Spin-wave Spectrum Research Articles

First-principles study of magnon-phonon interactions in gadolinium iron garnet

We obtained the spin-wave spectrum based on a first-principles method of exchange constants, calculated the phonon spectrum by the first-principles phonon calculation method, and extracted the broadening of the magnon spectrum, $\Delta \omega$, induced by magnon-phonon interactions in gadolinium iron garnet (GdIG). Using the obtained exchange constants, we reproduce the experimental Curie temperature and the compensation temperature from spin models using Metropolis Monte Carlo (MC) simulations. In the lower-frequency regime, the fitted positions of the magnon-phonon dispersion crossing points are consistent with the inelastic neutron scattering experiment. We found that the $\Delta \omega$ and magnon wave vector $k$ have a similar relationship in YIG. The broadening of the acoustic spin-wave branch is proportional to $k^{2}$, while that of the YIG-like acoustic branch and the optical branch are a constant. At a specific $k$, the magnon-phonon thermalization time of $\tau_{mp}$ are approximately $10^{-9}$~s, $10^{-13}$~s, and $10^{-14}$~s for acoustic branch, YIG-like acoustic branch, and optical branch, respectively. This research provides specific and effective information for developing a clear understanding of the spin-wave mediated spin Seebeck effect and complements the lack of lattice dynamics calculations of GdIG.

Spin dynamics, antiferrodistortion and magnetoelectric interaction in multiferroics. The case of BiFeO3

AbstractWe present a theoretical study of the spin dynamics in perovskite-like multiferroics with homogeneous magnetic order in the presence of external magnetic and electric fields. A particular example of such material is BeFeO3 in which the spin cycloid can be suppressed by application of external magnetic field, doping or by epitaxial strain. Understanding the effect of the external electric field on the spin-wave spectrum of these systems is required for devices based on spin wave interference and other innovative advances of magnonics and spintronics. Thus, we propose a model for BiFeO3 in which the thermodynamic potential is expressed in terms of polarization \boldsymbol{P}, antiferrodistortion \boldsymbol{\Omega}, antiferromagnetic moment \boldsymbol{L} and magnetization \boldsymbol{M}. Based on this model, we derive the corresponding equations of motion and demonstrate the existence of electromagnons, that is, magnons that can be excited by electric fields. These excitations are closely related to the magnetoelectric effect and the dynamics of the antiferrodistortion \boldsymbol{\Omega}. Specifically, the influence of the external electric field on the magnon spectra is due to reorientation of both polarization \boldsymbol{P} and antiferrodistortion \boldsymbol{\Omega} under the influence of the electric field and is linked to emergence of a field-induced anisotropy.

Anomalous Diffusion and Localization in a Positionally Disordered Quantum Spin Array.

Disorder in quantum systems can lead to the disruption of long-range order in the ground state and to the localization of the elementary excitations. Here we exhibit an alternative paradigm, by which disorder preserves long-range order in the ground state, while it localizes the elementary excitations above it, introducing a stark dichotomy between static properties-mostly sensitive to the density of states of excitations-and nonequilibrium dynamical properties-sensitive to the spatial structure of excitations. We exemplify this paradigm with a positionally disordered 2d quantum Ising model with r^{-6} interactions, capturing the internal-state physics of Rydberg-atom arrays. Disorder is found to lead to multifractality and localization of the spin-wave excitations above a ferromagnetic ground state; as a result, the spreading of entanglement and correlations starting from a factorized state exhibits anomalous diffusion with a continuously varying dynamical exponent, interpolating between ballistic and arrested transport. Our findings are directly relevant for the low-energy dynamics in quantum simulators of quantum Ising models with power-law decaying interactions.

Neutron inelastic scattering study of rare-earth orthoferrite HoFeO3

By the single crystal inelastic neutron scattering the orthoferrite HoFeO3 was studied. We show that the spin dynamics of the Fe subsystem does not change through the spin-reorientation transitions. The observed spectrum of magnetic excitations was analyzed in the frames of linear spin-wave theory. Within this approach the antiferromagnetic exchange interactions of nearest neighbors and next nearest neighbors were obtained for Fe subsystem. Parameters of Dzyaloshinskii-Moriya interactions at Fe subsystem were refined. The temperature dependence of the gap in Fe spin-wave spectrum indicates the temperature evolution of the anisotropy parameters. The estimations for the values of Fe-Ho and Ho-Ho exchange interaction were made as well.

Magnetic properties and spin wave spectra of a ferromagnetic monolayer with 2D tetragonal structure: An application for Co2S2 monolayer

In this paper, the magnetic properties, thermal spin fluctuation and the spin wave spectra of a 2D tetragonal ferromagnetic monolayer with Heisenberg model including single-ion anisotropy are studied using functional integral method. Influence of exchange interaction at edge on these properties of the monolayer is also considered. The model is applied for a new robust ferromagnetic monolayer with the 2D tetragonal structure, Co2S2, in which the exchange interaction between magnetic atoms and non-magnetic atoms is included due to hybridization between Co 3d states and S 3p states.

Localized spin waves at low temperatures in a cobalt carbide nanocomposite

We study magnetic, transport, and thermal properties of Co2C and Co3C nanocomposites mixed in a 1:1 ratio. The nanocomposite has clusters with an average diameter of 40 ± 15 nm. We show that the behavior of the nanocomposite is completely different from that of only Co3C or Co2C. We observed that with decreasing temperature, the saturation magnetization MS(T) increases, with a steep rise seen below 100 K. A detailed analysis shows that the increase in MS(T) down to 100 K is explained via a surface spin freezing model. However, below 100 K, the steep increase in MS(T) is explained by a finite size effect related to the confinement of spin waves within nanoparticles. Heat capacity measurements show a broad peak at 100 K along with a low temperature anomaly at 43 K (=Tex). Resistance measurements of the nanocomposite show metallic behavior at high T with an anomalous feature appearing at Tex, which is near the T regime, where MS(T) begins to increase steeply. A measurement of the temperature gradients across the sample thickness indicates an abrupt change in thermal conductivity at Tex. Our results suggest a transformation from a magnetically coupled state with a continuous spectrum of spin waves into a magnetically decoupled state below 100 K with confined spin waves.

Spin-wave gap collapse in Rh-doped Sr2IrO4

We use resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge to study the effect of hole doping upon the Jeff=1/2 Mott-insulating state in Sr2IrO4, via Rh replacement of the Ir site. The spin-wave gap, associated with XY-type spin-exchange anisotropy, collapses with increasing Rh content, prior to the suppression of the Mott-insulating state and in contrast to electron doping via La substitution of the Sr site. At the same time, despite heavy damping, the d-d excitation spectra retain their overall amplitude and dispersion character. A careful study of the spin-wave spectrum reveals that deviations from the J1-J2-J3 Heisenberg used to model the pristine system disappear at intermediate doping levels. These findings are interpreted in terms of a modulation of Ir-Ir correlations due to the influence of Rh impurities upon nearby Ir wave functions, even as the single-band Jeff=1/2 model remains valid up to full carrier delocalization. They underline the importance of the transition metal site symmetry when doping pseudospin systems such as Sr2IrO4.

Nonlinear spin waves in ferromagnetic/superconductor hybrids

This work is focused on the numerical investigation of spin waves that propagate in nonlinear ferromagnet/superconductor bilayered films and periodic structures. The nonlinearity in these hybrid structures emerges due to the non-monotonous dependence of magnetization of a superconducting subsystem on the magnetic field, which is characterized by the superconducting critical field. It is shown that at relatively high amplitudes of spin waves in comparison to the superconducting critical field, the spin-wave spectrum changes drastically: the spin-wave spectral line can either bifurcate or stretch continuously depending on the type of considered superconductor. In addition, in the case of propagation of spin waves with relatively high amplitude in periodic magnonic metamaterials, additional zero-group-velocity modes appear that are known as flatbands. Overall, these findings suggest a versatile way for tunability of the spin-wave spectrum in nonlinear ferromagnet/superconductor structures by changing the excitation signal in respect to the superconducting critical field.

Orbitally-resolved ferromagnetism of monolayer CrI3

Few-layer CrI3 is the most known example among two-dimensional (2D) ferromagnets, which have attracted growing interest in recent years. Despite considerable efforts and progress in understanding the properties of 2D magnets both from theory and experiment, the mechanism behind the formation of in-plane magnetic ordering in chromium halides is still under debate. Here, we propose a microscopic orbitally-resolved description of ferromagnetism in monolayer CrI3. Starting from first-principles calculations, we construct a low-energy model for the isotropic Heisenberg exchange interactions. We find that there are two competing contributions to the long-range magnetic ordering in CrI3: (i) Antiferromagnetic Anderson’s superexchange between half-filled t2g orbitals of Cr atoms; and (ii) Ferromagnetic exchange governed by the Kugel–Khomskii mechanism, involving the transitions between half-filled t2g and empty eg orbitals. Using numerical calculations, we estimate the exchange interactions in momentum-space, which allows us to restore the spin-wave spectrum, as well as estimate the Curie temperature. Contrary to the nearest-neighbor effective models, our calculations suggest the presence of sharp resonances in the spin-wave spectrum at 5–7 meV, depending on the vertical bias voltage. Our estimation of the Curie temperature in monolayer CrI3 yields 55–65 K, which is in good agreement with experimental data.

Study of High-Frequency Magneto-Elastic Waves Using a Low-Frequency Alternating Magnetic Field

Magnetically ordered materials belong to systems with broad spectra of collective magnetic oscillations, spin waves, and systems with the highest degree of nonlinearity. We consider the possibility of studying spin waves using high-frequency harmonics, the possibility of parametric excitation of high-frequency collective magnetic oscillations using alternating magnetic fields of the lower frequency. As a model system allowing us to show proof of the principle, we use a system of magnetoelastic waves (MEWs) of high-temperature antiferromagnet with easy-plane anisotropy. The modulation method is used when an additional RF magnetic field was applied to the sample, which yielded satellites at the multiple of the pump field frequency microwave signal that passed the sample in a helix resonator when the parametric pump threshold was exceeded. We observed the process of parametric excitation of MEWs up to 64 harmonics of the pump field at a pump power up to 30 dBm. Our research is of interest for magnetic materials of nano sizes.

Chiral magnonic edge states in ferromagnetic skyrmion crystals controlled by magnetic fields

Achieving control over magnon spin currents in insulating magnets - where dissipation due to Joule heating is highly suppressed - is an active area of research that could lead to energy-efficient spintronics applications. However, magnon spin currents supported by conventional systems with uniform magnetic order have proven hard to control. An alternative approach that relies on topologically protected magnonic edge states of spatially periodic magnetic textures has recently emerged. A prime example of such textures is the ferromagnetic skyrmion crystal which hosts chiral edge states providing a platform for magnon spin currents. Here, we show, for the first time, an external magnetic field can drive a topological phase transition in the spin wave spectrum of a ferromagnetic skyrmion crystal. The topological phase transition is signaled by the closing of a low-energy bulk magnon gap at a critical field. In the topological phase, below the critical field, two topologically protected chiral magnonic edge states lie within this gap, but they unravel in the trivial phase, above the critical field. Remarkably, the topological phase transition involves an inversion of two magnon bands that at the $\Gamma$ point correspond to the breathing and anticlockwise modes of the skyrmions in the crystal. Our findings suggest that an external magnetic field could be used as a knob to switch on and off magnon spin currents carried by topologically protected chiral magnonic edge states.

Spin-wave oscillations in gradient ferromagnets: Exactly solvable models

The method of searching for the profiles of the gradient dependence of the material parameters of matter on the coordinates that allow the exact solution of wave equations, developed previously for electromagnetic and elastic waves, was generalized to spin waves in gradient ferromagnets. Such profiles were found and exact solutions of the wave equations for a ferromagnet with uniaxial magnetic anisotropy β(z) or exchange α(z) varying in space were obtained. The obtained solutions were used to develop the theory of spin-wave resonance in gradient thin magnetic films. The dependences of the eigenfunctions mn(z), the frequencies of the discrete spectrum ωn, and the high-frequency susceptibility χn on the number of spectral levels n were found. The cardinal differences between the spin-wave spectra of films with gradients β(z) and α(z) are shown. The variable anisotropy β(z) changes the shape of the energy potential of the magnetic film and leads to a change in the discrete spectrum for frequencies ωn(n) lower than the frequency of the gradient potential well or potential barrier ωc. The variable exchange α(z) does not change the shape of the energy potential. Spin-wave oscillations occur in a rectangular potential well created by the surfaces of the film, regardless of profile α(z). The discrete frequency spectrum ωn(n) is quadratic on n, or has negligible deviations from the quadratic, for all n. An analytical expression for the effective exchange parameter is obtained. Exact solutions of the Schrödinger equation with spatially dependent effective mass m(z) were found for the profile of m(z) inverse to the function of α(z).

Spin wave excitations of magnetic metalorganic materials

The Organic Materials Database (OMDB) is an open database hosting about 22,000 electronic band structures, density of states and other properties for stable and previously synthesized 3-dimensional organic crystals. The web interface of the OMDB offers various search tools for the identification of novel functional materials such as band structure pattern matching and density of states similarity search. In this work the OMDB is extended to include magnetic excitation properties. For inelastic neutron scattering we focus on the dynamical structure factor $S(\mathbf{q},\omega)$ which contains information on the excitation modes of the material. We introduce a new dataset containing atomic magnetic moments and Heisenberg exchange parameters for which we calculate the spin wave spectra and dynamic structure factor with linear spin wave theory and atomistic spin dynamics. We thus develop the materials informatics tools to identify novel functional organic and metalorganic magnets.

Reflection-less width-modulated magnonic crystal

The interest in artificial magnetic media such as magnonic crystals increased substantially in recent years due to their potential applications in information processing at microwave frequencies. The main features of these crystals are the presence of band gaps in the spin-wave spectra, usually formed due to Bragg reflections of spin-waves on the artificially created periodic structures. Here, we study spin-wave propagation in longitudinally magnetized width- and thickness-modulated yttrium iron garnet waveguides by means of Brillouin light scattering and microwave spectroscopy techniques. It is found that the width modulated crystal does not manifest noticeable Bragg reflections, but still demonstrates a pronounced band gap in its transmission characteristic. The phenomenon can be explained by the destructive interference between different frequency-degenerated spin-wave modes excited by the crystal. Such a reflection-less crystal is promising for future design of multi-element magnonic devices.

Magnonic Weyl states in Cu2OSeO3

The multiferroic ferrimagnet Cu$_2$OSeO$_3$ with a chiral crystal structure attracted a lot of recent attention due to the emergence of magnetic skyrmion order in this material. Here, the topological properties of its magnon excitations are systematically investigated by linear spin-wave theory and inelastic neutron scattering. When considering Heisenberg exchange interactions only, two degenerate Weyl magnon nodes with topological charges $\pm$2 are observed at high-symmetry points. Each Weyl point splits into two as the symmetry of the system is further reduced by including into consideration the nearest-neighbor Dzyaloshinsky-Moriya interaction, crucial for obtaining an accurate fit to the experimental spin-wave spectrum. The predicted topological properties are verified by surface state and Chern number analysis. Additionally, we predict that a measurable thermal Hall conductivity can be associated with the emergence of the Weyl points, the position of which can be tuned by changing the crystal symmetry of the material.

Investigation of phonons and magnons in [Ni80Fe20/Au/Co/Au]10 multilayers

The dispersion relations of surface acoustic waves and spin waves propagating in magnetic [Ni80Fe20/Au/Co/Au]10 multilayers deposited on a silicon substrate have been investigated by high-resolution Brillouin spectroscopy. We measured the spectra of spin waves for two canonical geometries where the spin waves propagate with the wave vector oriented parallel and perpendicular to the direction of static magnetization in-plane magnetized Py layer. We investigated experimentally the crossing of phononic and magnonic dispersion relations and discussed the mechanism of magnetoelastic interaction in this system.

Edge localization of spin waves in antidot multilayers with perpendicular magnetic anisotropy

We study the spin-wave dynamics in nanoscale antidot lattices based on Co/Pd multilayers with perpendicular magnetic anisotropy. Using time-resolved magneto-optical Kerr effect measurements we demonstrate that the variation of the antidot shape introduces significant change in the spin-wave spectra, especially in the lower frequency range. By employing micromagnetic simulations we show that additional peaks observed in the measured spectra are related to narrow shell regions around the antidots, where the magnetic anisotropy is reduced due to the Ga+ ion irradiation during the focused ion beam milling process of the antidot fabrication. The results point at new possibilities for exploitation of localized spin waves in out-of-plane magnetized thin films, which are easily tunable and suitable for magnonics applications.

Effects of molecular adsorption on the spin-wave spectrum and magnon relaxation in two-dimensional Cr2Ge2Te6.

In this work, we performed detailed first-principles calculation and theoretical analysis to investigate the effect of molecular adsorption on the spin-wave spectrum and magnon relaxation in a Cr2Ge2Te6 (CGT) monolayer. It is found that NH3, NO, and NO2 adsorption can enhance the exchange constant of CGT, which can result in a blue-shift in the spin-wave spectrum. At 30 K, by means of a thorough investigation of many possible lattice configurations excited by thermal fluctuation, we identify the magnon scattering rate from the intrinsic lattice vibrational modes, and find that the relaxation of optical and acoustic magnons exhibits a completely different wave vector dependence. Moreover, although the adsorption of NO2 and NH3 molecules has a negligible influence on the magnon-phonon interaction, the adsorption of NO molecules results in a significant increase in magnon scattering strength. In the long-wavelength limit, the interlayer vibrational modes induced by NO adsorption increase the magnon-phonon scattering strength by ∼12.7%. The remarkable interlayer magnon-phonon interaction is ascribed to the strong CGT-NO coupling and large molecular vibration amplitude. Considering the importance of magnon relaxation time in the application of spin devices, we suggest that both the impacts on the exchange interaction and scattering rate must be considered when manipulating two-dimensional magnets by surface functionalization.

Influence of nonmagnetic dielectric spacers on the spin-wave response of one-dimensional planar magnonic crystals

The one-dimensional planar magnonic crystals are usually fabricated as a sequence of stripes intentionally or accidentally separated by non-magnetic spacers. The influence of spacers on shaping the spin wave spectra is complex and still not completely clarified. We performed the detailed numerical studies of the one-dimensional single- and bi-component magnonic crystals comprised of a periodic array of thin ferromagnetic stripes separated by non-magnetic spacers. We showed that the dynamic dipolar interactions between the stripes mediated by non-magnetic spacer, even ultra-narrow, significantly shift up the frequency of the ferromagnetic resonance and simultaneously reduce the spin wave group velocity, which is manifested by the flattening of the magnonic band. We attributed these changes in the spectra to the modifications of dipolar pinning and shape anisotropy both dependent on the width of the spacers and the thickness of the stripes, as well as to the dynamical magnetic volume charges formed due to inhomogeneous spin wave amplitude.

Inelastic light scattering in the spin cluster Mott insulator Cu2OSeO3

Clusters of single spins form the relevant spin entities in the formation of long-range magnetic order in spin cluster Mott insulators. Such type of spin order bears resemblance to molecular crystals, and we therefore may expect a prototypical spin wave spectrum which can be divided into low-energy external and high-energy internal cluster spin wave modes. Here, we study high-energy spin cluster excitations in the spin cluster Mott insulator Cu$_{2}$OSeO$_{3}$ by means of spontaneous Raman scattering. Multiple high-energy optical magnon modes are observed, of which the Raman-activity is shown to originate in the Elliot-Loudon scattering mechanism. Upon crossing the long-range ordering transition temperature the magnetic modes significantly broaden, corresponding to scattering from localized spin excitations within the spin clusters. Different optical phonon modes show a strong temperature dependence, evidencing a strong magnetoelectric coupling between optical phonons and the high-energy spin cluster excitations. Our results support the picture that Cu$_{2}$OSeO$_{3}$ can be regarded as a solid-state molecular crystal of spin nature.