Spin-wave Velocity Research Articles

Control of spin-wave polarity and velocity using a ferrimagnetic domain wall

We present a theoretical study of the scattering of spin waves by a domain wall (DW) in a ferrimagnetic (FiM) spin chain in which two sublattices carry spins of unequal magnitudes. We find that a narrow but atomically smooth FiM DW exhibits a different behavior in comparison with similarly smooth ferromagnetic and antiferromagnetic DWs due to the inequivalence of the two sublattices. Specifically, for sufficiently weak anisotropy, the smaller spin at the center of the DW is found to become precisely normal to the easy axis, selecting an arbitrary direction in the xy plane and thereby breaking the U(1) spin-rotational symmetry spontaneously. This particular form of a FiM DW does not occur in antiferromagnetic systems and is shown to lead to a strong dependence of spin-wave scattering pattern on the state of polarization of the spin wave, which can be either right-handed or left-handed, suggesting the utilization of such a narrow DW as a spin-wave filter. Moreover, we find that in the case of an atomically sharp DW, where all the spins point either up or down due to strong easy-axis anisotropy and therefore the polarization of the spin wave is conserved upon transmission, the wave vector of the spin-wave changes after passing through the DW leading to a change in the group velocity of the spin wave. This change of the wave vector indicates the acceleration or deceleration of the spin waves and thus a sharp FiM DW could serve as a spin-wave accelerator or decelerator in spintronics devices, offering a functionality absent in a ferromagnetic and an antiferromagnetic counterpart. Our results indicate that FiM spin textures can interact with spin waves distinctly from ferromagnetic and antiferromagnetic counterparts, suggesting that they may offer spin-wave functionalities that are absent in more conventional magnets. Published by the American Physical Society 2024

Excitation of exchange spin waves in a magnetic insulator thin film at cryogenic temperatures

Spin waves and their quanta, magnons, are promising candidates for next-generation electronic devices, due to their low-power consumption and compatibility with radio-frequency-based electronic devices. For achieving magnon-based hybrid quantum systems for quantum memory and computation, the investigation of spin-wave propagation at cryogenic temperatures is highly required. In this article, we report the excitation and detection of exchange spin waves with wavelengths of tens of nanometers in an yttrium iron garnet (YIG) thin film at cryogenic temperatures. We find that the exchange spin waves are unidirectional in all temperature ranges, owing to the chiral dynamical dipolar coupling between the spin-wave mode in the YIG and the ferromagnetic resonance mode in the cobalt nanowire. Notably, a high exchange spin-wave group velocity of 2 km s−1 at 10 K is observed. Our results are promising for the development of high-speed and energy-efficient quantum magnonic devices operating at cryogenic temperatures.

Spin-Frame Field Theory of a Three-Sublattice Antiferromagnet.

We present a nonlinear field theory of a three-sublattice hexagonal antiferromagnet. The order parameter is the spin frame, an orthogonal triplet of vectors related to sublattice magnetizations and spin chirality. The exchange energy, quadratic in spin-frame gradients, has three coupling constants, only two of which manifest themselves in the bulk. As a result, the three spin-wave velocities satisfy a universal relation. Vortices generally have an elliptical shape with the eccentricity determined by the Lamé parameters.

Resonant generation of propagating second-harmonic spin waves in nano-waveguides

Generation of second-harmonic waves is one of the universal nonlinear phenomena that have found numerous technical applications in many modern technologies, in particular, in photonics. This phenomenon also has great potential in the field of magnonics, which considers the use of spin waves in magnetic nanostructures to implement wave-based signal processing and computing. However, due to the strong frequency dependence of the phase velocity of spin waves, resonant phase-matched generation of second-harmonic spin waves has not yet been achieved in practice. Here, we show experimentally that such a process can be realized using a combination of different modes of nano-sized spin-wave waveguides based on low-damping magnetic insulators. We demonstrate that our approach enables efficient spatially-extended energy transfer between interacting waves, which can be controlled by the intensity of the initial wave and the static magnetic field.

Frequency-selective coherent propagating spin waves induced by localized perpendicular magnetic anisotropy nanofilm stack

Magnonics has long been hailed as a promising technology poised to overcome the heat dissipation challenges in traditional electronic devices. With the escalating integration level of magnon devices, the demand arises for lower external field excitation conditions, coupled with enhanced coherence and frequency-selective excitation characteristics. In this proposal, we suggest introducing a localized perpendicular magnetic anisotropy nanofilm stack into the spin-wave transmission channel to finely regulate the propagation characteristics of spin waves. This adjustment can be achieved by altering the width and period of the stack in both horizontal and vertical dimensions. Additionally, the optimal transmission characteristics of spin waves are achieved at low frequencies (1–1.67 GHz) and in the presence of small magnetic fields (0–20 mT). Frequency-selective spin waves with triggering stability can effectively prevent signal folding resulting from changes in microwave power within the range of −30 to 0 dBm. At 1.08 GHz, the group velocity of frequency-selective spin waves can be increased by up to 2.86 times. This innovative method of regulating spin waves presents a potential alternative pathway for the development of future magnonic circuits.

Giant anisotropic Gilbert damping and spin wave propagations in single-crystal magnetic insulator

Gilbert damping in magnetic systems describes the relaxation of magnetization. This term was phenomenologically introduced into the Landau–Lifschitz–Gilbert (LLG) equation to describe spin dynamics. In most studies, such as magnetic random access memory, spin-wave propagations, and microwave devices, it has been assumed that the Gilbert damping is an isotropic constant. In this study, we uncover a giant anisotropic Gilbert damping parameter of up to 431% in single-crystal thin films of epitaxial [100]-oriented yttrium iron garnet (YIG) using angle-dependent ferromagnetic resonance. In contrast, the Gilbert damping parameter of a [111]-oriented YIG film is almost isotropic. The observed anisotropic damping is shown to have a similar fourfold symmetry with magneto-crystalline anisotropy. The anisotropic spin-wave group velocity (vg), relaxation time (τ), and decay length (ld) were also experimentally evaluated through spin-wave spectra of [100]-oriented YIG thin film. We developed the LLG equation with the introduction of an anisotropic orbital Gilbert damping term. This anisotropic orbital damping originates from the crystal-field dominated anisotropic spin–orbit coupling and orbital-related magnon–phonon coupling. Our results extend the understanding of the mechanism of anisotropic Gilbert damping in single-crystal magnetic insulators with strong magneto-crystalline anisotropy.

Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions

Standard relativistic hydrodynamics has been successful in describing the properties of the strongly interacting matter produced in the heavy-ion collision experiments. Recently, there has been a significant theoretical advancement in this field to explain spin polarization of hadrons emitted in these processes. Although current models have successfully explained some of the experimental data based on the coupling between spin polarization and vorticity of the medium, they still lack a clear understanding of the differential measurements. This is commonly interpreted as an indication that the spin needs to be treated as an independent degree of freedom whose dynamics is not entirely bound to flow circulation. In particular, if the spin is a macroscopic property of the system, in equilibrium its dynamics should follow hydrodynamic laws. Here, we develop a framework of relativistic hydrodynamics which includes spin degrees of freedom from the quantum kinetic theory for Dirac fermions and use it for modeling the dynamics of matter. Following experimental observations, we assume that the polarization effects are small and derive conservation laws for the net baryon current, the energy–momentum tensor and the spin tensor based on the de Groot–van Leeuwen–van Weert definitions of these currents. We present various properties of the spin polarization tensor and its components, analyze the propagation properties of the spin polarization components, and derive the spin-wave velocity for arbitrary statistics. We find that only the transverse spin components propagate, analogously to the electromagnetic waves. Finally, using our framework, we study the space–time evolution of the spin polarization for the systems respecting certain space–time symmetries and calculate the mean spin polarization per particle, which can be compared to the experimental data. We find that, for some observables, our spin polarization results agree qualitatively with the experimental findings and other model calculations.

Spin wave dispersion of ultra-low damping hematite ( α−Fe2O3 ) at GHz frequencies

Low magnetic damping and high group velocity of spin waves (SWs) or magnons are two crucial parameters for functional magnonic devices. Magnonics research on signal processing and wave-based computation at GHz frequencies focused on the artificial ferrimagnetic garnet ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ (YIG) so far. We report on spin wave spectroscopy studies performed on the natural mineral hematite ($\ensuremath{\alpha}{\text{-Fe}}_{2}{\text{O}}_{3}$), which is a canted antiferromagnet. By means of broadband GHz spectroscopy and inelastic light scattering, we determine a damping coefficient of $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and magnon group velocities of a few 10 km/s, respectively, at room temperature. Covering a large regime of wave vectors up to $k\ensuremath{\approx}24\phantom{\rule{0.16em}{0ex}}\mathrm{rad}/\textmu{}\mathrm{m}$, we find the exchange stiffness length to be relatively short and only about 1 \AA{}. In a small magnetic field of 30 mT, the decay length of SWs is estimated to be 1.1 cm similar to the best YIG. Still, inelastic light scattering provides surprisingly broad and partly asymmetric resonance peaks. Their characteristic shape is induced by the large group velocities, low damping, and distribution of incident angles inside the laser beam. Our results promote hematite as an alternative and sustainable basis for magnonic devices with fast speeds and low losses based on a stable natural mineral.

Propagating spin-wave spectroscopy in a liquid-phase epitaxial nanometer-thick YIG film at millikelvin temperatures

Performing propagating spin-wave spectroscopy of thin films at millikelvin temperatures is the next step toward the realization of large-scale integrated magnonic circuits for quantum applications. Here, we demonstrate spin-wave propagation in a 100 nm-thick yttrium-iron-garnet (YIG) film at temperatures down to 45 mK, using stripline nanoantennas deposited on YIG surface for electrical excitation and detection. The clear transmission characteristics over the distance of 10 μ m are measured and the extracted spin-wave group velocity and the YIG saturation magnetization agree well with the theoretical values. We show that the gadolinium-gallium-garnet (GGG) substrate influences the spin-wave propagation characteristics only for the applied magnetic fields beyond 75 mT, originating from a GGG magnetization up to 62 kA / m at 45 mK. Our results show that the developed fabrication and measurement methodologies enable the realization of integrated magnonic quantum nanotechnologies at millikelvin temperatures.

The numerical value for a universal quantity of a two-dimensional dimerized quantum antiferromagnet

The numerical value of a universal quantity associated with the quantum critical regime, namely χuc2/T, for a two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using the quantum Monte Carlo simulations (QMC). Here χu, c, and T are the uniform susceptibility, the spin-wave velocity, and the temperature, respectively. By simulating large lattices at moderately low temperatures, we find χuc2/T∼0.32. Our estimation of χuc2/T deviates from the related analytic prediction but agrees with recent numerical calculations of other 2D dimerized spin-1/2 antiferromagnets.

Local Ward identities for collective excitations in fermionic systems with spontaneously broken symmetries

We derive Ward identities for fermionic systems exhibiting a gauge symmetry that gets globally broken. In particular, we focus on the relation that connects the gauge field response functions to the transverse susceptibilities of the order parameter. We find that the long-wavelength and zero energy limit of the former are related to the coefficients of a low-energy expansion of the latter. We examine three physical cases: the superconductor, the N\'eel antiferromagnet and the spiral magnet. In the case of a metallic spiral magnet that completely breaks the SU(2) spin symmetry we explicitly show that the Ward identities are fulfilled within the random phase approximation. We subsequently derive microscopic expressions for the spin stiffnesses and spin wave velocities, which can be plugged into low energy models to study the effect of long-wavelength bosonic fluctuations on top of mean-field solutions.

Spin waves in spin hydrodynamics

The propagation properties of spin degrees of freedom are analyzed in the framework of relativistic hydrodynamics with spin based on the de Groot van Leeuwen--van Weert definitions of the energy-momentum and spin tensors. We derive the analytical expression for the spin wave velocity for arbitrary statistics and show that it goes to half the speed of light in the ultrarelativistic limit. We find that only the transverse degrees of freedom propagate, analogously to electromagnetic waves. Finally, we consider the effect of dissipative corrections and calculate the damping coefficients for the case of Maxwell-J\"uttner statistics.

Metallic Nitride and Carbide Perovskites: History and Prospects

Energy-level diagrams for cubic metallic Fe4N and Mn4N were proposed by Goodenough in the late 1960s. Fe4N is ferromagnetic, but Mn4N is ferrimagnetic with a large moment on Mnc at the cube corner site and a much smaller antiparallel contribution from Mnf at the three face-centre sites. Neutron diffraction revealed noncollinear ferrimagnetism with no compensation where the Mnf moments form 120° triangular antiferromagnetic sublattices but are tilted out of the kagome (111) planes to give the small net sublattice moment. A rich variety of magnetic ordering exists in the ternary Mn3−xM′xN metallic perovskites. Partial substitution of nonmagnetic M′ on Mnc sites leads to a tunable ferrimagnetic compensation point. Two possible antiferromagnetic modes in the kagome planes are a topological Γ4g mode, and a nontopological Γ5g mode where the in-plane components of the Mnf spins lie, respectively, perpendicular and parallel to the edges if the triangles in the kagome planes . Interest in the metallic perovskites has revived with the availability of high-quality thin films that facilitate measurements of magneto-transport properties, strain effects and spin wave velocity. The range of magnetic structures, magnetotransport, magnetocaloric and magnetovolume effects is exceptionally large. The topological ferrimagnets exhibit large anomalous Hall effects. The magnetism is compared with materials where N is replaced by C.

Fast long-wavelength exchange spin waves in partially compensated Ga:YIG

Spin waves in yttrium iron garnet (YIG) nano-structures attract increasing attention from the perspective of novel magnon-based data processing applications. For short wavelengths needed in small-scale devices, the group velocity is directly proportional to the spin-wave exchange stiffness constant λex. Using wave vector resolved Brillouin light scattering spectroscopy, we directly measure λex in Ga-substituted YIG thin films and show that it is about three times larger than for pure YIG. Consequently, the spin-wave group velocity overcomes the one in pure YIG for wavenumbers k > 4 rad/μm, and the ratio between the velocities reaches a constant value of around 3.4 for all k > 20 rad/μm. As revealed by vibrating-sample magnetometry and ferromagnetic resonance spectroscopy, Ga:YIG films with thicknesses down to 59 nm have a low Gilbert damping (α<10−3), a decreased saturation magnetization μ0MS≈20 mT, and a pronounced out-of-plane uniaxial anisotropy of about μ0Hu1≈95 mT, which leads to an out-of-plane easy axis. Thus, Ga:YIG opens access to fast and isotropic spin-wave transport for all wavelengths in nano-scale systems independently of dipolar effects.

Dynamics of magnetic collective modes in square- and triangular-lattice Mott insulators at finite temperature

We study the equilibrium dynamics of magnetic moments in the Mott insulating phase of the Hubbard model on the square and triangular lattice. We rewrite the Hubbard interaction in terms of an auxiliary vector field and use a recently developed Langevin scheme to study its dynamics. A thermal noise, derivable approximately from the Keldysh formalism, allows us to study the effect of finite temperature. At strong coupling, $U\ensuremath{\gg}t$, where $U$ is the local repulsion and $t$ the nearest-neighbor hopping, our results reproduce the well known dynamics of the nearest-neighbor Heisenberg model with exchange $J\ensuremath{\sim}\mathcal{O}({t}^{2}/U)$. These include crossover from weakly damped dispersive modes at temperature $T\ensuremath{\ll}J$ to strong damping at $T\ensuremath{\sim}\mathcal{O}(J)$, and diffusive dynamics at $T\ensuremath{\gg}J$. The crossover temperatures are naturally proportional to $J$. To highlight the progressive deviation from Heisenberg physics as $U/t$ reduces we compute an effective exchange scale ${J}_{\mathrm{eff}}(U)$ from the low-temperature spin-wave velocity. We discover two features in the dynamical behavior with decreasing $U/t$: (i) the low-temperature dispersion deviates from the Heisenberg result, as expected, due to longer range and multispin interactions, and (ii) the crossovers between weak damping, strong damping, and diffusion take place at noticeably lower values of $T/{J}_{\mathrm{eff}}$. We relate this to enhanced mode coupling, in particular to thermal amplitude fluctuations, at weaker $U/t$. A comparison of the square and triangular lattice reveals the additional effect of geometric frustration on damping.

Classical many-body chaos with and without quasiparticles

We study correlations, transport and chaos in a Heisenberg magnet as a classical model many-body system. By varying temperature and dimensionality, we can tune between settings with and without symmetry breaking and accompanying collective modes or quasiparticles. We analyse both conventional and out-of-time-ordered spin correlators (`decorrelators') to track the spreading of a spatiotemporally localised perturbation -- the wingbeat of the butterfly -- as well as transport coefficients and Lyapunov exponents. We identify a number of qualitatively different regimes. Trivially, at $T=0$, there is no dynamics at all. In the limit of low temperature, $T=0^+$, integrability emerges, with infinitely long-lived magnons; here the wavepacket created by the perturbation propagates ballistically, yielding a lightcone at the spin wave velocity which thus subsumes the butterfly velocity; inside the lightcone, a pattern characteristic of the free spin wave spectrum is visible at short times. On top of this, residual interactionslead to spin wave lifetimes which, while divergent in this limit, remain finite at any nonzero $T$. At the longest times, this leads to a `standard' chaotic regime; for this regime, we show that the Lyapunov exponent is simply proportional to the inverse spin-wave lifetime. Visibly strikingly, between this and the `short-time' integrable regimes, a scarred regime emerges: here, the decorrelator is spatiotemporally highly non-uniform, being dominated by rare and random scattering events seeding secondary lightcones. As the spin correlation length decreases with increasing $T$, the distinction between these regimes disappears and at high temperature the previously studied chaotic paramagnetic regime emerges. For this, we elucidate how, somewhat counterintuitively, the ballistic butterfly velocity arises from a diffusive spin dynamics.

Long-range spin-wave propagation in transversely magnetized nano-scaled conduits

Magnonics attracts increasing attention in the view of low-energy computation technologies based on spin waves. Recently, spin-wave propagation in longitudinally magnetized nano-scaled spin-wave conduits was demonstrated, proving the fundamental feasibility of magnonics at the sub-100 nm scale. Transversely magnetized nano-conduits, which are of great interest in this regard as they offer a large group velocity and a potentially chirality-based protected transport of energy, have not yet been investigated due to their complex internal magnetic field distribution. Here, we present a study of propagating spin waves in a transversely magnetized nanoscopic yttrium iron garnet conduit of 50 nm width. Space and time-resolved microfocused Brillouin-light-scattering spectroscopy is employed to measure the spin-wave group velocity and decay length. A long-range spin-wave propagation is observed with a decay length of up to (8.0 ± 1.5) μm and a large spin-wave lifetime of up to (44.7 ± 9.1) ns. The results are supported with micromagnetic simulations, revealing a broad single-mode frequency range and the absence of a mode localized to the edges. Furthermore, a frequency nonreciprocity for counter-propagating spin waves is observed in the simulations and the experiment, caused by the trapezoidal cross section of the structure. The revealed long-distance spin-wave propagation on the nano-scale is particularly interesting for an application in spin-wave devices, allowing for long-distance transport of information in magnonic circuits and low-energy device architectures.

Theory of spin waves in a hexagonal antiferromagnet

We construct a field-theoretic description of spin waves in hexagonal antiferromagnets with three magnetic sublattices and coplanar $120^\circ$ magnetic order. The three Goldstone modes can be separated by point-group symmetry into a singlet $\alpha_{0}$ and a doublet $(\beta_x,\beta_y)$. The $\alpha_0$ singlet is described by the standard theory of a free relativistic scalar field. The field theory of the $(\beta_x,\beta_y)$ doublet is analogous to the theory of elasticity of a two-dimensional isotropic solid with distinct longitudinal and transverse "speeds of sound". The well-known Heisenberg models on the triangular and kagome lattices with nearest-neighbour exchange turn out to be special cases with accidental degeneracy of the spin-wave velocities. The speeds of sound can be readily calculated for any lattice model. We apply this approach to the compounds of the Mn$_3$X family with stacked kagome layers.

Propagation of Spin-Wave Packets in Individual Nanosized Yttrium Iron Garnet Magnonic Conduits.

Modern-day CMOS-based computation technology is reaching its fundamental limitations. The emerging field of magnonics, which utilizes spin waves for data transport and processing, proposes a promising path to overcome these limitations. Different devices have been demonstrated recently on the macro- and microscale, but the feasibility of the magnonics approach essentially relies on the scalability of the structure feature size down to the extent of a few 10 nm, which are typical sizes for the established CMOS technology. Here, we present a study of propagating spin-wave packets in individual yttrium iron garnet (YIG) conduits with lateral dimensions down to 50 nm. Space and time-resolved microfocused Brillouin-light-scattering (BLS) spectroscopy is used to characterize the YIG nanostructures and measure the spin-wave decay length and group velocity directly. The revealed magnon transport at the scale comparable to the scale of CMOS proves the general feasibility of magnon-based data processing.

3D analytical model of skyrmion-like structures in an antiferromagnet with DMI

The purpose of the research is the construction of the analytical model for description of a number of topological objects in a two-sublattice antiferromagnet with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) including vortices, antivortices, skyrmions, antiskyrmions, skyrmioniums and their bound states, which are the exact dynamic solutions of the nonlinear Landau-Lifshitz equations. “Relativistic contraction” of skyrmion-like topological object size in the direction of motion is demonstrated for “subcritical” case when its velocity is less than spin wave velocity in antiferromagnet. Lorentz-like “supercritical” transformation are found for skyrmion-like magnetic structures moving with velocity greater than spin wave velocity in antiferromagnet. In particular, the results of the analytical model are applied for an antiferromagnet in the form of cylindrical nanoshell; in this case, there are more than one solution of the nonlinear Landau-Lifshitz equations for the same boundary and initial conditions. It means that vortices, skyrmions, skyrmioniums and their bound states represent the ground state and the excited states in an antiferromagnetic cylindrical nanoshell. The particular cases of the exact static solutions of the nonlinear Landau-Lifshitz equations include the well-known one-dimensional solutions such as Bloch domain, Neel domain wall, Shirobokov domain structure, antiferromagnetic vortices, two-dimensional Belavin-Polyakov soliton, three-dimensional Hodenkov soliton and target type soliton. The results of this paper can be used for further development of theory of the antiferromagnetic soliton and skyrmion physics. Besides, the exact dynamic solutions of the nonlinear Landau-Lifshitz equations can serve as the reference solutions for testing the results of micromagnetic simulations.