Nonreciprocal Spin Waves Research Articles

Nonreciprocal damping of spin waves propagating in magnetic domain walls induced by Dzyaloshinskii-Moriya interaction

The nonreciprocity of spin waves refers to the phenomenon that spin waves propagating in opposite directions display different features. This phenomen becomes a fundamental requirement for implementing magnon logic architectures. The nonreciprocal transportion of spin waves induced by Dzyaloshinskii-Moriya interaction (DMI) has been studied extensively. It is characterized by a shift of spin-wave dispersion. Here we report another feature of the DMI-induced nonreciprocity, i.e., the nonreciprocal spin wave damping. We find that the spin waves propagating with opposite wave vectors in magnetic domain wall have different damping, which is frequency dependent and especially evident in low frequancy range. For spin waves with sufficient low frequencies (around 1 GHz), the damping nonreciprocity is so extreme that spin waves can transport only in one direction, thus realizing the spin-wave diode function. The theoretical predictions are validated by micromagnetic simulations. The findings in this work points out a new feature of DMI-induced spin wave nonreciprocity and may be exploited for designing novel magnonic devices.

Unidirectional propagation of zero-momentum magnons

We report on experimental observation of unidirectional propagation of zero-momentum magnons in synthetic antiferromagnet consisting of strained CoFeB/Ru/CoFeB trilayer. Inherent non-reciprocity of spin waves in synthetic antiferromagnets with uniaxial anisotropy results in smooth and monotonous dispersion relation around Gamma point, where the direction of the phase velocity is reversed, while the group velocity direction is conserved. The experimental observation of this phenomenon by intensity-, phase-, and time-resolved Brillouin light scattering microscopy is corroborated by analytical models and micromagnetic simulations.

Nonreciprocal spin-wave beam transport in a metallized T-shaped magnonic junction

Nonreciprocal spin-wave beam transport in a metallized T-shaped magnonic junction

Nonreciprocity of spin waves by chiral fluctuations induced in the conical state

Nonreciprocity in chiral magnets is promising for applications in chiral spintronics. Spin-wave nonreciprocity happens when applying an external magnetic field to a chiral magnet while a stream of particles parallel to the field flows through it. Here, we found through micromagnetic simulations that, in the absence of lattice chirality, the excitation spectra of spin waves in the conical magnetic state depend on the relative orientations of the spin-polarized current and the external magnetic field applied along the magnetic helix axis. When both are in the same direction, the spin component of the magnet along the helical axis increases with time while the chiral index decreases. Statistical analysis shows that the spin fluctuations are anisotropic, where the fluctuations along the helical axis have chiral characters as multi-modal, high-frequency, and low-intensity. We give an intuitive interpretation of these observations from the point of view of symmetry breaking and explore the factors affecting the nonreciprocity of the spin-wave spectrum, guiding experimental observations.

Nonreciprocal spin-wave transport in an asymmetric three-dimensional magnonic coupler

Nonreciprocal spin-wave transport in an asymmetric three-dimensional magnonic coupler

Magnitostaticheskiy mekhanizm narusheniya kiral'noy simmetrii v mnogosloynykh magnitnykh strukturakh

It is shown that the energy of a ferromagnetic film deposited onto a paramagnetic or superconducting substrate acquires a contribution in the form of the Dzyaloshinskii–Moriya interaction. This contribution appears as a result of the magnetostatic interaction of the magnetization of the ferromagnetic film with the magnetization induced by it in a paramagnet or by the supercurrent in the superconductor and leads to the removal of the chiral degeneracy, nonreciprocity of spin waves, and the formation of chiral states such as magnetic skyrmions. Our estimates indicate the possibility of experimental observation of predicted effects.

Spin waves in monolayers of transition-metal dichalcogenides with Dzyaloshinskii–Moriya interaction

Dzyaloshinski–Moriya interaction, known also as the antisymmetric exchange coupling, leads to a variety of interesting spin phenomena, like spin canting, skyrmion formation, nonreciprocal spin wave propagation, and others. In this paper we analyze spin waves in monolayers of two-dimensional van–der–Waals materials, such as Vanadium–based dichalcogenides, VX2 (X=S, Se, Te) and other materials of similar symmetry. The considerations are limited to a collinear spin ground state, stabilized by a sufficiently strong magnetic anisotropy. The theoretical analysis is performed within the general spin wave theory based on the Holstein–Primakoff–Bogoliubov transformation.

Antiferromagnetic magnon spintronic based on nonreciprocal and nondegenerated ultra-fast spin-waves in the canted antiferromagnet α-Fe2O3.

Spin-waves in antiferromagnets hold the prospects for the development of faster, less power-hungry electronics and promising physics based on spin superfluids and coherent magnon condensates. For both these perspectives, addressing electrically coherent antiferromagnetic spin-waves is of importance, a prerequisite that has been so far elusive, because, unlike ferromagnets, antiferromagnets couple weakly to radiofrequency fields. Here, we demonstrate the detection of ultra-fast nonreciprocal spin-waves in the dipolar exchange regime of a canted antiferromagnet using both inductive and spintronic transducers. Using time-of-flight spin-wave spectroscopy on hematite (α-Fe2O3), we find that the magnon wave packets can propagate as fast as 20 kilometers/second for reciprocal bulk spin-wave modes and up to 6 kilometers/second for surface spin-waves propagating parallel to the antiferromagnetic Néel vector. We lastly achieve efficient electrical detection of nonreciprocal spin-wave transport using nonlocal inverse spin-Hall effects. The electrical detection of coherent nonreciprocal antiferromagnetic spin-waves paves the way for the development of antiferromagnetic and altermagnet-based magnonic devices.

Suppression of spin-wave nonreciprocity due to interfacial Dzyaloshinskii-Moriya interaction by lateral confinement in magnetic nanostructures

Suppression of spin-wave nonreciprocity due to interfacial Dzyaloshinskii-Moriya interaction by lateral confinement in magnetic nanostructures

Spin-wave nonreciprocity at the spin-flop transition region in synthetic antiferromagnets

We investigate the frequency nonreciprocity in CoFeB/Ru/CoFeB synthetic antiferromagnets near the spin-flop transition region, where the magnetic moments in the two ferromagnetic layers are noncollinear. Using conventional Brillouin light scattering, we perform systematic measurements of the frequency nonreciprocity as a function of an external magnetic field. At near zero magnetic field, where the antiparallel alignment of the magnetic moments in the two layers is established, we observe a significant frequency nonreciprocity of up to a few GHz, which vanishes when the relative magnetization orientation switches into the parallel configuration at a large magnetic field. For the intermediate values of the magnetic field, where the system transitions from the antiparallel to the parallel orientation, a nonmonotonous dependence of the frequency nonreciprocity is found, with a maximum frequency shift around the spin-flop critical point. This nontrivial dependence of the nonreciprocity versus field is attributed to the nonmonotonous dependence of the dynamic dipolar interaction, which is the main factor that causes asymmetry in the dispersion relation. Furthermore, we found that the sign of the frequency shift changes even without switching the polarity of the bias field. These results show that one can precisely control the nonreciprocal propagation of spin waves via field-driven magnetization reorientation.

Magnetic Damping and Dzyaloshinskii-Moriya Interactions in Pt/Co2FeAl/MgO Systems Grown on Si and MgO Substrates.

Spin-pumping-induced damping and interfacial Dzyaloshinskii-Moriya interaction (iDMI) have been studied in Pt/Co2FeAl/MgO systems grown on Si or MgO substrates as a function of Pt and Co2FeAl (CFA) thicknesses. For this, we combined vibrating sample magnetometry (VSM), microstrip ferromagnetic resonance (MS-FMR), and Brillouin light scattering (BLS). VSM measurements of the magnetic moment at saturation per unit area revealed the absence of a magnetic dead layer in both systems, with a higher magnetization at saturation obtained for CFA grown on MgO. The key parameters governing the spin-dependent transport through the Pt/CFA interface, including the spin mixing conductance and the spin diffusion length, have been determined from the CFA and the Pt thickness dependence of the damping. BLS has been used to measure the spin wave non-reciprocity via the frequency mismatch between the Stokes and anti-Stokes lines. iDMI has been separated from the contribution of the interface perpendicular anisotropy difference between Pt/CFA and CFA/MgO. Our investigation revealed that both iDMI strength and spin pumping efficiency are higher for CFA-based systems grown on MgO due to its epitaxial growth confirmed by MS-FMR measurements of the in-plane magnetic anisotropy. This suggests that CFA grown on MgO could be a promising material candidate as a spin injection source via spin pumping and for other spintronic applications.

High wave vector non-reciprocal spin wave beams

We report unidirectional transmission of micron-wide spin waves beams in a 55 nm thin YIG. We downscaled a chiral coupling technique implementing Ni80Fe20 nanowires arrays with different widths and lattice spacing to study the non-reciprocal transmission of exchange spin waves down to λ ≈ 80 nm. A full spin wave spectroscopy analysis of these high wavevector coupled-modes shows some difficulties to characterize their propagation properties, due to both the non-monotonous field dependence of the coupling efficiency, and also the inhomogeneous stray field from the nanowires.

Nonreciprocal spin waves in ferrimagnetic domain-wall channels

We theoretically investigate the propagation of spin waves confined in a N\'eel-type ferrimagnetic domain-wall channel in the presence of the interfacial Dzyaloshinskii-Moriya interaction (DMI). We observe a nonreciprocal spin-wave propagation induced by the antisymmetric chiral DMI, which can be manipulated by changing the net angular momentum or the polarity of domain walls. Considering that the band gap of spin waves excited in domain walls is significantly reduced, the three-magnon processes are applied to nonlinearly detect this bounded mode in the narrow channel, which enables us to quantify the frequency and the wave vector by analyzing the spectrum of the transmitted spin wave outside the domain wall and to determine the DMI strength. These findings are useful for fabricating energy-efficient magnetic devices and measuring the interfacial DMI in ultra narrow ferrimagnetic stripes.

Nonreciprocal spin waves driven by left-hand microwaves

It is a conventional wisdom that a left-hand microwave cannot efficiently excite the spin wave (SW) in ferromagnets, due to the constraint of angular momentum conservation. In this work, we show that the left-hand microwave can drive nonreciprocal SWs in the presence of a strong ellipticity-mismatch between the microwave and precessing magnetization. A critical frequency is predicted, at which the left-hand microwave cannot excite SWs. Away from it the SW amplitude sensitively depends on the ellipticity of left-hand microwaves, in sharp contrast to the case driven by right-hand ones. By tuning the microwave frequency, we observe a switchable SW non-reciprocity in a ferromagnetic single layer. A mode-dependent mutual demagnetizing factor is proposed to explain this finding. Our work advances the understanding of the photon-magnon conversion, and paves the way to designing diode-like functionalities in nano-scaled magnonics.

Omnidirectional flat bands in chiral magnonic crystals

The magnonic band structure of two-dimensional chiral magnonic crystals is theoretically investigated. The proposed metamaterial involves a three-dimensional architecture, where a thin ferromagnetic layer is in contact with a two-dimensional periodic array of heavy-metal square islands. When these two materials are in contact, an anti-symmetric exchange coupling known as the Dzyaloshinskii–Moriya interaction (DMI) arises, which generates nonreciprocal spin waves and chiral magnetic order. The Landau–Lifshitz equation and the plane-wave method are employed to study the dynamic magnetic behavior. A systematic variation of geometric parameters, the DMI constant, and the filling fraction allows the examination of spin-wave propagation features, such as the spatial profiles of the dynamic magnetization, the isofrequency contours, and group velocities. In this study, it is found that omnidirectional flat magnonic bands are induced by a sufficiently strong Dzyaloshinskii–Moriya interaction underneath the heavy-metal islands, where the spin excitations are active. The theoretical results were substantiated by micromagnetic simulations. These findings are relevant for envisioning applications associated with spin-wave-based logic devices, where the nonreciprocity and channeling of the spin waves are of fundamental and practical scientific interest.

Spin-wave nonreciprocity and formation of lateral standing spin waves in CoFeB/Ta/NiFe meander-shaped films

Studying the spin-wave (SW) propagation in 3D periodic structures opens new possibilities for joining functional units placed on the different layers of the magnonic circuitry. In the path toward 3D magnonics, the main challenge is the fabrication of large-scale 3D magnetic structures with nanometric precision control of geometry and material composition. In this work, we study the dependence on the Ta spacer thickness of the magnonic band structure, measured by Brillouin light scattering spectroscopy, of CoFeB/Ta/NiFe meander-shaped bilayers fabricated on pre-patterned Si substrate with thickness steps of 50 nm. Both propagating and stationary SW modes are observed. While the frequency of the dispersive mode slightly depends on the Ta spacer thickness, the frequency position of the three stationary modes in the lowest frequency range of the spectra significantly increases by increasing the Ta thickness. Micromagnetic calculations indicate that each of the three stationary modes is composed of a doublet of modes whose frequency separation, within each doublet, increases by increasing the mode frequency. The origin of this frequency separation is ascribed to the dynamic dipolar coupling between the magnetic layers that generate a significant frequency nonreciprocity of counterpropagating SWs. For these reasons, the investigated structures offer potential application as the nonreciprocal versatile interconnections performing the frequency selective regimes of signal propagation in magnonic circuits.

Nonreciprocal propagation of spin waves in a bilayer magnonic waveguide based on yttrium-iron garnet films

Objectives. Nonreciprocal spin wave effects can manifest themselves in metalized films of ferrite garnets. By studying the dynamics of spin waves in micro- and nano-scale magnetic films, the possibility of using multilayer dielectric films of yttrium iron garnet (YIG) to ensure the manifestation of the nonreciprocity effect is demonstrated. This approach offers advantages compared to the use of a layered YIG/metal structure due to significantly lower spin-wave losses in the two-layer YIG film consisting of layers with different values of magnetization. Such films can be used in logical elements to create controllable Mach-Zehnder interferometers based on magnonic principles. The purpose of this work is to reconcile the concept of nonreciprocal spin-wave propagation of a signal with the simultaneous manifestation of the effects arising from the propagation of spin waves in microwave guides formed by finite-width YIG films.Methods. We used an experimental microwave spectroscopy method based on a vector network analyzer along with a finite difference method to perform a numerical simulation of the dispersion characteristics of spin waves in two-layer magnonic microwave guides. An analytical model was also used to obtain a dispersion equation based on the magnetostatic approximation.Results. Based on measurements of the amplitude and phase responses, the possible coexistence of two frequency ranges for the propagation of a spin-wave signal in a two-layer magnon microwave guide based on a YIG film formed by two layers with different values of saturation magnetization was demonstrated. Regimes of nonreciprocal propagation of a spin-wave signal were revealed. A numerical model was using to study the formation mechanisms of spin wave modes in the spectrum of a two-layer structure formed due to the finite dimensions of the microwave guide. An analytical model was used to evaluate the transformation of the mode spectrum. The experimental data are in good agreement with the results of the proposed numerical and analytical models.Conclusions. The possibility of frequency-selective propagation of spin waves in a magnon microwaveguide consisting of two layers with different saturation magnetization values is demonstrated. Multimode propagation of spin waves can occur inside a two-layer structure in two frequency ranges. At the same time, this process is accompanied by a strong nonreciprocity of spin-wave signal propagation, which manifests itself in a change in the amplitude and phase responses when the direction of the external magnetic field is reversed. The proposed two-layer spin-wave waveguide concept can be used in the manufacture of magnon interconnects and magnon interferometers with the support of multiband regimes of operation.

Curvilinear spin-wave dynamics beyond the thin-shell approximation: Magnetic nanotubes as a case study

Surface curvature of magnetic systems can lead to many static and dynamic effects which are not present in flat systems of the same material. These emergent magnetochiral effects can lead to frequency nonreciprocity of spin waves, which has been shown to be a bulk effect of dipolar origin and is related to a curvature-induced symmetry breaking in the magnetic volume charges. So far, such effects have been investigated theoretically mostly for thin shells, where the spatial profiles of the spin waves can be assumed to be homogeneous along the thickness. Here, using a finite-element dynamic-matrix approach, we investigate the transition of the spin-wave spectrum from thin to thick curvilinear shells, at the example of magnetic nanotubes in the vortex state. With increasing thickness, we observe the appearance of higher-order radial modes which are strongly hybridized and resemble the perpendicular-standing spin waves (PSSWs) in flat films. Along with an increasing dispersion asymmetry, we uncover the curvature-induced nonreciprocity of the mode profiles. This is explained in a very simple, general picture for thick curvilinear shells, considering the inhomogeneity of the emergent geometric volume charges along the thickness of the shell. Such curvature-induced mode-profile asymmetry also leads to nonreciprocal hybridization, which can facilitate unidirectional spin-wave propagation. With that, we also show how curvature allows for nonlinear three-wave splitting of a higher-order radial mode into secondary modes which can also propagate unidirectionally. We believe that our study provides a significant contribution to the understanding of the spin-wave dynamics in curvilinear magnetic systems, and also advertises these for novel magnonic applications.

Temperature-sensitive spin-wave nonreciprocity induced by interlayer dipolar coupling in ferromagnet/paramagnet and ferromagnet/superconductor hybrid systems

Spin-wave (SW) spectra have theoretically been studied in a thin film of a ferromagnet (FM) on a substrate from a paramagnet (PM) (an FM above the critical temperature) or from superconductor (SC). A spin wave propagating in the FM induces the dynamic magnetization and superconducting current in the underlying PM and SC, respectively, which affect the SW propagation by their magnetic fields. As a result of this interaction, the SW spectrum becomes nonreciprocal to depend on the sign of the SW wave vector q. We show that the nonreciprocal contribution to the SW spectra in FM/PM and FM/SC systems is given by the frequency shift of {\Delta}{\omega}(q)={\omega}(q)-{\omega}(-q)=a(T)({\tau}{\cdot}q) with {\tau}=(n{\times}M) being the toroidal magnetic moment, M the FM magnetization, n the unit vector normal to the FM/PM(SC) interface, and a(T) the temperature-dependent constant of a dipole nature, whose sign depends on the substrate type. As the {\Delta}{\omega}(T) dependence is strong at temperatures T close to the critical temperature Tc for the FM-PM or normal metal-SC transition, one gets a possibility to control the frequency SW nonreciprocity with temperature variation near Tc. The dipolar mechanism we propose for SW frequency nonreciprocity is promising for introducing this property of SW propagation into functional devices.

Generation of nonreciprocity in gapless spin waves by chirality injection

In chiral magnets with intrinsic inversion symmetry breaking, it has been known that two spin waves moving in opposite directions can propagate at different velocities, exhibiting a phenomenon called magnetochiral nonreciprocity which allows for realizations of certain spin logic devices such as a spin-wave diode. Here, we theoretically demonstrate that the spin-wave nonreciprocity can occur without intrinsic bulk chirality in certain magnets including easy-cone ferromagnets and easy-cone antiferromagnetic. Specifically, we show that nonlocal injection of a spin current from proximate normal metals to easy-cone magnets engenders a non-equilibrium chiral spin texture, on top of which spin waves exhibit nonreciprocity proportional to the injected spin current. One notable feature of the discovered nonreciprocal spin waves is its gapless nature, which can lead to a large thermal rectification effect at sufficiently low temperatures. We envision that nonlocal electric injection of chirality into otherwise nonchiral magnets may serve as a versatile route to realize electrically controllable magnetochiral phenomena in a wide class of materials.