high energy band and low energy band both close and reopen at the Dirac points when the system reaches the critical value of interlayer exchange coupling interaction. In magnon systems, such physical phenomena typically relate to topological phase transitions. When calculating the Berry curvature and Chern numbers for the bands in the aforementioned process, it is found that the sign of the Berry curvature reverses and the Chern numbers change when the critical value of interlayer exchange coupling interaction strength is reached, confirming that a topological phase transition occurs indeed. Introducing two other types of interlayer exchange coupling interactions in this process can lead various novel topological phases to occur in the system. The enhancement of interlayer easy-axis anisotropy interactions is likely to impede the topological phase transitions occurring in the system. We find that a major distinction between bilayer honeycomb ferromagnets and their single-layer counterparts lies in the fact that during a topological phase transition, the sign of the magnon thermal Hall coefficient does not change; on the contrary, abrupt shift in the thermal Hall coefficient curve occurs which can be seen as an indicator of topological phase transition of bilayer honeycomb ferromagnets, and is also reflected in the change in magnon Nernst coefficient. The research results of this work can provide theoretical support for developing novel spintronic devices with enhanced information transmission capabilities by using bilayer honeycomb ferromagnetic materials, and can also provide theoretical reference for studing other bilayer ferromagnetic systems.

Pseudo-Landau levels of hexagonal lattice quantum antiferromagnets under bending strain

The pseudo-Landau energy levels of a hexagonal lattice quantum antiferromagnet under bending strain are studied by linear spin-wave theory (LSWT) and quantum Monte Carlo method (QMC). Using the linear spin wave theory, the magnetic pseudo-Landau energy level can be found to appear at the high-energy end of the magnon spectrum, and the energy level spacing is proportional to the square root of the energy level index. The linear spin wave theory and the quantum Monte Carlo method both indicate that at the same size, the local magnetization gradually weakens with the gradual increase of the strain strength. Additionally, the antiferromagnetic order continuously weakens in the <i>y</i>-direction under the same strain strength. This occurs because the Heisenberg chain on the upper boundary becomes decoupled into an isolated vertical chain, leading to the destruction of the magnetic order near the upper boundary. The quantum Monte Carlo method provides a more accurate antiferromagnetic sequence evolution, that is, the vertical correlation at the upper boundary is unchanged and the horizontal correlation increases under a specific strain intensity. This affects the magnetization intensity, so that the local magnetization shows an upward trend at the upper boundary. The results contribute to the understanding of the effect of bending strain on spin excitations, and this effect may be observed in two-dimensional quantum magnetic material experiments.

Thermal Hall conductivity on kagome-lattice antiferromagnets

Thermal Hall conductivity κxy and Hall spin conductivity σxy in the nearest-neighbors antiferromagnetic Heisenberg model on kagome lattice with out-of-plane Dzyaloshinskii-Moriya interaction (DMI), which has been an active area of study in condensed matter physics, are studied using the linear spin-wave theory. We analize the effect of this coupling on the behavior of κxy as well as σxy as well. For all cases analyzed, the behavior of κxy and σxy as a function of temperature T is analyzed where the behavior obtained for T finite, being due to the magnons thermally excited. We get a strong effect of temperature and DMI interaction on the behavior of both conductivities.

Thermodynamic, entanglement and spin Hall conductivity on kagome-honeycomb lattice system

Thermodynamics quantities as entropy, specific heat and magnetic susceptibility are studied in the next-nearest-neighbors Heisenberg model on honeycomb-kagome lattice also nominated as edge-centered honeycomb lattice model. Using the linear spin-wave approach, we get all thermodynamics quantities as a function of temperature T. Moreover, we study the entanglement negativity as quantifier of quantum entanglement and the spin Hall conductivity. All the thermodynamics quantities as well as entanglement negativity and spin Hall conductivity present a rising behavior with the temperature. Moreover, we obtain that all quantities analyzed drop to zero at low-temperature limit as has been obtained experimentally for many magnetic compounds.

Magnetic Structures and Spin-Wave Excitations in Rare-Earth Iron Garnets Near the Compensation Temperature

We introduce a simple model for the ferrimagnetic non-collinear “magnetic umbrella” states of rare-earth iron garnets (REIG), common when the rare-earth moments have non-zero orbital angular momentum. The spin-wave excitations are calculated within linear spin wave theory and temperature effects via mean-field theory. This could be used to determine the magnetic polarization of each mode and thereby the spin currents generated by thermal excitations including the effects of mixed chirality. The spectra reproduce essential features seen in more complete models, with hybridization between the rare earth crystal field excitations and the propagating mode on the iron moments. By the symmetry of the model, only one rare earth mode hybridizes, inducing a gap at zero wave number and level repulsion at finite frequency. At the compensation point, the hybridization gap closes and finally, as we approach the Néel temperature, the hybridization gap appears to reopen. The chirality of the lowest mode changes its sign around the frequency at which the level repulsion occurs. This is important to estimate the spin current generation in REIGs.

Spurious Symmetry Enhancement in Linear Spin Wave Theory and Interaction-Induced Topology in Magnons.

Linear spin wave theory (LSWT) is the standard technique to compute the spectra of magnetic excitations in quantum materials. In this Letter, we show that LSWT, even under ordinary circumstances, may fail to implement the symmetries of the underlying ordered magnetic Hamiltonian leading to spurious degeneracies. In common with pseudo-Goldstone modes in cases of quantum order by disorder these degeneracies tend to be lifted by magnon-magnon interactions. We show how, instead, the correct symmetries may be restored at the level of LSWT. In the process we give examples, supported by nonperturbative matrix product based time evolution calculations, where symmetry dictates topological features but where LSWT fails to implement them. We also comment on possible spin split magnons in MnF_{2} and similar rutiles by analogy to recently proposed altermagnets.

Capturing dynamical correlations using implicit neural representations

Understanding the nature and origin of collective excitations in materials is of fundamental importance for unraveling the underlying physics of a many-body system. Excitation spectra are usually obtained by measuring the dynamical structure factor, S(Q, ω), using inelastic neutron or x-ray scattering techniques and are analyzed by comparing the experimental results against calculated predictions. We introduce a data-driven analysis tool which leverages ‘neural implicit representations’ that are specifically tailored for handling spectrographic measurements and are able to efficiently obtain unknown parameters from experimental data via automatic differentiation. In this work, we employ linear spin wave theory simulations to train a machine learning platform, enabling precise exchange parameter extraction from inelastic neutron scattering data on the square-lattice spin-1 antiferromagnet La2NiO4, showcasing a viable pathway towards automatic refinement of advanced models for ordered magnetic systems.

Temperature-induced magnonic Chern insulator in collinear antiferromagnets

Thermal fluctuation in magnets causes temperature-dependent self-energy corrections in magnons; however, its effects on the topological orders of magnons is not well explored. Here we demonstrate that such corrections can induce a Chern insulating phase in two-dimensional collinear antiferromagnets with sublattice asymmetries by increasing temperature. We present the phase diagram of the system and show that the trivial magnon bands at zero temperature exhibit Chern insulating phase above a critical temperature before the paramagnetic phase transition. The self-energy corrections close and reopen the band gap at $\mathrm{\ensuremath{\Gamma}}$ or $\mathbf{K}$ points, accompanied by a magnon chirality switch and nontrivial Berry curvature transition. The thermal Hall effect of magnons or detecting the magnon polarization can highlight the experimentally prominent signatures of the topological transitions. We include the numerical results based on the van der Waals magnet ${\mathrm{MnPS}}_{3}$, calling for experimental implementation. Our work presents a paradigm for constructing topological phases that is beyond the linear spin wave theory.

Magnetic quantum and spin-wave behavior of three-layer graphene-like materials

This study examines the spin-wave and magnetic quantum behavior of three-layer graphene-like based on the Heisenberg model. The system is diagonally solved for Hamiltonian quantities using the linear spin wave theory and postponed Green's functions. The effects of exchange coupling, anisotropy, and spin quantum number on the resonance frequency and quantum fluctuation are discussed, providing a basis for regulating resonance frequency and quantum fluctuation.

Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves

We propose a new scheme of modifying spin waves so as to describe the thermodynamic properties of various noncollinear antiferromagnets with particular interest in a comparison between edge- versus corner-sharing triangular-based lattices. The well-known modified spin-wave theory for collinear antiferromagnets diagonalizes a bosonic Hamiltonian subject to the constraint that the total staggered magnetization be zero. Applying this scheme to frustrated noncollinear antiferromagnets ends in a poor thermodynamics, missing the optimal ground state and breaking the local U(1) rotational symmetry. We find such a plausible double-constraint condition for spin spirals as to spontaneously go back to the traditional single-constraint condition at the onset of a collinear Néel-ordered classical ground state. We first diagonalize only the bilinear terms in Holstein-Primakoff boson operators on the order of spin magnitude S and then bring these linear spin waves into interaction in a perturbative rather than variational manner. We demonstrate specific-heat calculations in terms of thus-modified interacting spin waves on various triangular-based lattices. In zero dimension, modified-spin-wave findings in comparison with finite-temperature Lanczos calculations turn out so successful as to reproduce the monomodal and bimodal specific-heat temperature profiles of the triangular-based edge-sharing Platonic and corner-sharing Archimedean polyhedral-lattice antiferromagnets, respectively. In two dimensions, high-temperature series expansions and tensor-network-based renormalization-group calculations are still controversial especially at low temperatures, and under such circumstances, modified spin waves interestingly predict that the specific heat of the kagome-lattice antiferromagnet in the corner-sharing geometry remains having both mid-temperature broad maximum and low-temperature narrow peak in the thermodynamic limit, while the specific heat of the triangular-lattice antiferromagnet in the edge-sharing geometry retains a low-temperature sharp peak followed by a mid-temperature weak anormaly in the thermodynamic limit. By further calculating one-magnon spectral functions in terms of our newly developed double-constraint modified spin-wave theory, we reveal that not only the elaborate modification scheme but also quantum corrections, especially those caused by the O(S 0) primary self-energies, are key ingredients in the successful description of triangular-based-lattice noncollinear antiferromagnets over the whole temperature range of absolute zero to infinity.