Elementary Magnetic Excitations Research Articles

Chiral and flat-band magnetic quasiparticles in ferromagnetic and metallic kagome layers.

Magnetic kagome metals are a promising platform to develop unique quantum transport and optical phenomena caused by the interplay between topological electronic bands, strong correlations, and magnetic order. This interplay may result in exotic quasiparticles that describe the coupled electronic and spin excitations on the frustrated kagome lattice. Here, we observe novel elementary magnetic excitations within the ferromagnetic Mn kagome layers in TbMn6Sn6 using inelastic neutron scattering. We observe sharp, collective acoustic magnons and identify flat-band magnons that are localized to a hexagonal plaquette due to the special geometry of the kagome layer. Surprisingly, we observe another type of elementary magnetic excitation; a chiral magnetic quasiparticle that is also localized on a hexagonal plaquette. The short lifetime of localized flat-band and chiral quasiparticles suggest that they are hybrid excitations that decay into electronic states.

Bethe strings in the spin dynamical structure factor of the Mott-Hubbard phase in the one-dimensional fermionic Hubbard model

The spectra and role in the spin dynamical properties of bound states of elementary magnetic excitations named Bethe strings that occur in some integrable spin and electronic one-dimensional models have recently been identified and realized in several materials by experiments. Corresponding theoretical studies have usually relied on the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field. At the isotropic point, it describes the large onsite repulsion U limit of the spin degrees of freedom of the one-dimensional fermionic Hubbard model with one electron per site in a magnetic field h. In this paper we consider the thermodynamic limit and study the effects of lowering the latter quantum problem ratio u=U/4t, where t is the first-neighbor transfer integral, on the line-shape singularities in regions at and just above the lower thresholds of the transverse and longitudinal spin dynamical structure factors. The most significant spectral weight contribution from Bethe strings leads to a gapped continuum in the spectrum of the spin dynamical structure factor +-. Our study focuses on the line shape singularities at and just above the gapped lower threshold of that continuum, which have been identified in experiments. Our results are consistent with the contribution of Bethe strings to the spin dynamical structure factor zz being small at low spin densities and becoming negligible upon increasing that density. Our results provide physically important information about how electron itinerancy affects the spin dynamics.

Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain

Recently there has been a renewed interest in the spectra and role in dynamical properties of excited states of the spin-1/2 Heisenberg antiferromagnetic chain in longitudinal magnetic fields associated with Bethe strings. The latter are bound states of elementary magnetic excitations described by Bethe-ansatz complex non-real rapidities. Previous studies on this problem referred to finite-size systems. Here we consider the thermodynamic limit and study it for the isotropic spin-1/2 Heisenberg XXX chain in a longitudinal magnetic field. We confirm that also in that limit the most significant spectral weight contribution from Bethe strings leads to (k,ω)-plane gapped continua in the spectra of the spin dynamical structure factors S+−(k,ω) and Sxx(k,ω)=Syy(k,ω). The contribution of Bethe strings to Szz(k,ω) is found to be small at low spin densities m and to become negligible upon increasing that density above m≈0.317. For S−+(k,ω), that contribution is found to be negligible at finite magnetic field. We derive analytical expressions for the line shapes of S+−(k,ω), Sxx(k,ω)=Syy(k,ω), and Szz(k,ω) valid in the (k,ω)-plane vicinity of singularities located at and just above the gapped lower thresholds of the Bethe-string states's spectra. As a side result and in order to provide an overall physical picture that includes the relative (k,ω)-plane location of all spectra with a significant amount of spectral weight, we revisit the general problem of the line-shape of the transverse and longitudinal spin dynamical structure factors at finite magnetic field and excitation energies in the (k,ω)-plane vicinity of other singularities. This includes those located at and just above the lower thresholds of the spectra that stem from excited states described by only real Bethe-ansatz rapidities.

Probing multi-spinon excitations outside of the two-spinon continuum in the antiferromagnetic spin chain cuprate Sr2CuO3

One-dimensional (1D) magnetic insulators have attracted significant interest as a platform for studying quasiparticle fractionalization, quantum criticality, and emergent phenomena. The spin-1/2 Heisenberg chain with antiferromagnetic nearest neighbour interactions is an important reference system; its elementary magnetic excitations are spin-1/2 quasiparticles called spinons that are created in even numbers. However, while the excitation continuum associated with two-spinon states is routinely observed, the study of four-spinon and higher multi-spinon states is an open area of research. Here we show that four-spinon excitations can be accessed directly in Sr2CuO3 using resonant inelastic x-ray scattering (RIXS) in a region of phase space clearly separated from the two-spinon continuum. Our finding is made possible by the fundamental differences in the correlation function probed by RIXS in comparison to other probes. This advance holds promise as a tool in the search for novel quantum states and quantum spin liquids.

Calculations of surface spin dynamics associated with biquadratic exchange and uniaxial anisotropy field in (S > 1) heisenberg ferromagnet by means of matching procedure.

Calculations within framework of both non-interacting spin-wave theory and random phase approximation have been carried out to investigate elementary magnetic excitations by scanning the occurrence of localized modes associated with surface spin dynamics. Mean field approximation and single spin-wave function theory in the context of semi-infinite Heisenberg ferromagnet are exploited. We exploit the mathematical formalism of matching method which starting from secular equation of spin motion established for the bulk of semi-infinite structure will make it possible to describe the symmetry properties of propagating (evanescent) precessional fields in parallel (perpendicular) direction to surface terrace. The localized states associated with surface are obtained by matching the properties of quantized propagating modes with evanescent modes occurring in vicinity of surface region. This mathematical procedure allows treating the continuity equations for spin precessional field amplitude operating in the border bulk media-surface region from their special suitable symmetry properties related to those induced by the broken translational symmetry arising from the existence of surface. The solutions are described considering the presence of uniaxial anisotropy field and biquadratic exchange as well as magnetic anisotropy field. The focus is on the existence, the nature as well as on the form and stability of localized surface modes. Also, obtained solutions are discussed qualitatively by observing the response of energy branches to the variation of strength of biquadratic exchange term and surface anisotropy field as well as magnetic exchange parameters occurring on the surface domain. Numerical examples of the localized modes energies associated with the surface are shown and they are found to exhibit various effects due to the strength of biquadratic exchange and magnetic anisotropy field under certain circumstances. The analytical formulation exposed in this work and its methodology based solely on the symmetry properties as well as the qualitative agreement describing our results with those obtained in the literature provide a considerable contribution to the surface spin dynamics calculations under the influence of biquadratic coupling and uniaxial anisotropy term. Moreover, the results obtained through matching procedure make it possible to remove an ambiguity concerning the existing disparities in analysis and interpretation of the main results already reported in literature.

Generation and annihilation time of magnetic droplet solitons

Magnetic droplet solitons were first predicted to occur in materials with uniaxial magnetic anisotropy due to a long-range attractive interaction between elementary magnetic excitations, magnons. A non-equilibrium magnon population provided by a spin-polarized current in nanocontacts enables their creation and there is now clear experimental evidence for their formation, including direct images obtained with scanning x-ray transmission microscopy. Interest in magnetic droplets is associated with their unique magnetic dynamics that can lead to new types of high frequency nanometer scale oscillators of interest for information processing, including in neuromorphic computing. However, there are no direct measurements of the time required to nucleate droplet solitons or their lifetime–experiments to date only probe their steady-state characteristics, their response to dc spin-currents. Here we determine the timescales for droplet annihilation and generation using current pulses. Annihilation occurs in a few nanoseconds while generation can take several nanoseconds to a microsecond depending on the pulse amplitude. Micromagnetic simulations show that there is an incubation time for droplet generation that depends sensitively on the initial magnetic state of the nanocontact. An understanding of these processes is essential to utilizing the unique characteristics of magnetic droplet solitons oscillators, including their high frequency, tunable and hysteretic response.

Observation of heavy spin-orbit excitons propagating in a nonmagnetic background: The case of (Ba,Sr)2YIrO6

We present a combined experimental and theoretical study of the elementary magnetic excitations in ${\mathrm{Ba}}_{2}{\mathrm{YIrO}}_{6}$ and ${\mathrm{Sr}}_{2}{\mathrm{YIrO}}_{6}$---the two most intensively discussed candidates for a new type of magnetic instability caused by exciton condensation. For both materials, high-resolution resonant inelastic x-ray scattering (RIXS) at the Ir ${L}_{3}$ edge reveals sharp excitations around 370 and 650 meV energy loss, which we identify as triplet and quintet spin-orbit excitons. While the momentum-dependent RIXS spectra reveal that both the triplet and the quintet propagate coherently within the nonmagnetic background of the singlet sites, these modes remain fully gapped. The Ir-Ir exchange interactions in both double perovskites are therefore not strong enough to overcome the magnetic gap and, hence, our results exclude an intrinsic magnetic instability due to a condensation of magnetic excitations for both ${\mathrm{Ba}}_{2}{\mathrm{YIrO}}_{6}$ and ${\mathrm{Sr}}_{2}{\mathrm{YIrO}}_{6}$.

From confined spinons to emergent fermions: Observation of elementary magnetic excitations in a transverse-field Ising chain

We report on spectroscopy study of elementary magnetic excitations in an Ising-like antiferromagnetic chain compound SrCo$_2$V$_2$O$_8$ as a function of temperature and applied transverse magnetic field up to 25 T. An optical as well as an acoustic branch of confined spinons, the elementary excitations at zero field, are identified in the antiferromagnetic phase below the N\'{e}el temperature of 5 K and described by a one-dimensional Schr\"{o}dinger equation. The confinement can be suppressed by an applied transverse field and a quantum disordered phase is induced at 7 T. In this disordered paramagnetic phase, we observe three emergent fermionic excitations with different transverse-field dependencies. The nature of these modes is clarified by studying spin dynamic structure factor of a 1D transverse-field Heisenberg-Ising (XXZ) model using the method of infinite time evolving block decimation. Our work reveals emergent quantum phenomena and provides a concrete system for testifying theoretical predications of one-dimension quantum spin models.

Coupled spin-light dynamics in cavity optomagnonics

Experiments during the past two years have shown strong resonant photon-magnon coupling in microwave cavities, while coupling in the optical regime was demonstrated very recently for the first time. Unlike with microwaves, the coupling in optical cavities is parametric, akin to optomechanical systems. This line of research promises to evolve into a new field of optomagnonics, aimed at the coherent manipulation of elementary magnetic excitations by optical means. In this work we derive the microscopic optomagnonic Hamiltonian. In the linear regime the system reduces to the well-known optomechanical case, with remarkably large coupling. Going beyond that, we study the optically induced nonlinear classical dynamics of a macrospin. In the fast cavity regime we obtain an effective equation of motion for the spin and show that the light field induces a dissipative term reminiscent of Gilbert damping. The induced dissipation coefficient however can change sign on the Bloch sphere, giving rise to self-sustained oscillations. When the full dynamics of the system is considered, the system can enter a chaotic regime by successive period doubling of the oscillations.

Spin-wave and electromagnon dispersions in multiferroicMnWO4as observed by neutron spectroscopy: Isotropic Heisenberg exchange versus anisotropic Dzyaloshinskii-Moriya interaction

High resolution inelastic neutron scattering reveals that the elementary magnetic excitations in multiferroic MnWO4 consist of low energy dispersive electromagnons in addition to the well-known spin-wave excitations. The latter can well be modeled by a Heisenberg Hamiltonian with magnetic exchange coupling extending to the 12th nearest neighbor. They exhibit a spin-wave gap of 0.61(1) meV. Two electromagnon branches appear at lower energies of 0.07(1) meV and 0.45(1) meV at the zone center. They reflect the dynamic magnetoelectric coupling and persist in both, the collinear magnetic and paraelectric AF1 phase, and the spin spiral ferroelectric AF2 phase. These excitations are associated with the Dzyaloshinskii-Moriya exchange interaction, which is significant due to the rather large spin-orbit coupling.

Long-living terahertz magnons in ultrathin metallic ferromagnets.

The main idea behind magnonics is to use the elementary magnetic excitations (magnons) for information transfer and processing. One of the main challenges, hindering the application of ultrafast terahertz magnons in magnonics, has been the short lifetime of these excitations in metallic ferromagnets. Here, we demonstrate that the engineering of the electronic structure of a ferromagnetic metal, by reducing its dimensionality and changing its chemical composition, opens a possibility to strongly suppress the relaxation channels of terahertz magnons and thereby enhance the magnons' lifetime. For the first time, we report on the long-lived terahertz magnons excited in ultrathin metallic alloy films. On the basis of the first-principles calculations, we explain the microscopic nature of the long lifetime being a consequence of the peculiar electronic hybridizations of the species. We further demonstrate a way of tailoring magnon energies (frequencies) by varying the chemical composition of the film.

Magnon BEC in Antiferromagnets with Suhl–Nakamura Interaction

From atomic physics one knows the phenomenon of Bose-Einstein con- densation (BEC), where a macroscopic ensemble of particles occupy coherently a single state. Similar phenomena were observed for different types of quasiparticles in condensed matter. Here we present the results of investigations on the BEC of elementary magnetic excitations—magnons—in antiferromagnets with a dynamical frequency shift.

Effect of the applied magnetic field and the layer thickness on the magnon properties in bilayers Co/Pt and symmetrical trilayer Pt/Co/Pt

We have studied the elementary magnetic excitations and their dynamics in multilayer Co(t Co)/Pt(t Pt) and Pt(t Pt)/Co(t Co)/Pt(t Pt) under an applied magnetic field. The Heisenberg hamiltonian used takes into account the magneto-crystalline and surface anisotropies, the exchange and dipolar interactions. The calculated excitation spectrum εN(k) presents a structure with two sub-bands corresponding to the magnons of surface and volume respectively. The existence of a gap of creating these magnons is also highlighted. The lifetimes deduced from these gaps are in good agreement with the results of previous studies. The thermal evolution of the magnetization mz indicates that the system undergoes a dimensional crossover 3D–2D when the temperature increases. The calculated and measured magnetizations are compared and they are in good agreement. The exchange integral and critical temperature values deduced from these adjustments are in very good agreement with the results of previous works.

Direct probing of the exchange interaction at buried interfaces

The fundamental interactions between magnetic moments at interfaces have an important impact on the properties of layered magnetic structures. Hence, a direct probing of these interactions is highly desirable for understanding a wide range of phenomena in low-dimensional solids. Here we propose a method for probing the magnetic exchange interaction at buried interfaces using spin-polarized electrons and taking advantage of the collective nature of elementary magnetic excitations (magnons). We demonstrate that, for the case of weak coupling at the interface, the low-energy magnon mode is mainly localized at the interface. Because this mode has the longest lifetime of the modes and has a finite spectral weight across the layers on top, it can be probed by electrons. A comparison of experimental data and first-principles calculations leads to the determination of the interface exchange parameters. This method may help the development of spectroscopy of buried magnetic interfaces.

Magnon Bose–Einstein condensation and spin superfluidity

Bose–Einstein condensation (BEC) is a quantum phenomenon of formation of a collectivequantum state in which a macroscopic number of particles occupy the lowest energy stateand thus is governed by a single wavefunction. Here we highlight the BEC in a magneticsubsystem—the BEC of magnons, elementary magnetic excitations. The magnon BEC ismanifested as the spontaneously emerging state of the precessing spins, in whichall spins precess with the same frequency and phase even in an inhomogeneousmagnetic field. The coherent spin precession was observed first in superfluid 3He-B and this domain was called the homogeneously precessing domain (HPD).The main feature of the HPD is the induction decay signal, which ranges overmany orders of magnitude longer than is prescribed by the inhomogeneity ofmagnetic field. This means that spins precess not with a local Larmor frequency, butcoherently with a common frequency and phase. This BEC can also be created andstabilized by continuous NMR pumping. In this case the NMR frequency playsthe role of a magnon chemical potential, which determines the density of themagnon condensate. The interference between two condensates has also beendemonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. Themain property is the existence of a spin supercurrent. This spin supercurrentflows separately from the mass current. Transfer of magnetization by the spinsupercurrent by a distance of more than 1 cm has been observed. Also related phenomenahave been observed: the spin current Josephson effect; the phase-slip processes atthe critical current; and the spin current vortex—a topological defect which isthe analog of a quantized vortex in superfluids and of an Abrikosov vortex insuperconductors; and so on. It is important to mention that the spin supercurrent is amagnetic phenomenon, which is not directly related to the mass superfluidity of 3He: it is the consequence of a specific antiferromagnetic ordering in superfluid 3He. Several different states of coherent precession have been observed in 3He-B: the homogeneously precessing domain (HPD); a persistent signal formed byQ-balls at very low temperatures; coherent precession with fractionalmagnetization; and two new modes of coherent precession in compressedaerogel. In compressed aerogel the coherent precession has been also found in 3He-A. We demonstrate that the coherent precession of magnetization is a true BEC ofmagnons, with the magnon interaction term in the Gross–Pitaevskii equation beingprovided by spin–orbit coupling which is different for different states of the magnonBEC.

Electron scattering and nuclear structure at the S-DALINAC

Results on ongoing research of elementary electric and magnetic nuclear excitations at the superconducting Darmstadt electron linear accelerator (S-DALINAC) are presented. In the first part of this lecture electric excitation modes in the continuum are discussed by way of two examples employing the coincident detection of inelastically scattered electrons in an (e,e′x) reaction. The first example is the reaction 48Ca(e,e′n) where the excitation and decay of isoscalar electric monopole and quadrupole giant resonances has been studied. The results on the strength distribution and the partial exhaustion of energy weighted sum rules are compared to those from RPA and second-RPA (SRPA) predictions as well as to those from hadronic reactions of the type (p,p′) and (p,p′n). The second example, a discussion of the 90Zr(e,e′p) reaction and its results, can be viewed as a direct proof that in coincidence reactions of the form (e,e′x) one is able to isolate and identify narrow weakly excited levels — here isobaric analog resonances — buried in the continuum and determine their excitation and decay properties and thus subtle nuclear structure properties. The second part of the lecture is concerned with high-resolution inelastic electron scattering under 180° which is selective with respect to magnetic excitations. Of those, first systematic studies on the hitherto scarcely explored magnetic quadrupole giant resonance which is mainly a spin-isospin excitation are presented. As an example, results for 48Ca and 90Zr, in which a strongly fragmented and quenched M2 strength has been detected, are compared to SRPA and sum rules approaches. Evidence is presented for a new excitation mode, the so called nuclear twist mode, and its parameters are determined. In the third part of the lecture, the possible use of transverse electron scattering form factors at low momentum transfer for an advocated test of in-medium modifications of vector mesons is critically examined, and finally an outlook is given on the nuclear physics research program at the S-DALINAC.

Semiclassical quantization of magnetic solitons

Description of magnetic, dynamic solitons in magnetically ordered crystals is based on both classical and quasi-classical mechanics. The magnetic soliton is regarded as a bound state of a large number of elementary magnetic excitations, i.e. magnons. It is shown that the semiclassical quantization of the magnetic soliton spectrum leads to results coincided exactly with the quantum spectrum of corresponding spin complexes. An unexpected periodic dependence of the soliton energy on the total soliton momentum is discussed. Such a dependence causes the Bloch oscillations of the magnetic soliton in the presence of a small gradient of the magnetic field. The linear dependence of the total soliton momentum on the time is calculated.

Low energy electron scattering and nuclear structure: a few selected examples of elementary electric and magnetic excitations

Notes of three lectures concerned with low energy electron scattering and nuclear structure are presented. The first part of the lectures dealt with a brief reminder of the definition of a giant resonance, its strength and fragmentation and of the method to determine reduced transition strengths which are the testing grounds for any comparison with a model. As an immediate application, the study of the electric quadrupole giant resonance in 28Si by means of single arm (e,e′) experiments, capture reactions and inelastic hadron scattering experiments has been discussed.Preliminary results of (e,e′x) coincidence measurements were also presented. The second and major part of the lectures has been concerned primarily with the present status and the perspectives of ground state magnetic dipole transitions. Selected examples of pure neutron M1 spin-flip excitations, of mixed neutron and proton excitations leading to the interference between spin and orbital magnetization, and of a recently discovered purely orbital mode in heavy deformed nuclei were presented and discussed in the light of recent model predictions as well as in connection with results from Gamow-Teller charge exchange reactions, high-resolution inelastic proton scattering and beta decay. The phenomenon of quenching of the observed transition strengths and magnetic moments has been used to point out a possible intimate relation between nuclear and subnuclear physics. The constituent quark model has been used to bridge the gap between the two fields. Finally, it was pointed out how the measured M1 transition strengths yield directly the paramagnetic susceptibilities of nuclei. After comparing those with values from atomic and nucleonic matter it has been found that they scale with the corresponding Fermi energies.

Multiple far-infrared magnetic excitations in CsCoCl3: a one-dimensional Ising-like antiferromagnet

The results of far-infrared absorption measurements on CsCoCl3 at 4.2K are reported for various magnetic fields applied along the c axis. The broad asymmetric band observed with a very rich structure seems to be unaffected by the magnetic field. The results for this Ising-like antiferromagnet are discussed in terms of elementary magnetic excitations: the even-fold clusters.

Inelastic Scattering of Slow Electrons from a Heisenfoerg Ferromagnet

AbstractThe magnetic inelastic scattering of low‐energy electrons by the (001) surface of a b.c.c. Heisenberg ferromagnet is considered. As a first step, the spectrum of elementary magnetic excitations is obtained, revealing the existence of optical and acoustic surface magnons, as well as a continuum of bulk magnons. The differential cross‐section for inelastic scattering shows the contribution of those types of excitations; localized niagnons give a delta function contribution, while the contribution due to the bulk states is qualitatively different depending on the value of the ratio of the exchange integrals for surface and bulk spins, thereby providing a method for investigating the exchange interactions at the surface.