Spin-wave Excitation Spectrum Research Articles

Spin wave excitations in low dimensional systems with large magnetic anisotropy

The low-energy excitation spectrum of a two-dimensional ferromagnetic material is dominated by single-magnon excitations that show a gapless parabolic dispersion relation with the spin wave vector. This occurs as long as magnetic anisotropy and anisotropic exchange are negligible compared to isotropic exchange. However, to maintain magnetic order at finite temperatures in extended systems, it is necessary to have sizable anisotropy to open a gap in the spin wave excitation spectrum. We consider four real two-dimensional systems for which ferromagnetic order at finite temperature has been observed or predicted. Density functional theory calculations of the total energy differences for different spin configurations permit us to extract the relevant parameters and connect them with a spin Hamiltonian. The corresponding values of the Curie temperature are estimated using a simple model and found to be mostly determined by the value of the isotropic exchange. The exchange and anisotropy parameters are used in a toy model of finite-size periodic chains to study the low-energy excitation spectrum, including single-magnon and two-magnon excitations. At low energies, we find that single-magnon excitations appear in the spectrum together with two-magnon excitations. These excitations present a gap that grows particularly for large values of the magnetic anisotropy or anisotropic exchange, relative to the isotropic exchange.

Spin dynamics, critical scattering and magnetoelectric coupling mechanism of Mn4Nb2O9

The spin dynamics of Mn4Nb2O9 were studied using inelastic neutron scattering. A dynamic model is proposed to explain the observed spin-wave excitation spectrum from Mn4Nb2O9. The model indicates that the exchange interactions along the chain direction are weakly ferromagnetic while the exchange interactions between the neighbour chains are strongly antiferromagnetic. The antiferromagnetic interactions on the two MnO6 octahedron networks are dominant in the spin dynamics of this compound. A spin gap of about 1.4 meV was observed at the zone centre, which is attributed to the weak easy-axis magnetic anisotropy of Mn2+ ions. Magnetic critical scattering from Mn4Nb2O9 was studied in the vicinity of its Néel temperature T N as well, indicating homogeneous development of magnetic correlations. According to the symmetry analysis and its magnetic structure, the weak magnetoelectric coupling effect in Mn4Nb2O9 is ascribed to the uncancelled exchange striction on the two non-equivalent Mn2+ sites.

Anticollinear order and degeneracy lifting in square lattice antiferromagnet LaSrCrO4

We report the static and dynamic magnetic properties of ${\mathrm{LaSrCrO}}_{4}$, a seemingly canonical spin-3/2 square-lattice antiferromagnet that exhibits frustration between magnetic layers---owing to their AB stacking---and offers a rare testbed to investigate accidental-degeneracy lifting in magnetism. Neutron diffraction experiments on single-crystal samples uncover a remarkable anticollinear magnetic order below ${T}_{N}$ = 170 K characterized by a N\'eel arrangement of the spins within each layer and an orthogonal arrangement between adjacent layers. To understand the origin of this unusual magnetic structure, we analyze the spin-wave excitation spectrum by means of inelastic neutron scattering and bulk measurements. A spectral gap of 0.5 meV, along with a spin-flop transition at 3.2 T, reflect the energy scale associated with the degeneracy-lifting. A minimal model to explain these observations requires both a positive biquadratic interlayer exchange and dipolar interactions, both of which are on the order of 10${}^{\ensuremath{-}4}$ meV, only a few parts per million of the dominant exchange interaction ${J}_{1}\ensuremath{\approx}11$ meV. These results provide direct evidence for the selection of a noncollinear magnetic structure by the combined effect of two distinct degeneracy lifting interactions.

Magnetic structure and exchange interactions in the Heisenberg pyrochlore antiferromagnet Gd2Pt2O7

The Heisenberg pyrochlore antiferromagnet ${\mathrm{Gd}}_{2}{\mathrm{Pt}}_{2}{\mathrm{O}}_{7}$ is one of a series of gadolinium pyrochlore compounds with a variety of B-site cations. Despite the expected simplicity of a spin-only ${\mathrm{Gd}}^{3+}$ Heisenberg interaction model, the gadolinium pyrochlore series exhibits various complex magnetic ground states at low temperature. ${\mathrm{Gd}}_{2}{\mathrm{Pt}}_{2}{\mathrm{O}}_{7}$ displays the highest temperature magnetic order of the series with ${T}_{N}=1.6$ K, which has been attributed to enhanced superexchange pathways facilitated by empty $5d\phantom{\rule{0.16em}{0ex}}{e}_{g}$ Pt orbitals. In this study, we use various neutron scattering techniques on an isotopically enriched polycrystalline $^{160}\mathrm{Gd}{}_{2}{\mathrm{Pt}}_{2}{\mathrm{O}}_{7}$ sample to examine the magnetic structure and spin-wave excitation spectrum below ${T}_{N}$ in order to extract the dominant exchange interactions. We find that the ground-state magnetic structure is the Palmer-Chalker state previously seen in ${\mathrm{Gd}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$ with an associated gapped excitation spectrum consistent with enhanced exchange interactions between further near-neighbor ${\mathrm{Gd}}^{3+}$ ions. We confirm this exchange model with analysis of the magnetic diffuse scattering in the paramagnetic regime using polarized neutrons.

Evidence for Magnetic Fractional Excitations in a Kitaev Quantum-Spin-Liquid Candidate α-RuCl3

It is known that α-RuCl3 has been studied extensively because of its proximity to the Kitaev quantum-spin-liquid (QSL) phase and the possibility of approaching it by tuning the competing interactions. Here we present the first polarized inelastic neutron scattering study on α-RuCl3 single crystals to explore the scattering continuum around the Γ point at the Brillouin zone center, which was hypothesized to be resulting from the Kitaev QSL state but without concrete evidence. With polarization analyses, we find that, while the spin-wave excitations around the M point vanish above the transition temperature T N, the pure magnetic continuous excitations around the Γ point are robust against temperature. Furthermore, by calculating the dynamical spin-spin correlation function using the cluster perturbation theory, we derive magnetic dispersion spectra based on the K–Γ model, which involves with a ferromagnetic Kitaev interaction of –7.2 meV and an off-diagonal interaction of 5.6 meV. We find this model can reproduce not only the spin-wave excitation spectra around the M point, but also the non-spin-wave continuous magnetic excitations around the Γ point. These results provide evidence for the existence of fractional excitations around the Γ point originating from the Kitaev QSL state, and further support the validity of the K–Γ model as the effective minimal spin model to describe α-RuCl3.

Reconfigurable 3D magnonic crystal: Tunable and localized spin-wave excitations in CoFeB meander-shaped film

In this work, we study experimentally by broadband ferromagnetic resonance measurements, the dependence of the spin-wave excitation spectra on the magnetic applied field in CoFeB meander-shaped films. Two different orientations of the external magnetic field were explored, namely parallel or perpendicular to the lattice cores. The interpretation of the field dependence of the frequency and spatial profiles of major spin-wave modes were obtained by micromagnetic simulations. We show that the vertical segments couple the horizontal sections of the structure and support the in-phase and out-of-phase spin-wave precession amplitude for several magnetic modes. The investigated structures could potentially be used for the design of tunable metasurfaces or in magnetic memories based on meandering 3D magnetic films.

Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model

We study the flat-band ferromagnetic phase of the Haldane-Hubbard model on a honeycomb lattice within a bosonization scheme for flat-band Chern insulators, focusing on the calculation of the spin-wave excitation spectrum. We consider the Haldane-Hubbard model with the noninteracting lower bands in a nearly-flat band limit, previously determined for the spinless model, and at 1/4-filling of its corresponding noninteracting limit. Within the bosonization scheme, the Haldane-Hubbard model is mapped into an effective interacting boson model, whose quadratic term allows us to determine the spin-wave spectrum at the harmonic approximation. We show that the excitation spectrum has two branches with a Goldstone mode and Dirac points at center and at the K and K' points of the first Brillouin zone, respectively. We also consider the effects on the spin-wave spectrum due to an energy offset in the on-site Hubbard repulsion energies and due to the presence of an staggered on-site energy term, both quantities associated with the two triangular sublattices. In both cases, we find that an energy gap opens at the K and K' points. Moreover, we also find some evidences for an instability of the flat-band ferromagnetic phase in the presence of the staggered on-site energy term. We provide some additional results for the square lattice topological Hubbard model previous studied within the bosonization formalism and comment on the differences between the bosonization scheme implementation for the correlated Chern insulators on both square and honeycomb lattices.

Role of charge doping and strain in the stabilization of in-plane ferromagnetism in monolayer at room temperature

We study the origin of in-plane ferromagnetism in monolayer VSe2 focusing on the effect of charge doping and mechanical strain. We start from an anisotropic spin Hamiltonian, estimate its parameters from density functional calculations, and determine the spectrum of spin-wave excitations. We show that 1T-VSe2 is characterized by relatively strong on-site Coulomb repulsion (U ≃ 5 eV), favoring an antiferromagnetic ground state, which contradicts experimental observations. We calculate the magnetic phase diagram as a function of charge doping and strain, and find a transition to the ferromagnetic state with in-plane easy axis under moderate hole doping (∼1014 cm−2). Analysis of spin-wave excitations in doped monolayer VSe2 reveals a gap due to the in-plane anisotropy, giving rise to long-range magnetic order well above 300 K, in agreement with recent experiments. Our findings suggest that experimentally available 1T-VSe2 monolayer samples might be intrinsically or extrinsically doped, which opens up the possibility for a controllable manipulation of their magnetic properties.

Effect of Dzyaloshinskii-Moriya interaction on magnetic vortex switching driven by radial spin waves

We theoretically investigate the radial-spin-wave induced magnetic vortex switching in the presence of Dzyaloshinskii-Moriya interaction (DMI). From micromagnetic simulations, we observe a circular-to-radial vortex phase transition by increasing the DMI strength. The radial spin-wave excitation spectrum for each magnetization configuration is analyzed, showing that the frequency of spin-wave mode with a given radial node number monotonically increases (decreases) with the DMI parameter of the radial (circular) vortex. Interestingly, we find that the DMI can significantly facilitate the polarity switching of the circular vortex driven by radial spin waves. Our work provides a new insight into the DMI effect on the vortex dynamics and is helpful for designing fast all-magnonic memory devices.

Micromagnetic Modeling of Spin-Wave Excitations in Corrugated YIG Films

In this paper, we study the features of the spin-wave excitation spectrum in a YIG film with a thickness of 0.4 μm and a magnetization of 1.1 kG corrugated due to the periodic relief of the substrate in the form of grooves with a width of 10 μm and a depth of 0.5 μm, with sloping walls, and a period of 20 μm by micromagnetic modeling. Calculations performed for the orientations of the external magnetic field applied in the film plane along (θ = 0) and across (θ = 90°) grooves show that film shape anisotropy leads to quantization of the spectrum and localization of the spin-wave excitations in various parts of the sample. In this case, the spatial distribution of the magnetization amplitude at frequencies in the spectrum at θ = 90° can be characterized by several spatial scales, differing by orders of magnitude. This is explained by the strong inhomogeneity of the ground state on the walls of the grooves at θ = 90°, which leads to the effective excitation of the short-wave part of the spectrum of spin waves in a periodic structure according to the Schlomann mechanism.

Spectrum of the Ferromagnetic Resonance of a Lattice of Orthogonal Permalloy Microwaveguides

The ferromagnetic resonance spectrum at a frequency of ~9.85 GHz for an in-plane magnetized 2D square lattice with the unit cell parameter а ≈ 15 μm consisting of orthogonal microwaveguides with a width of w ≈ 5 μm on the basis of a permalloy film with thickness of d ≈ 90 nm has been experimentally and numerically investigated. It is shown that upon variation in the angle θ between the magnetic field direction and the unit cell axis, the total spectrum of spin-wave excitations of the lattice can be presented as a superposition of the spectra of separate permalloy microstrips magnetized at angles θ and π/2–θ and regions corresponding to the lattice nodes. It has been found that, in the case of magnetization along the lattice diagonal (θ ≈ 45о), excitations localized at the lattice nodes dominate in the spectrum, whereas, at θ ≈ 0 and 90°, the main contribution is made by excitations localized mainly on the microwaveguide segments between the lattice nodes; at θ ≈ 10°–13° and 18–20°, “repulsion” of absorption lines in the spectrum is observed.

Tunable spin waves in diluted magnetic semiconductor nanoribbon

The spin wave excitation spectrum in diluted magnetic semiconductor (DMS) nanoribbons was calculated by taking account of the quantum confinement effect of carriers and spin waves. By introducing the boundary condition for the spin waves, we derived the spin wave dispersion using the path-integral formulation and Green's function method. It was shown that the spin wave excitation spectrum is discrete due to the confinement effect and strongly dependent on the carrier density, the magnetic ion density, and the width of the nanoribbon. When the width of the nanoribbon is beyond the typical nanoscales, the size effect on the excitation energies of the spin waves disappears in our calculation, which is in qualitative agreement with no obvious size effect observed in the as-made nanodevices of (Ga,Mn)As in this size regime. Our results provide a potential way to control the spin waves in the DMS nanoribbon not only by the carrier density and the magnetic ion density but also by the nanostructure geometry.

Surface effects on ferromagnetic resonance in magnetic nanocubes

We study the effect of surface anisotropy on the spectrum of spin-wave excitations in a magnetic nanocluster and compute the corresponding absorbed power. For this, we develop a general numerical method based on the (undamped) Landau–Lifshitz equation, either linearized around the equilibrium state leading to an eigenvalue problem or solved using a symplectic technique. For box-shaped clusters, the numerical results are favorably compared to those of the finite-size linear spin-wave theory. Our numerical method allows us to disentangle the contributions of the core and surface spins to the spectral weight and absorbed power. In regard to the recent developments in synthesis and characterization of assemblies of well defined nano-elements, we study the effects of free boundaries and surface anisotropy on the spin-wave spectrum in iron nanocubes and give orders of magnitude of the expected spin-wave resonances. For an iron nanocube, we show that the absorbed power spectrum should exhibit a low-energy peak around 10 GHz, typical of the uniform mode, followed by other low-energy features that couple to the uniform mode but with a stronger contribution from the surface. There are also high-frequency exchange-mode peaks around 60 GHz.

Magnetic order and spin excitations in the Kitaev–Heisenberg model on a honeycomb lattice

We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev - Heisenberg model proposed for A2IrO3 (A=Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation (RPA) for four different ordered phases, observed in the parameter space of the model: antiferomagnetic, stripe, ferromagnetic, and zigzag phases. The N\'{e}el temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na2IrO3.

Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets

Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er2Ti2O7, with the ground state selection proceeding by order by disorder induced through the effects of quantum fluctuations. This identification assumes the smallness of the effect of virtual crystal field fluctuations that could provide an alternative route to picking the ground state. Here we show that this order by virtual crystal field fluctuations is not only significant, but competitive with the effects of quantum fluctuations. Further, we argue that higher-multipolar interactions that are generically present in rare-earth magnets can dramatically enhance this effect. From a simplified bilinear-biquadratic model of these multipolar interactions, we show how the virtual crystal field fluctuations manifest in Er2Ti2O7 using a combination of strong coupling perturbation theory and the random phase approximation. We find that the experimentally observed psi2 state is indeed selected and the experimentally measured excitation gap can be reproduced when the bilinear and biquadratic couplings are comparable while maintaining agreement with the entire experimental spin-wave excitation spectrum. Finally, we comments on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets.

Flat-band ferromagnetism and spin waves in topological Hubbard models

We study the flat-band ferromagnetic phase of a topological Hubbard model within a bosonization formalism and, in particular, determine the spin-wave excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling whose free-electron term is the \pi-flux model with topologically nontrivial and nearly flat energy bands. The electron spin is introduced such that the model either explicitly breaks time-reversal symmetry (correlated flat-band Chern insulator) or is invariant under time-reversal symmetry (correlated flat-band $Z_2$ topological insulator). We generalize for flat-band Chern and topological insulators the bosonization formalism [Phys. Rev. B 71, 045339 (2005)] previously developed for the two-dimensional electron gas in a uniform and perpendicular magnetic field at filling factor \nu=1. We show that, within the bosonization scheme, the topological Hubbard model is mapped into an effective interacting boson model. We consider the boson model at the harmonic approximation and show that, for the correlated Chern insulator, the spin-wave excitation spectrum is gapless while, for the correlated topological insulator, gapped. We briefly comment on the possible effects of the boson-boson (spin-wave--spin-wave) coupling.

Investigations on thermodynamic properties of the three sub-lattice spin frustrated chain

The spin frustration related to the high-[Formula: see text] superconductivity has received much attention. In this paper, based on the Jordan–Wigner transformation and Green’s function method, we study the magnetic and thermodynamic properties of the three sub-lattice spin frustrated chains. It is found that there are three branches for the spin–wave excitation spectra at zero temperature. Among them, two belong to nature excitation patterns with antiferromagnetic interaction and the third one is band gap excitation spectrum with ferromagnetic nature. The specific heat capacity of sub-lattice spin system presents complex characteristics with the change of temperature due to the intense competition between the ferromagnetic and antiferromagnetic interactions. It is also shown that the increase of the ferromagnetic action is helpful to the value of net spin.

Spin excitation spectra of spin–orbit coupled bosons in an optical lattice**Project supported by the National Natural Science Foundation of China (Grant Nos. 11347197, 11404225, and 11474205).

Spin-wave excitation plays important roles in the investigation of the magnetic phases. In this paper, we study the spin-wave excitation spectra of two-component Bose gases with spin–orbit coupling in a deep square optical lattice using the spin-wave theory. We find that, while the excitation spectrum of the vortex crystal phase is gapless with a linear dispersion in the vicinity of the minimum point, the spectra of the commensurate spiral spin phase and the skyrmion crystal phase are gapped. Significantly, the spin fluctuations strongly destabilize the classical ground state of the skyrmion phase with the appearance of an imaginary part in the eigenfrequencies of spin excitations. Such features of the spin excitation spectra provide further insights into the exotic spin phases.

Magnetic order and spin excitations in layered Heisenberg antiferromagnets with compass-model anisotropies

The spin-wave excitation spectrum, the magnetization, and the N\'{e}el temperature for the quasi-two-dimensional spin-1/2 antiferromagnetic Heisenberg model with compass-model interaction in the plane proposed for iridates are calculated in the random phase approximation. The spin-wave spectrum agrees well with data of Lanczos diagonalization. We find that the Neel temperature is enhanced by the compass-model interaction and is close to the experimental value for Ba2IrO4.

Azimuthal spin wave modes in an elliptical nanomagnet with single vortex configuration

In comparison with uniformly magnetized states, vortex structures demonstrate a rich frequency spectrum of spin-wave (SW) excitations. However, a detailed theoretical description of the magnetic modes is generally still a challenge due to the difficulty of analytic calculation, except for the well-defined symmetric circular states. In contrast, the method of micromagnetic simulations combined with Fourier analysis is shown to be very powerful for gaining insight into the nature of magnetic excitation modes. Vortex excitation modes have been reported to be directly influenced by the geometric symmetry of the elements and/or the nature of the initial perturbation of pulse field. In order to understand how the reduced symmetry affects the vortex SW modes, we perform the micromagnetic simulations on vortex modes excited in a submicron-sized thin ellipse. In order to excite the spin-wave modes, a short in-plane Gaussian field pulse is applied along the short axis direction. After the pulse, the off-centered vortex core moves following an elliptical trajectory around its equilibrium position. Simulations provide the time evolution of the local magnetizations (at each discretization point) and dynamics of the spatially averaged magnetization. To determine the mode frequencies, the spectrum is obtained from the average magnetization through Fourier transformation from time domain the frequency domain. By means of Fourier analysis, a variety of azimuthal SW modes can be observed in the excitation spectrum. The ellipse in single vortex state has a twofold rotational symmetry with a rotation of πup around the z-axis (out-of plane) and can be described by the C2 group. The observed azimuthal modes can be divided into two categories according to their symmetry. Two modes occur alternately with increasing azimuthal number, indicating that the magnetic excitation modes remain to keep the symmetry of the ellipse structure. Their frequencies are found to increase linearly with the azimuthal index number. An increase of the SW frequency with increasing number of nodal planes is rather well known, which results from the competition between exchange and dipolar energy terms. According to the temporal evolution of the ellipse's spatially averaged energy densities, our micromagnetic simulation shows that the average exchange energy is significantly higher than the magnetostatic energy, suggesting that the exchange interaction plays a more important role in the excitation modes. The exchange energy density is mainly focused on the core origin while the largest contribution of the magnetostatic energy is distributed near the long axis. Thus, we can conclude that the exchange interaction provides the principal contribution to the vortex energy in such small ellipses with a single vortex state, resulting in the increasing frequency versus the azimuthal number, that is observed.