Exchange-dominated Spin Waves Research Articles

Spatially inhomogeneous inverse Faraday effect provides tunable nonthermal excitation of exchange dominated spin waves

Abstract We demonstrate optical nonthermal excitation of exchange dominated spin waves of different orders in a magnetophotonic crystal. The magnetophotonic structure consists of a thin magnetic film and a Bragg stack of nonmagnetic layers to provide a proper nonuniform interference pattern of the inverse Faraday effect induced by light in the magnetic layer. We found a phenomenon of the pronounced phase slippage of the inverse Faraday effect distribution when the pump wavelength is within the photonic band gap of the structure. It allows to tune the interference pattern by a slight variation of light wavelength which results in the modification of excitation efficiency of the different order spin waves. The approach can be applied for different magnetic dielectrics expanding their application horizons for spin-wave based devices.

Excitation and modulation of exchange spin waves in CoFeB films

Spin waves in nanostructures have great potential to be future spintronic information carriers. Here, we report the excitation and modulation of exchange spin waves in Co20Fe60B20 (CoFeB) films by varying magnetic anisotropy. In a 50 nm-thick CoFeB film, the effective excitation of perpendicular standing spin waves (PSSWs) is achieved due to the uniaxial anisotropy induced by oblique sputtering. Additionally, patterning the films into a periodic array of rectangles enables the excitation of both exchange-dominated surface spin waves and PSSWs, with the modulation of spin waves achievable by altering the length–width ratio of the rectangle. It is worth noting that PSSWs are present in the easy axis, whereas surface spin waves are observed in the hard axis, emphasizing the significant influence of shape anisotropy on spin waves. Furthermore, we demonstrate the existence of PSSW in a CoFeB/Pb(Mg1/3Nb2/3)O3-Pb0.7Ti0.3O3 (PMN-PT) multiferroic heterostructure. The resonance field of PSSW can be shifted by applying electric fields, which originates from the strain anisotropy driven by the piezoelectric effect. These findings are expected to provide valuable insights for the development of energy-efficient spintronic devices and high-frequency data processing systems.

Micromagnetic study of inertial spin waves in ferromagnetic nanodots

Here we report the possibility to excite ultra-short spin waves in ferromagnetic thin-films by using time-harmonic electromagnetic fields with terahertz frequency. Such ultra-fast excitation requires to include inertial effects in the description of magnetization dynamics. In this respect, we consider the inertial Landau-Lifshitz-Gilbert (iLLG) equation and develop analytical theory for exchange-dominated inertial spin waves. The theory predicts a finite limit for inertial spin wave propagation velocity, as well as spin wave spatial decay and lifetime as function of material parameters. Then, guided by the theory, we perform numerical micromagnetic simulations that demonstrate the excitation of ultra-short inertial spin waves (20 nm long) propagating at finite speed in a confined magnetic nanodot. The results are in agreement with the theory and provide the order of magnitude of quantities observable in realistic ultra-fast dynamics experiments.

Comparison of spin-wave transmission in parallel and antiparallel magnetic configurations

Parallel (P) and antiparallel (AP) configurations are widely applied in magnetic heterostructures and have significant impacts on the spin-wave transmission in magnonic devices. In the present study, a theoretical investigation was conducted into the transmission of exchange-dominated spin waves with nanoscale wavelengths in a type of heterostructure including two magnetic media, of which the magnetization state can be set to the P (AP) configuration by ferromagnetic (antiferromagnetic) interfacial exchange coupling (IEC). The boundary conditions in P and AP cases were derived, by which the transmission and reflection coefficients of spin waves were analytically given and numerically calculated. In the P configuration, a critical angle $\theta_{\textrm{c}}$ always exists and has a significant influence on the transmission. Spin waves are refracted and reflected when the incident angle $\theta_{\textrm{i}}$ is smaller than the critical angle ($\theta_{\textrm{i}} < \theta_{\textrm{c}}$), while total reflection occurs as $\theta_{\textrm{i}} \geq \theta_{\textrm{c}}$. In the AP configuration, the spin-wave polarizations of medium 1 and 2 are inverse, that is, right-handed (RH) and left-handed (LH), leading to the total reflection being independent of $\theta_{\textrm{i}}$. As demonstrated by the difference in spin-wave transmission properties between the P ($\theta_{\textrm{i}} < \theta_{\textrm{c}}$) and AP cases, there is a polarization-dependent scattering. However, as $\theta_{\textrm{i}}$ exceeds $\theta_{\textrm{c}}$, the P ($\theta_{\textrm{i}} > \theta_{\textrm{c}}$) case exhibits similarities with the AP case, where the transmitted waves are found to be evanescent in medium 2 and their decay lengths are investigated.

Confined dipole and exchange spin waves in a bulk chiral magnet with Dzyaloshinskii-Moriya interaction

The Dzyaloshinskii-Moriya interaction (DMI) has an impact on excited spin waves in the chiral magnet Cu$_2$OSeO$_3$ by means of introducing asymmetry on their dispersion relations. The confined eigenmodes of a chiral magnet are hence no longer the conventional standing spin waves. Here we report a combined experimental and micromagnetic modeling study by broadband microwave spectroscopy we observe confined spin waves up to eleventh order in bulk Cu$_2$OSeO$_3$ in the field-polarized state. In micromagnetic simulations we find similarly rich spectra. They indicate the simultaneous excitation of both dipole- and exchange-dominated spin waves with wavelengths down to (47.2 $\pm$ 0.05) nm attributed to the exchange interaction modulation. Our results suggest DMI to be effective to create exchange spin waves in a bulk sample without the challenging nanofabrication and thereby to explore their scattering with noncollinear spin textures.

Nonreciprocal emergence of hybridized magnons in magnetic thin films

Magnons (the quanta of spin waves), unlike electrons, do not suffer from Ohmic losses, which makes them an attractive information carrier in communication and data processing. The possibility of nonreciprocal magnon propagation is of great practical relevance to directional communications, particularly when the nonreciprocity is steerable through magnons themselves in a monologic magnonic device. This work demonstrates explicitly such nonreciprocity in the mode profiles of magnons in ${\mathrm{Ni}}_{79}{\mathrm{Fe}}_{21}$ thin films. Evidence of nonreciprocal emergence of hybridized dipole-exchange spin waves at two surfaces of ${\mathrm{Ni}}_{79}{\mathrm{Fe}}_{21}$ nanofilms deposited on a surface oxide silicon substrate is provided by studying magnon transmission and asymmetry via Brillouin light scattering measurements. The dipole-dominated spin wave and exchange-dominated spin wave are found to be localized near the top and bottom surfaces, respectively, and travel along opposite directions. The nonreciprocity and the localization can be tuned by an in-plane magnetic field. Our findings provide a simple and flexible approach to nonreciprocal all-magnon logic devices highly compatible with silicon-based integrated circuit technology.

Magnon valve effect and resonant transmission in a one-dimensional magnonic crystal

We theoretically investigate the transmission of exchange-dominated spin waves in a one-dimensional magnonic crystal (MC) with a periodic exchange bias field. By recasting the Landau-Lifshitz-Gilbert equation into an effective Schr\"odinger equation and establishing spin-wave functions, it is found that MCs with upward (up) and downward (down) magnetization, respectively, correspond to the rectangular $N$-fold barriers and wells for magnons. The broadband transmission spectra in up and down states are systematically investigated. We show the phenomena of the magnon resonant transmission in both states and calculate the resonant transmission wave functions, which are related to the magnon density. Our results also show a transmission spectra shift effect (TSSE) between up and down states, which is found to be general in this system. Furthermore, the TSSE is useful to design a type of magnon valve, the magnonic-crystal-based magnon valve (MCMV), which has a large on/off ratio and bandwidth. By high-throughput screening, 125 000 groups of parameters of the MC are calculated, and 1948 parameter groups of high-performance MCMVs are screened out. Our work clarifies the physical details of the exchange-dominated spin-wave transmission in rectangular $N$-fold barriers and wells and also provides a promising route for designing novel magnonic devices.

Spin-waves generation at the thickness step of yttrium iron garnet film

We report on the experimental observation of short, exchange-dominated spin waves (EDSW) generation by a thickness step in the ferrite waveguide under microwave pumping. This effect was explored both experimentally (using mirco-Brillouin light scattering technique) and theoretically (by micromagnetic simulation) for the sample magnetized along the step and for two cases of pumping: a uniform microwave pumping of the step and its pumping through a magnetostatic surface wave (MSSW) traveling across the step. It was shown that efficiency of EDSW generation caused by MSSW scattering on the thickness step increases with the frequency (or wave number) while for the case of the uniform pumping, the generation efficiency demonstrates the opposite behavior.

Dipole-dominated dissipative magnetic solitons in quasi-one-dimensional spin-torque oscillators

It is well-known that a spin-transfer torque caused by a dc electric current can excite in a two-dimensional ferromagnetic film exchange-dominated magnetic solitons, often called “spin-wave bullets”, under the condition of a negative nonlinear shift of spin wave frequency. In this work, we demonstrate that in a quasi-one-dimensional (1D) case, e.g., in a nanowire spin-Hall oscillator, it is possible to excite a stable dissipative magnetic soliton, which is dominated by the dipole-dipole interaction. This dissipative magnetic soliton can be described in the framework of a 1D Ginzburg-Landau auto-oscillator model, and has the shape similar to that of the exchange-dominated spin wave bullet, but with a different spatial localization law. The influence of the dipolar interaction makes possible the stabilization of a dissipative soliton in a relatively large (micron-sized) active area of the oscillator, which is in a sharp contrast with the two-dimensional case, where the excitation of a stable spin-wave bullet was observed only in relatively small active areas having typical sizes of the order of 100 nm. The characteristics and possible applications of these dipole-dominated spin wave bullets are discussed.

Spin-wave transmission through an internal boundary: Beyond the scalar approximation

The transmission and reflection of a spin wave at an internal boundary created by the local variation of anisotropy (or a bias magnetic field) are studied taking into account not only the changes in the wave amplitude, but also the changes in the wave polarization. It is shown that the account of the changes in the spin-wave polarization before and after the boundary leads to (i) increase of the spin-wave amplitude reflection coefficient, (ii) appearance of an additional phase shift $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}\ensuremath{\ne}0,\ensuremath{\pi}$ in both transmitted and reflected waves, and (iii) creation of additional evanescent waves in the vicinity of the boundary. It is also shown that even when significant changes in the transmitted wave polarization take place at the boundary, a spin wave could pass a finite-width boundary without reflection, if a certain resonance condition is satisfied. The effect of the polarization change at an internal boundary is especially pronounced for the exchange-dominated spin waves, while in the case of the dipole-dominated spin waves, this effect can vanish completely for certain configurations of the static magnetization.

Efficient excitation of exchange dominated spin waves in oblique deposited CoFeB thin films

Spin waves play a vital role as potential data carriers in low power wave-like computing and high-frequency spintronic devices, which stimulate intensive studies on the efficient excitation of spin waves in magnetic thin films. Here, we suggest a controllable approach for the efficient excitation of perpendicular standing spin waves (PSSWs) in a series of CoFeB/Si thin films by the oblique angle deposition technique. It is experimentally demonstrated that the intensity of the PSSW mode can be enhanced significantly with increased oblique angle, and a comparable intensity of spin wave to that of uniform FMR mode is achieved at an oblique angle of 39°. Moreover, the dependence of in-plane anisotropy field Hk, exchange constant A, as well as intrinsic Gilbert damping α on oblique deposition angle are also investigated.

Optical determination of the exchange stiffness constant in an iron garnet

Brillouin light scattering measurements were performed in the backscattering geometry on a Bi-substituted rare earth iron garnet. We observed two different peaks: One is attributed to a surface spin wave in the dipole-exchange regime while the other is referred to as a backscattering magnon mode, because the incident light in this case was scattered backward by exchange-dominated spin wave inside the material. We propose a method to estimate the exchange stiffness constant from the frequency of the backscattering magnon mode. The obtained value is comparable with the previously reported values for Y3Fe5O12.

Current induced multi-mode propagating spin waves in a spin transfer torque nano-contact with strong perpendicular magnetic anisotropy

Current induced spin wave excitations in spin transfer torque nano-contacts are known asa promising way to generate exchange-dominated spin waves at the nano-scale. It has been shown that when these systems are magnetized in the film plane, broken spatial symmetry of the field around the nano-contact induced by the Oersted field opens the possibility for spin wave mode co-existence including a non-linear self-localized spin-wave bullet and a propagating mode. By means of micromagnetic simulations, here we show that in systems with strong perpendicular magnetic anisotropy (PMA) in the free layer, two propagating spin wave modes with different frequency and spatial distribution can be excited simultaneously. Our results indicate that in-plane magnetized spin transfer nano-contacts in PMA materials do not host a solitonic self-localized spin-wave bullet, which is different from previous studies for systems with in plane magnetic anisotropy. This feature renders them interesting for nano-scale magnonic waveguides and crystals since magnon transport can be configured by tuning the applied current.

Spectral control of elastic dynamics in metallic nano-cavities

We show how the elastic response of metallic nano-cavities can be tailored by tuning the interplay with an underlying phononic superlattice. In particular, we exploit ultrafast optical excitation in order to address a resonance mode in a tungsten thin film, grown on top of a periodic MgO/ZrO2 multilayer. Setting up a simple theoretical model, we can explain our findings by the coupling of the resonance in the tungsten to an evanescent surface mode of the superlattice. To demonstrate a second potential benefit of our findings besides characterization of elastic properties of multilayer samples, we show by micromagnetic simulation how a similar structure can be utilized for magneto-elastic excitation of exchange-dominated spin waves.

Tunable Short-Wavelength Spin-Wave Emission and Confinement in Anisotropy-Modulated Multiferroic Heterostructures

We report on the generation and confinement of short-wavelength spin waves in a continuous film with periodically modulated magnetic anisotropy. The concept, which is demonstrated for strain-coupled Co40Fe40B20/BaTiO3 heterostructures, relies on abrupt rotation of magnetic anisotropy at the boundaries of magnetic stripe domains. In combination with an external bias field, this modulation of magnetic anisotropy produces a lateral variation of the effective magnetic field, leading to local spin-wave excitation when irradiated by a microwave magnetic field. In domains with small effective field, spin waves are perfectly confined by the spin gap in neighboring domains. In contrast, standing spin waves in domains with large effective field radiate into neighboring domains. Using micromagnetic simulation, we show that the wavelength of emitted spin waves is tunable from a few micrometers down to about 100 nm by rotation of the bias field. Importantly, the orientation of the wave front remains fixed. We also demonstrate that dynamic fluctuations of the effective magnetic field produce exchange-dominated spin waves at single anisotropy boundaries. The multiferroic heterostructures presented here enable the use of global excitation fields from a microwave antenna to emit tunable spin waves.

Efficient Excitation of High-Frequency Exchange-Dominated Spin Waves in Periodic Ferromagnetic Structures

Ferromagnetic resonance and spin waves have been used in miniaturized devices for rf and microwave applications, but large magnetic bias fields are required for the high frequencies at which most satellites operate, for example. Exploiting perpendicular standing spin waves in an innovative way, the authors excite spin-wave resonance at frequencies above 20 GHz with bias fields below 100 Oe, which can be realized with small, lightweight permanent magnets, or electromagnets with current sources that would not require cooling.

Lifetime and mean free path of spin waves in ultrathin cobalt films

Miniaturization of magnon-based devices into the nanometer range would require the utilization of exchange-dominated spin waves of nanometer wavelength. In experiment and theory we show that the intrinsic lifetime and mean free path of the homogeneous acoustic spin wave in ultrathin cobalt films is sufficiently long for such applications provided that the films are atomically flat. The presence of surface steps, however, shortens lifetime and mean free path. The experimental data are consistent with a model which assumes that steps act as perfect sinks for spin waves.

Generation of Propagating Spin Waves From Edges of Magnetic Nanostructures Pumped by Uniform Microwave Magnetic Field

Thin-film patterned magnetic nanostructures are widely employed within perceived magnonic device architectures to guide and/or manipulate spin waves for data processing and communication purposes. Here, using micromagnetic simulations, we explore how the internal magnetic field nonuniformity inherent to patterned magnetic nanostructures can also be exploited to create spin-wave sources. The spin-wave emission is achieved through the resonant excitation of finite-sized regions of increased effective magnetic field formed near the edges of patterned structures. The phenomenon is rather universal and could be used to generate magnetodipole, dipole-exchange, and exchange dominated spin waves. Depending on the frequency of excitation and parameters of the nanostructures, the emitted spin waves may form either highly directional spin-wave caustic beams or more regular plane spin waves.

Homodyne-detected ferromagnetic resonance of in-plane magnetized nanocontacts: Composite spin-wave resonances and their excitation mechanism

This work provides a detailed investigation of the measured in-plane field-swept homodyne-detected ferromagnetic resonance (FMR) spectra of an extended Co/Cu/NiFe pseudo spin valve stack using a nanocontact (NC) geometry. The magnetodynamics are generated by a pulse-modulated microwave current and the resulting rectified dc mixing voltage, which appears across the NC at resonance, is detected using a lock-in amplifier. Most notably, we find that the measured spectra of the NiFe layer are composite in nature and highly asymmetric, consistent with the broadband excitation of multiple modes. Additionally, the data must be fit with two Lorentzian functions in order to extract a reasonable value for the Gilbert damping of the NiFe. Aided by micromagnetic simulations, we conclude that (i) for in-plane fields the rf Oersted field in the vicinity of the NC plays the dominant role in generating the observed spectra, (ii) in addition to the FMR mode, exchange dominated spin waves are also generated, and (iii) the NC diameter sets the mean wavevector of the exchange dominated spin wave, in good agreement with the dispersion relation.

Propagating spin waves excited by spin-transfer torque: A combined electrical and optical study

Nanocontact spin-torque oscillators are devices in which the generation of propagating spin waves can be sustained by spin transfer torque. In the present paper, we perform combined electrical and optical measurements in a single experimental setup to systematically investigate the excitation of spin waves by a nanocontact spin-torque oscillator and their propagation in a Ni80Fe20 extended layer. By using microfocused Brillouin light scattering we observe an anisotropic emission of spin waves, due to the broken symmetry imposed by the inhomogeneous Oersted field generated by the injected current. In particular, spin waves propagate on the side of the nanocontact where the Oersted field and the in-plane component of the applied magnetic field are antiparallel, while propagation is inhibited on the opposite side. Moreover, propagating spin waves are efficiently excited only in a limited frequency range corresponding to wavevectors inversely proportional to the size of the nanocontact. This frequency range obeys the dispersion relation for exchange-dominated spin waves in the far field, as confirmed by micromagnetic simulations of similar devices. The present results have direct consequences for spin wave based applications, such as synchronization, computation, and magnonics.