Magnon Spectrum Research Articles

Easy-Plane Antiferromagnet in Tilted Field: Gap in Magnon Spectrum and Susceptibility

Easy-Plane Antiferromagnet in Tilted Field: Gap in Magnon Spectrum and Susceptibility

Magnetic excitations in the topological semimetal YbMnSb2

We report neutron scattering measurements on YbMnSb$_2$ which shed new light on the nature of the magnetic moments and their interaction with Dirac fermions. Using half-polarized neutron diffraction we measured the field-induced magnetization distribution in the paramagnetic phase and found that the magnetic moments are well localised on the Mn atoms. Using triple-axis neutron scattering we measured the magnon spectrum throughout the Brillouin zone in the antiferromagnetically ordered phase, and we determined the dominant exchange interactions from linear spin-wave theory. The analysis shows that the interlayer exchange is five times larger than in several related compounds containing Bi instead of Sb. We argue that the coupling between the Mn local magnetic moments and the topological band states is more important in YbMnSb$_2$ than in the Bi compounds.

Generation of magnonic frequency combs via a two-tone microwave drive

Magnonic frequency combs, a direct analog of optical frequency combs in the field of spin waves, have recently received considerable attentions due to their potential applications in high-precision magnonic frequency metrology. However, due to the weak nonlinear interaction of magnons, it is difficult to generate a wide-bandwidth magnonic frequency comb under a low power drive. Here, we present an efficient mechanism for the generation of a wide-bandwidth magnonic frequency comb via a two-tone microwave driving in a magnomechanical system. Numerical simulations show that the magnetostrictive effect can be greatly enhanced by the beat frequency signal from the two-tone microwave driving field, and a robust magnonic frequency comb can be observed at low power. Furthermore, abundant nonperturbative features appear in the magnonic spectrum, implying that the magnons as bosons may also be similar to photons in atom-molecular systems. Our scheme thus provides a pathway for the generation of a flat magnonic frequency comb under a low-power driving condition that may be beneficial for precision metrology based on magnonic platforms as well as the understanding of nonlinear magnomechanic dynamics.

The \(120^{0}\) ordered phase of the spin-1 \(J_{1} - J_{2}\) antiferromagnetic Heisenbeberg model on a triangular lattice

We study the effect of quantum and thermal fluctuations on the excitation energy spectrum and sublattice magnetization of the 1200 ordered phase of the spin-1 antiferromagnetic Heisenberg model on a triangular lattice with nearest J1 and next-nearest-neighbor J2 exchange interactions. The auxiliary fermionic representation of the spin operators within a functional integral formalism with an imaginary Lagrange multiplier is employed to retain an exact constraint of single particle occupancy. Representing the classical ground state by Luttinger-Tisza ordering vector Q one may consider the fluctuation contributions to the free energy of the system in the entire range of the coupling parameters. We derived the magnon spectrum in one-loop approximation and the magnetization taking into account thermal fluctuations. The obtained results are compared with the result of the linear spin-wave approximation and experimental findings on compound NiGa2S4.

Microscopic parameters of the van der Waals CrSBr antiferromagnet from microwave absorption experiments

Microwave absorption experiments employing a phase-sensitive external resistive detection are performed for a topical van der Waals antiferromagnet CrSBr. The field dependence of two resonance modes is measured in an applied field parallel to the three principal crystallographic directions, revealing anisotropies and magnetic transitions in this material. To account for the observed results, we formulate a microscopic spin model with a bi-axial single-ion anisotropy and inter-plane exchange. Theoretical calculations give an excellent description of full magnon spectra enabling us to precisely determine microscopic interaction parameters for CrSBr.

Magnon-Fluxon Interaction in Coupled Superconductor/Ferromagnet Hybrid Periodic Structures

We study the magnon propagation in a micrometer-size ferromagnetic waveguide affected by the proximity to a superconductor that hosts a vortex formation. By solving the time-dependent Ginzburg-Landau equations of superconductivity, we obtain the equilibrium state of the vortex configuration and the associated stray fields that act on the magnetic dynamics. Spin wave dynamics in the presence of the superconductors are inferred from the Landau-Lifschitz equation. For a quantitative comparison, the simulations are performed under the experimental conditions as reported by Dobrovolskiy et al. (Nature Physics, 15, 477 (2019)). We found that the presence of the vortex lattice leads to the formation of a Bloch-like band structure in the magnon spectrum. The width and the number of allowed bands are found to depend mainly on the in-plane component of the vortex field along the waveguide. A shift to lower energies of the lowest-order-allowed bands occurs due to the confinement of the magnonic modes above the locations of the superconductor vortices. We also studied the role of the films thickness. At least two GHz-frequency backward-volume magnetostatic spin waves modes are observed at the top and bottom surfaces (in addition to these magnetostatic surface modes, the vertical confinement can also give rise to longer-wavelength and low-frequency perpendicular standing spin waves). Effects of the vortex fields are found to depend strongly on the type of the magnon modes. It is found that the effect of the superconducting vortices of the spin waves can be emulated well by the stray fields of air-separated magnetic nanocubes of appropriate dimensions.

Magnetic excitations, phase diagram, and order-by-disorder in the extended triangular-lattice Hubbard model

The dynamical structure factor is an important observable of quantum magnets but due to numerical and theoretical limitations, it remains a challenge to make predictions for Hubbard-like models beyond one dimension. In this work, we study the magnetic excitations of the triangular lattice Hubbard model including next-nearest-neighbor hopping. Starting from the expected ${120}^{\ensuremath{\circ}}$ and stripe magnetic orders, we compute the magnon spectra within a self-consistent random phase approximation. In the stripe phase, we generically find accidental zero modes related to a classical degeneracy known from the corresponding ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model. We extend the order-by-disorder mechanism to Hubbard systems and show how quantum fluctuations stabilize the stripe order. In addition, the frustration-induced condensation of magnon modes allows us to map out the entire phase diagram which is in remarkable agreement with recent numerical works. We discuss connections to experiments on triangular lattice compounds and the relation of our results to the proposed chiral spin liquid phase.

Measurement of the spin-wave stiffness and energy gap in the magnon spectrum of amorphous ferromagnets by small-angle scattering of polarized neutrons

This work studies the magnetic excitations of amorphous ferromagnetic alloys (Fe40Ni40P14 11B6 and Fe48Ni34P18) by small-angle polarized neutron scattering in the geometry when the magnetic field is inclined towards the neutron beam direction. Polarized neutrons are used in order to extract the scattering arising from the spin waves only. In this case, the energy-integrated neutron cross section contains a component which depends on neutron polarization and has a left–right asymmetry in the plane determined by the directions of the field and the neutron beam. Small-angle polarized neutron scattering measurements on spin waves in amorphous iron–nickel alloys were performed at different values of the external magnetic field H and neutron wavelength λ. The spin-wave spectrum is quadratic in terms of the momentum transfer and contains both a field gap and an inherent gap Δ of a non-field nature: E q = Aq 2 + gμB H + Δ. Only by measuring simultaneously two dependencies of the cut-off angle θc – on the applied magnetic field and on the neutron wavelength – is it possible to obtain reliable information about the spin-wave stiffness and the spin-wave gap in these amorphous ferromagnetic systems.

Localized Surface Magnon Modes in Cubic Ferromagnetic Lattices

A theoretical formalism for calculating the bulk and surface spin modes in Heisenberg semi-infinite lattices is presented on a ferromagnetic cubic network of spins, coupled via nearest and next-nearest neighbors exchange interactions. The magnetic surface can be considered as semi-infinite slabs at the end of the bulk structures. The breakdown of translation symmetry, in the normal direction of the surface, gives rise to localized spin wave modes in its neighborhood. The localized magnon spectrum is derived as elements of a Landauer-type scattering matrix, in the three cubic lattices sc, bcc and fcc. The magnon properties are simulated and determined numerically for each cubic lattice by using the matching technique. The observed fluctuations in the numerical results demonstrate the interference magnon effects between scattered spinwaves and the localized magnon states, generated by the surface region with characteristic Fano resonances. In cubic leads, the localized surface spin states are sensitive to the local magnetic coupling and the incident direction in the surface boundary. In this contribution, the normalized energy of spinwaves arising from the absence of translation symmetry is analyzed for each cubic system as a function of the exchange integral parameters. This addresses the dependence of the surface magnon on the different possibilities of the of the exchange parameters variation from softening to hardening in the neighborhood of the surface region.

Magnetic structures and excitations in sawtooth olivine chalcogenides Mn2SiX4 (X = S, Se).

The Mn lattice in olivine chalcogenide Mn2SiX4 (X = S, Se) compounds forms a sawtooth, which is of special interest in magnetism owing to the possibility of realizing flat bands in magnon spectra, a key component in magnonics. In this work, we investigate the Mn2SiX4 olivines using magnetic susceptibility, and X-ray and neutron diffraction. We have determined the average and local crystal structures of Mn2SiS4 and Mn2SiSe4 using synchrotron X-ray, neutron diffraction, and X-ray total scattering data followed by Rietveld and pair distribution function analyses. It is found from the pair distribution function analysis that the Mn triangle that constitutes the sawtooth is isosceles in Mn2SiS4 and Mn2SiSe4. The temperature evolution of magnetic susceptibility of Mn2SiS4 and Mn2SiSe4 shows anomalies below 83 K and 70 K, respectively, associated with magnetic ordering. From the neutron powder diffraction measurements the magnetic space groups of Mn2SiS4 and Mn2SiSe4 are found to be Pnma and Pnm'a', respectively. We find that the Mn spins adopt a ferromagnetic alignment on the sawtooth in both Mn2SiS4 and Mn2SiSe4 but along different crystallographic directions for the S and the Se compounds. From the temperature evolution of Mn magnetic moments obtained from refining neutron diffraction data, the transition temperatures are accurately determined as TN(S) = 83(2) K and TN(Se) = 70.0(5) K. Broad diffuse magnetic peaks are observed in both the compounds, and are prominently seen close to TN, suggesting the presence of a short-range magnetic order. The magnetic excitations studied using inelastic neutron scattering reveal a magnon excitation with an energy corresponding to approximately 4.5 meV in both S and Se compounds. Spin correlations are observed to persist up to 125 K much above the ordering temperature and we suggest the possibility of short-range spin correlations responsible for this.

Влияние большой одноионной анизотропии на динамические и статические свойства негейзенберговского ферримагнетика

The influence of a large single-ion anisotropy of the “easy plane” type on the phase states and spectra of elementary excitations of a ferrimagnet with sublattices S=1 and σ=1/2 and non-Heisenberg exchange interaction for a sublattice with S=1 is studied. It is shown that for different ratios of the material parameters of the system, only one phase state is possible, characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). The condition for sublattice spin compensation is determined, as well as the behavior of the spectra of elementary excitations near the spin compensation line. In the vicinity of the spin compensation line, the magnon spectra are "antiferromagnetically similar".

Effect of large single-ion anisotropy on the dynamic and static properties of a non-heisenberg ferrimagnet

The influence of a large single-ion anisotropy of the "easy plane" type on the phase states and spectra of elementary excitations of a ferrimagnet with sublattices S = 1 and sigma=1/2 and non-Heisenberg exchange interaction for a sublattice with S = 1 is studied. It is shown that for different ratios of the material parameters of the system, only one phase state is possible, characterized by both vector and tensor order parameters (quadrupole-ferrimagnetic). The condition for sublattice spin compensation is determined, as well as the behavior of the spectra of elementary excitations near the spin compensation line. In the vicinity of the spin compensation line, the magnon spectra are "antiferromagnetically similar". Keywords: large single-ion anisotropy, biquadratic exchange interaction, ferrimagnet.

Calculated magnetic exchange interactions in the van der Waals layered magnet CrSBr

Intrinsic van der Waals materials layered magnets have attracted much attention, especially the air-stable semiconductor CrSBr. Herein, we carry out a comprehensive investigation of both bulk and monolayer CrSBr using the first-principles linear-response method. Through the calculation of the magnetic exchange interactions, it is confirmed that the ground state of bulk CrSBr is A-type antiferromagnetic, while there are five sizable large intralayer exchange interactions with small magnetic frustration, which results in a relatively high magnetic transition temperature of both bulk and monolayer CrSBr. Moreover, the significant electron doping effect and strain effect are demonstrated, with further increased Curie temperature for monolayer CrSBr, as well as an antiferromagnetic to ferromagnetic phase transition for bulk CrSBr. We also calculate the magnon spectra using linear spin-wave theory. These features of CrSBr can be helpful to clarify the microscopic magnetic mechanism and promote the application in spintronics.

Spin Seebeck effect in W-type and Z-type hexagonal ferrite thin films

The spin Seebeck effect was studied in thin films of hexagonal ferrites of W-type SrCo2−xZnxFe16O27 with x = 0, 1, and 2 and Z-type with the composition Sr3Co2Fe24O41. The present data were compared with the previously obtained data on Y-type Ba2Zn2−xCoxFe12O22 with x = 0 and 2. Our work showed that the SSE signal can also be generated in materials with complicated crystal and magnetic structures. Hexaferrites with the magnetic easy plane were selected except for uniaxial W-type with x = 2, for which the highest saturated SSE 0.144 μV/K was observed; however, magnetic field above 1 T must be applied to achieve saturation. For low field application, hexaferrites with easy magnetization in ab-plane are more suitable, namely, Y-type with x = 2 or W-type with x = 1. SSE is suppressed in Co-substituted hexaferrites due to the random distribution of Co among various sites. Therefore, the Co cations interfere with the long-range magnetic ordering and diminish the spin-wave propagation. Additional suppression of SSE might be invoked by the higher magnetic anisotropy of the Co-substituted hexaferrites, which opens a gap in the magnon spectrum and, thus, reduces the contribution of lower energy magnons with longer diffusion length.

Heat capacity and thermal conductivity of CdCr2Se4 ferromagnet: Magnetic field dependence, experiment and calculations

The low-temperature specific heat capacity and thermal conductivity under magnetic field 0–13 T is investigated on polycrystalline sample of the ferromagnetic insulator CdCr2Se4, possessing spinel structure with magnetic Cr3+ ions in the octahedrally coordinated sites. The phonon (lattice) and magnon contributions are separated by their characteristic temperature dependencies and by quenching of the magnon component under high magnetic fields in the isothermal measurements. The results are analyzed with respect to formulas for model systems and confronted with ab-initio calculations of phonon and magnon spectra. The theoretical formula for the field-induced quenching of magnon heat capacity is well reproduced, but there are two kinds of deviations from expected behavior deserving attention: (1) Heat capacity at low fields is by several percent lower than expected and approaches the theoretical curve only above ∼0.5 T. We propose that the zero-field magnon heat capacity is diminished by a presence of magnetic domain walls and the expected field dependence is restored when magnetic field converts the sample into a single domain state. (2) The suppression of magnon heat capacity under high magnetic field is incomplete. While the data follow well the theoretical line for given temperature as regards the curvature, the final saturation seems to tend several percent above the expected value for lattice heat capacity. We propose that this behavior is related to the phonon-magnon coupling arising due to Zeeman gap in the magnon spectra and subsequent formation of intersection points with the phonon spectra. The thermal conductivity has shown substantial deviations with respect to model predictions as concerns temperature dependence of the phonon contribution and suppression of the magnon contribution in markedly lower magnetic fields than predicted by the model. We ascribe this discrepancy to a complex character of the intergrain heat transfer.

Time-dependent strain-tuned topological magnon phase transition

Collinear magnets in honeycomb lattices under the action of time-dependent strains are investigated. Given the limits of high-frequency periodically varying deformations, we derive an effective Floquet theory for spin systems that results in the emergence of a spin chirality. We find that the coupling between magnons and spin chirality depends on the details of the strain such as the spatial dependence and applied direction. Magnonic fluctuations about the ferromagnetic state are determined, and it is found that spatially homogeneous strains drive the magnon system into topologically protected phases. In particular, we show that certain uniform strain fields play the role of an out-of-plane nearest-neighbor Dzyaloshinskii-Moriya interaction. Furthermore, we explore the application of nonuniform strains, which lead to a confinement of magnon states that for uniaxial strains propagates along the direction that preserves translational symmetry. Our work demonstrates a direct way in which to manipulate the magnon spectrum based on time-dependent strain engineering that is relevant for exploring topological transitions in quantum magnonics.

Dynamics of spin- 12 J1–J2 model on the triangular lattice

We discuss spin-$\frac12$ $J_1$--$J_2$ model on the triangular lattice using recently proposed bond-operator theory (BOT). In agreement with previous discussions of this system, we obtain four phases upon $J_2$ increasing: the phase with $120^\circ$ ordering of three sublattices, the spin-liquid phase, the state with the collinear stripe order, and the spiral phase. The $120^\circ$ and the stripe phases are discussed in detail. All calculated static characteristics of the model are in good agreement with previous numerical findings. In the $120^\circ$ phase, we observe the evolution of quasiparticles spectra and dynamical structure factors (DSFs) upon approaching the spin-liquid phase. Some of the considered elementary excitations were introduced first in our recent study of this system at $J_2=0$ using the BOT. In the stripe phase, we observe that the doubly degenerate magnon spectrum known from the spin-wave theory (SWT) is split by quantum fluctuations which are taken into account more accurately in the BOT. As compared with other known findings of the SWT in the stripe state, we observe additional spin-1 and spin-0 quasiparticles which give visible anomalies in the transverse and longitudinal DSFs. We obtain also a special spin-0 quasiparticle named singlon who produces a peak only in four-spin correlator and who is invisible in the longitudinal DSF. We show that the singlon spectrum lies below energies of all spin-0 and spin-1 excitations in some parts of the Brillouin zone. Singlon spectrum at zero momentum can be probed by the Raman scattering.

Unidirectional Chiral Magnonics in Cylindrical Synthetic Antiferromagnets

Progress in spintronics continues briskly, with many different approaches and physical phenomena underlying candidate technologies. This study uses modern spin-wave theory to predict the magnonic spectrum of a cylindrical synthetic antiferromagnet consisting of two coaxial nanotubes. The proposed device incorporates two coupled ferromagnetic nanotubes hosting oppositely magnetized vortices. Nonreciprocal features of the proposed architecture are provided by both intra- and interlayer dipolar coupling. Unidirectional spin-wave behavior is found, which may impact the realization of low-power magnonic devices operating at nano- to micrometer scales.

Spin interaction and magnetism in cobaltate Kitaev candidate materials: An ab initio and model Hamiltonian approach

In the quest for materials hosting Kitaev spin liquids, much of the efforts have been focused on the fourth- and fifth-row transition metal compounds, which are spin-orbit coupling assisted Mott insulators. Here, we study the structural and magnetic properties of 3$d$ transition metal oxides, Na$_2$Co$_2$TeO$_6$ and Na$_3$Co$_2$SbO$_6$. The partial occupancy of sodium in former compound is addressed using a cluster expansion, and a honeycomb lattice of sodiums is found to be energetically favored. Starting from the \textit{ab initio} band structures, a many-body second order perturbation theory leads to a pseudospin-$\frac{1}{2}$ Hamiltonian with estimated magnetic interactions. We show that the experimentally observed zigzag magnetic state is stabilized only when the first neighbor Kitaev coupling dominates over the Heisenberg term, both of which are highly suppressed due to presence of $e_g$ orbitals. A third neighbor Heisenberg interaction is found dominant in both these compounds. We also present a phase diagram for Na$_2$Co$_2$TeO$_6$ by varying the electron-electron and spin-orbit interactions. The computed spin excitation spectra are found to capture essential features of recent experimental magnon spectrum, lending support to our results.

Small-angle neutron scattering in the fully polarized phase of noncollinear magnets with interfacial-like Dzyaloshinskii-Moriya interaction

Spin waves in non-collinear magnets with $C_{nv}$ symmetry are discussed in the context of inelastic neutron scattering in small-angle scattering geometry. In the framework of minimal model including exchange coupling, Dzayloshinskii-Moriya interaction (DMI) and single-ion anisotropy, we consider the system properties at moderate external fields and in the high-field fully polarized phase. In the latter case, the magnon spectrum is gapped and non-reciprocal due to DMI with the minimum perpendicular to the field direction for in-plane field and is ferromagnetic-like for the field along the high-symmetry axis. Inelastic small-angle neutron scattering in the fully polarized phase (SWSANS) is considered in four different geometries. It is shown that analysis of field dependence of the SWSANS cutoff feature in these geometries allows determining all important parameters of the model. Possibility of the proposed method utilization in thin films with interfacial DMI is also discussed.