Spin-wave Dispersion Relation Research Articles

Single shot acquisition of spatially resolved spin wave dispersion relations using X-ray microscopy

For understanding magnonic materials the fundamental characterization of their frequency response is essential. However, determining full dispersion relations and real space wavelength measurements are challenging and time-consuming tasks. We present an approach for spin wave excitation by a modified Sinc pulse, which combines a cosine signal with a conventional Sinc function. The resulting adjustable frequency bands lead to a broadband spin wave excitation at uniform power levels. Subsequently, time resolved scanning transmission X-ray microscopy is used for direct imaging of all excited spin waves in real space. To demonstrate the capabilities of this approach, a modified Sinc excitation of an ultra-thin yttrium-iron-garnet film is shown that simultaneously reveals phase, amplitude, and k-space information from a single measurement. Consequently, this approach allows a fast and thorough access to the full dispersion relation including spatial maps of the individual spin wave modes, enabling complete characterization of magnonic materials down to the nanoscale in real and reciprocal space.

Scattering of exchange spin waves from a helimagnetic layer sandwiched between two semi-infinite ferromagnetic media

We have calculated the scattering (reflection and transmission) coefficients of linear exchange spin waves normally incident upon a helimagnetic layer sandwiched between two semi-infinite ferromagnetic media. Our calculations show that, despite the helimagnetic order induced in the layer by the Dzyaloshinskii-Moriya interaction (DMI), the scattering is reciprocal and insensitive to the presence of the helimagnetic order in the layer. This comes as a result of the disappearance of the DMI from the boundary conditions in the considered geometry under the small-amplitude approximation and from the specific form of the nonreciprocity of the spin-wave dispersion relation in the helimagnetic material. We show that the helimagnetic layer's interfaces act as a system of two semicrossed polarizers for the circularly polarized spin waves incident from the ferromagnetic media. This results from the ellipticity of the magnetic precession induced by the easy-plane anisotropy in the helimagnetic layer. Our calculations also reveal the importance of evanescent solutions to correctly describe the spin-wave scattering in samples with elliptical precession. Our findings will aid development of magnonic devices containing helimagnetic constituents.

Spin waves in decorated lattices

The XXZ Heisenberg model is used to study the dispersion relation of spin waves propagating in decorated planar square and triangular lattices. A superposition of interpenetrating lattices will be used to generate the composed systems. The decorations are introduced in order to generate systems with more than one atom per unit cell. The formalism applied here allows us to study different types of decorated lattices according to the relative position between each other controlled by the parameters α and β. By using the Holstein–Primakoff transformation we obtained the SW dispersion relation for the decorated lattices considered here. The obtained numerical results show the effects of both (i) the relative position of the interpenetrating lattices and (ii) the intra-lattice and inter-lattice exchange couplings on the spin waves dispersion relation.

Slow-Wave-Based Nanomagnonic Diode

Spin waves, the collective excitations of the magnetic order parameter, and magnons, the associated quasiparticles, are envisioned as possible data carriers in future wave-based computing architectures. On the road towards spin-wave computing, the development of a diode-like device capable of transmitting spin waves in only one direction, thus allowing controlled signal routing, is an essential step. Here, we report on the design and experimental realization of a microstructured magnonic diode in a ferromagnetic bilayer system. Effective unidirectional propagation of spin waves is achieved by taking advantage of nonreciprocities produced by dynamic dipolar interactions in transversally magnetized media, which lack symmetry about their horizontal midplane. More specifically, dipolar-induced nonreciprocities are used to engineer the spin-wave dispersion relation of the bilayer system so that the group velocity is reduced to very low values for one direction of propagation, and not for the other, thus producing unidirectional slow spin waves. Brillouin light scattering and propagating spin-wave spectroscopy are used to demonstrate the diode-like behavior of the device, the composition of which was previously optimized through micromagnetic simulations. simulations.

Nanometer-thick YIG-based magnonic crystals: Bandgap dependence on groove depth, lattice constant, and film thickness

We report on bandgap tuning in magnonic crystals made of nanometer-thick yttrium iron garnet (YIG) films with CoFeB-filled grooves via a variation of the groove depth, lattice constant, and film thickness. Using broadband spin-wave spectroscopy, we demonstrate bandgap widening in a 260-nm-thick YIG crystal when the grooves are deepened from half to full film thickness. Importantly, low-loss spin-wave transmission in the allowed bands of the magnonic crystal is almost unaffected by the patterning of fully discrete YIG stripes. Downscaling of the YIG film thickness to 35 nm decreases the bandgap size through a flattening of the spin-wave dispersion relation. We show that a reduction in the lattice constant effectively compensates for this trend. Our experimental results are corroborated by micromagnetic simulations, providing relevant information for the design of ultrathin YIG-based magnonic crystals with optimized bandgaps and spin-wave transmission properties.

Chiral Magnonics: Reprogrammable Nanoscale Spin Wave Networks Based on Chiral Domain Walls.

SummarySpin waves offer promising perspectives as information carriers for future computational architectures beyond conventional complementary metal-oxide-semiconductor (CMOS) technology, owing to their benefits for device minimizations and low-ohmic losses. Although plenty of magnonic devices have been proposed previously, scalable nanoscale networks based on spin waves are still missing. Here, we demonstrate a reprogrammable two-dimensional spin wave network by combining the chiral exchange spin waves and chiral domain walls. The spin-wave network can be extended to two dimensions and offers unprecedented control of exchange spin waves. Each cell in the network can excite, transmit, and detect spin waves independently in the chiral domain wall, and spin-wave logics are also demonstrated. Our results open up perspectives for integrating spin waves into future logic and computing circuits and networks.

Electric field effect on spin waves: Role of magnetic moment current

We show that a static electric field E x gives rise to a shift of the spin wave dispersion relation in the direction of the wave number q y of the quantity . This effect is caused by the magnetic moment current carried by the spin wave itself which generates an additional phase proportional to the electric field, as in the Aharonov-Casher effect. This effect is independent of the possibly present magneto-electric effects of insulating ferromagnets and superimposes to them.

Snell's law for spin waves at a 90° magnetic domain wall

We report the experimental observation of the refraction and reflection of propagating magnetostatic spin waves crossing a 90° domain wall (DW). Time-resolved magneto-optical imaging was used to observe the propagation dynamics of magnetostatic spin waves. Due to the magnetization rotation across such a DW, the dispersion relation of magnetostatic spin waves rotates by 90°. This results in a change in the propagation dynamics of spin waves on both sides of the DW. We observed the refraction and reflection of magnetostatic spin waves at the DW and reveal their characteristics that include negative refraction. The incident-angle dependence of the refraction angle is explained by the wavenumber conservation along the DW, quite similar to the case of Snell's law for light.

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.

Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides

Spin waves are investigated in yttrium iron garnet waveguides with a thickness of 39nm and widths ranging down to 50nm, i.e., with an aspect ratio thickness over width approaching unity, using Brillouin light scattering spectroscopy. The experimental results are verified by a semianalytical theory and micromagnetic simulations. A critical width is found, below which the exchange interaction suppresses the dipolar pinning phenomenon. This changes the quantization criterion for the spin-wave eigenmodes and results in a pronounced modification of the spin-wave characteristics. The presented semianalytical theory allows for the calculation of spin-wave mode profiles and dispersion relations in nanostructures.

Propagating spin waves in nanometer-thick yttrium iron garnet films: Dependence on wave vector, magnetic field strength, and angle

We present a comprehensive investigation of propagating spin waves in nanometer-thick yttrium iron garnet (YIG) films. We use broadband spin-wave spectroscopy with integrated coplanar waveguides (CPWs) and microstrip antennas on top of continuous and patterned YIG films to characterize spin waves with wave vectors up to 10 rad/$\mu$m. All films are grown by pulsed laser deposition. From spin-wave transmission spectra, parameters such as the Gilbert damping constant, spin-wave dispersion relation, group velocity, relaxation time, and decay length are derived and their dependence on magnetic bias field strength and angle is systematically gauged. For a 40-nm-thick YIG film, we obtain a damping constant of $3.5 \times 10^{-4}$ and a maximum decay length of 1.2 mm. Our experiments reveal a strong variation of spin-wave parameters with magnetic bias field and wave vector. Spin-wave properties change considerably up to a magnetic bias field of about 30 mT and above a field angle of $\theta_{H} = 20^{\circ}$, where $\theta_{H} = 0^{\circ}$ corresponds to the Damon-Eshbach configuration.

Doping-induced states near the Mott transition in the presence of antiferromagnetic order

A central issue of the Mott transition is how electronic states change in the Mott transition. Here, by taking into account spin fluctuation around the mean-field state using the random-phase approximation, electronic states exhibiting the spin-wave dispersion relation shifted by the Fermi momenta are shown to emerge in the Mott gap on doping an antiferromagnetically ordered Mott insulator. This characteristic contrasts with that of the mean-field approximation where doping does not induce electronic states in the gap. The results imply that this characteristic is general and fundamental to the Mott transition even in the presence of antiferromagnetic order.

Frequency linewidth and decay length of spin waves in curved magnetic membranes

The curvature of a magnetic membrane was presented as a means of inducing nonreciprocities in the spin-wave (SW) dispersion relation (see [Ot\'alora et al. Phys. Rev. Lett., 2016 117, 227203] and [Ot\'alora et al. Phys. Rev. B., 2017 95, 184415]), thereby expanding the toolbox for controlling SWs. In this paper, we further complement this toolbox by analytically showing that the membrane curvature is also manifested in the absorption of SWs, leading to a difference in the frequency linewidth (or lifetime) of counterpropagating magnons. Herein, we studied the nanotubular case, predicting changes of approximately greater than 10% and up to 20% in the frequency linewidth of counterpropagating SWs for a wide range of nanotube radii ranging from 30 nm to 260 nm and with a thickness of 10 nm. These percentages are comparable to those that can be extracted from experiments on heavy metal/magnetic metal sandwiches, wherein linewidth asymmetry results from an interfacial Dzyaloshinskii-Moriya interaction (DMI). We also show that the interplay between the frequency linewidth and group velocity leads to asymmetries in the SW decay length, presenting changes between 10\% and 22\% for counterpropagating SWs in the frequency range of 2 - 10 GHz. For the case of the SW dispersion relation, the predicted effects are identified as the classical dipole-dipole interaction, and the analytical expression of the frequency linewidth has the same mathematical form as in thin films with the DMI. Furthermore, we present limiting cases of a tubular geometry with negligible curvature such that our analytical model converges to the case of a planar thin film known from the literature. Our findings represent a step forward toward the realization of three-dimensional curvilinear magnonic devices.

180°-phase shift of magnetoelastic waves observed by phase-resolved spin-wave tomography

We have investigated optically excited magnetoelastic waves by phase-resolved spin-wave tomography (PSWaT). PSWaT reconstructs the dispersion relation of spin waves together with their phase information by using time-resolved magneto-optical imaging for spin-wave propagation followed by an analysis based on the convolution theorem and a complex Fourier transform. In PSWaT spectra for a Bi-doped garnet film, we found a 180°-phase shift of magnetoelastic waves at around the crossing of the dispersion relations of spin and elastic waves. The result is explained by a coupling between spin waves and elastic waves through the magnetoelastic interaction. We also propose an efficient way for the phase manipulation of magnetoelastic waves by rotating the orientation of magnetization less than 10°.

Weak localization of magnons in chiral magnets

We report on the impact of the Dzyaloshinskii-Moriya interaction on the coherent backscattering of spin waves in a disordered magnetic material. This interaction breaks the inversion symmetry of the spin-wave dispersion relation, such that $\omega_\mathbf{k} = \omega_{2\mathbf{K}^\mathrm{I}-\mathbf{k}} \neq \omega_{-\mathbf{k}}$, where $\mathbf{K}^\mathrm{I}$ is related to the Dzyaloshinskii-Moriya vectors. As a result of numerical investigations we find that the backscattering peak of a wave packet with initial wave vector $\mathbf{k}_0$ shifts from $-\mathbf{k}_0$ to $2\mathbf{K}^\mathrm{I}-\mathbf{k}_0$, such that the backscattering wave vector and the initial wave vector are in general no longer antiparallel. The shifted coherence condition is explained by a diagrammatic approach and opens up an avenue to measure sign and magnitude of the Dzyaloshinskii-Moriya interaction in weakly disordered chiral magnets.

Frequency and wavenumber selective excitation of spin waves through coherent energy transfer from elastic waves

Using spin-wave tomography (SWaT), we have investigated the excitation and the propagation dynamics of optically-excited magnetoelastic waves, i.e. hybridized modes of spin waves and elastic waves, in a garnet film. By using time-resolved SWaT, we reveal the excitation dynamics of magnetoelastic waves through coherent-energy transfer between optically-excited pure-elastic waves and spin waves via magnetoelastic coupling. This process realizes frequency and wavenumber selective excitation of spin waves at the crossing of the dispersion relations of spin waves and elastic waves. Finally, we demonstrate that the excitation mechanism of the optically-excited pure-elastic waves, which are the source of the observed magnetoelastic waves, is dissipative in nature.

Spin-wave beam propagation in ferromagnetic thin films with graded refractive index: Mirage effect and prospective applications

Using analysis of iso-frequency contours of the spin-wave dispersion relation, supported by micromagnetic simulations, we study the propagation of spin-wave (SW) beams in thin ferromagnetic films through the areas of the inhomogeneous refractive index. We compare the transmission and reflection of SWs in areas with gradual and step variation of the SW refractive index. In particular, we show the mirage effect for SWs with narrowing SW beam width, and an application of the gradual modulation of the SWs refractive index as a diverging lens. Furthermore, we study the propagation of SWs in ferromagnetic stripe with modulated refractive index. We demonstrate that the system can be considered as the graded-index waveguide, which preserves the width of the SW beam for a long distance-the property essential for prospective applications of magnonics.

Phase-resolved spin-wave tomography

The propagation dynamics of spin waves are represented by their dispersion relations. Recently, we have developed a method, called spin-wave tomography (SWaT), to obtain a dispersion relation of spin waves in the long wavelength regime, the so-called pure magnetostatic waves. In our previous studies on SWaT, phase information of spin waves is disregarded. In this report, we demonstrate an advanced SWaT analysis, called phase-resolved spin-wave tomography (PSWaT), to realize the direct observation of the amplitude and the phase of spin waves. The PSWaT spectra are obtained by separating the real and the imaginary components of the complex Fourier transform in the SWaT analysis. We demonstrate the PSWaT spectra of spin waves excited by photo-induced demagnetization in a Bi-doped garnet film, reflecting the characteristic features of the complex dynamical susceptibility affected by magnetostatic coupling in the film.

Magnetic excitations in metallic antiferromagnets Fe0.5Mn0.5 and Fe0.7Mn0.3

Magnetic excitations in the metallic antiferromagnet Fe0.5Mn0.5 were investigated using the inelastic neutron scattering technique at low temperatures well below the antiferromagnetic transition temperatures (TN). The observed peak positions in low energies well sit on the antiferromagnetic dispersion relation reported in the early study. However, the peak positions in higher energies shift to higher energies than that of the antiferromagnetic spin wave dispersion relation. This behavior is the same as one of the behaviors suggesting that the spin waves merge with the continuum of the individual particle-hole excitations at higher energies in Fe0.7Mn0.3.

All-optical observation and reconstruction of spin wave dispersion

To know the properties of a particle or a wave, one should measure how its energy changes with its momentum. The relation between them is called the dispersion relation, which encodes essential information of the kinetics. In a magnet, the wave motion of atomic spins serves as an elementary excitation, called a spin wave, and behaves like a fictitious particle. Although the dispersion relation of spin waves governs many of the magnetic properties, observation of their entire dispersion is one of the challenges today. Spin waves whose dispersion is dominated by magnetostatic interaction are called pure-magnetostatic waves, which are still missing despite of their practical importance. Here, we report observation of the band dispersion relation of pure-magnetostatic waves by developing a table-top all-optical spectroscopy named spin-wave tomography. The result unmasks characteristics of pure-magnetostatic waves. We also demonstrate time-resolved measurements, which reveal coherent energy transfer between spin waves and lattice vibrations.