Properties Of Spin Waves Research Articles

Tunable spin wave properties in [Co/Ni80Fe20]r multilayers with the number of bilayer repetition

Tunability of spin waves in [Co/Ni80Fe20]r multilayer films by varying the number of bilayer repetition (r) is investigated using Brillouin light scattering (BLS) spectroscopy. Conventional magnetometry shows a monotonic increase in the in-plane anisotropy with r. BLS spectra show a number of distinct modes, which were found to be Damon–Eshbach and perpendicular standing spin wave modes confined in several bilayers with different mode numbers by macrospin modelling. The extracted values of the magnetic parameters from the spin wave measurements agree reasonably well with the magnetometry results. A qualitative analysis of the dependence of BLS intensity of PSSW modes on the corresponding thickness has also been performed using a light-scattering theory for confined geometries. The results of the calculations are in agreement with experimental data.

Growth and spin-wave properties of thin Y3Fe5O12 films on Si substrates

We describe synthesis of submicron Y3Fe5O12 (YIG) films sputtered on Si substrates and present results of the investigation of ferromagnetic resonance (FMR) and spin waves in YIG/SiO2/Si structures. It is found that decrease of the annealing time leads to essential reduction of the FMR linewidth ΔH and, consequently, to reduction of relaxation losses of spin waves. Spin-wave propagation in in-plane magnetized YIG/SiO2/Si structures is studied. We observe the asymmetry of amplitude-frequency characteristics of the Damon-Eshbach spin waves caused by different localizations of spin waves at the free YIG surface and at the YIG/SiO2 interface. Growth of the generating microwave power leads to spin-wave instability and changes amplitude-frequency characteristics of spin waves.

Role of the antiferromagnetic pinning layer on spin wave properties in IrMn/NiFe based spin-valves

Brillouin light scattering (BLS) was exploited to study the spin wave properties of spin-valve (SV) type samples basically consisting of two 5 nm-thick NiFe layers (separated by a Cu spacer of 5 nm), differently biased through the interface exchange coupling with an antiferromagnetic IrMn layer. Three samples were investigated: a reference SV sample, without IrMn (reference); one sample with an IrMn underlayer (10 nm thick) coupled to the bottom NiFe film; one sample with IrMn underlayer and overlayer of different thickness (10 nm and 6 nm), coupled to the bottom and top NiFe film, respectively. The exchange coupling with the IrMn, causing the insurgence of the exchange bias effect, allowed the relative orientation of the NiFe magnetization vectors to be controlled by an external magnetic field, as assessed through hysteresis loop measurements by magneto-optic magnetometry. Thus, BLS spectra were acquired by sweeping the magnetic field so as to encompass both the parallel and antiparallel alignment of the NiFe layers. The BLS results, well reproduced by the presented theoretical model, clearly revealed the combined effects on the spin dynamic properties of the dipolar interaction between the two NiFe films and of the interface IrMn/NiFe exchange coupling.

Spin Waves in Two and Three Dimensional Magnetic Materials

The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.

Spin Waves in Two and Three Dimensional Magnetic Materials

The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.

Spin Waves in One Dimensional Magnetic Material

Using Heisenberg model, the equations of motion for the dynamic properties of spin waves in three dimensions were obtained and solved analytically up to an exponential operator representation. Second order Suzuki Trotter decomposition method with evolution operator solution was applied to obtain the numerical solutions by making it closer to real spin systems. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for one dimensional lattice by investigating the occurrence, temperature dependence and spin-spin interaction dependence of the spin waves. A visualization technique was used to show the existence of many spin wave components below the Curie temperature of the system. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor. Energy conservation of the algorithm is also shown.

Spin Waves in One Dimensional Magnetic Material

Using Heisenberg model, the equations of motion for the dynamic properties of spin waves in three dimensions were obtained and solved analytically up to an exponential operator representation. Second order Suzuki Trotter decomposition method with evolution operator solution was applied to obtain the numerical solutions by making it closer to real spin systems. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for one dimensional lattice by investigating the occurrence, temperature dependence and spin-spin interaction dependence of the spin waves. A visualization technique was used to show the existence of many spin wave components below the Curie temperature of the system. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor. Energy conservation of the algorithm is also shown.

Spin wave emission in field-driven domain wall motion

A domain wall (DW) in a nanowire can propagate under a longitudinal magnetic field by emitting spin waves (SWs). We numerically investigated the properties of SWs emitted by the DW motion, such as frequency and wave number, and their relation with the DW motion. For a wire with a low transverse anisotropy and in a field above a critical value, a DW emits SWs to both sides (bow and stern), while it oscillates and propagates at a low average speed. For a wire with a high transverse anisotropy and in a weak field, the DW emits mostly stern waves, while the DW distorts itself and the DW center propagates forward like a drill at a relative high speed.

Waveguide properties in two-dimensional magnonic crystals with line defects

Abstract The waveguide properties of spin waves through line defects in two-dimensional magnonic crystals are investigated by numerical calculating band structures and magnetization-field distributions of the defect modes. The results show that the spin waves are very well localized in the line defects, and the size of the defect bodies has an obvious influence on the defect modes existing in the frequency regime of the gap. It will provide us a theoretical foundation in the designing of spin-wave waveguides with different shapes.

Spin-wave propagation in the presence of interfacial Dzyaloshinskii-Moriya interaction

In ferromagnetic thin films, broken inversion symmetry and spin-orbit coupling give rise to interfacial Dzyaloshinskii-Moriya interactions. Analytic expressions for spin-wave properties show that the interfacial Dzyaloshinskii-Moriya interaction leads to nonreciprocal spin-wave propagation, i.e., different properties for spin waves propagating in opposite directions. In favorable situations, it can increase the spin-wave attenuation length. Comparing measured spin-wave properties in ferromagnet/normal metal bilayers and other artificial layered structures with these calculations could provide a useful characterization of the interfacial Dzyaloshinskii-Moriya interactions.

Nonreciprocity of spin waves in metallized magnonic crystal

The nonreciprocal properties of spin waves in metallized one-dimensional bi-component magnonic crystal composed of two materials with different magnetizations are investigated numerically. Nonreciprocity leads to the appearance of indirect magnonic band gaps for magnonic crystals with both low and high magnetization contrast. Specific features of the nonreciprocity in low contrast magnonic crystals lead to the appearance of several magnonic band gaps located within the first Brillouin zone for waves propagating along the metallized surface. Analysis of the spatial distribution of dynamic magnetization amplitudes explains the mechanism of dispersion band formation and hybridization between magnonic bands in magnonic crystals with metallization.

Spin torque ferromagnetic resonance with magnetic field modulation

We demonstrate a technique of broadband spin torque ferromagnetic resonance (ST-FMR) with magnetic field modulation for measurements of spin wave properties in magnetic nanostructures. This technique gives great improvement in sensitivity over the conventional ST-FMR measurements, and application of this technique to nanoscale magnetic tunnel junctions (MTJs) reveals a rich spectrum of standing spin wave eigenmodes. Comparison of the ST-FMR measurements with micromagnetic simulations of the spin wave spectrum allows us to explain the character of low-frequency magnetic excitations in nanoscale MTJs.

The quasi-one-dimensional character of spin waves in K2Fe7Se8

The ground state phase diagram, the physical properties of spin waves and the dynamic structure factor of the new family of 122 iron-vacancy ordered compound K2Fe7Se8 are theoretically investigated based on the J1–J2 Heisenberg model. Four antiferromagnetic phases are found to be stable in the reasonable physical parameter region. The dispersion relations of the spin waves for the newly discovered AFM2 and AFM3 phases are studied using the linearized spin wave theory. Two acoustic spin wave branches and 12 optical spin wave branches are present in both the AFM2 and AFM3 phases, and each of them are twofold degenerate. One more interesting finding is that the spin waves of K2Fe7Se8 have the quasi-one-dimensional character at the high frequency range. To offer theoretical guidance for the further neutron scattering experiments, the inelastic neutron scattering patterns for the AFM2 and AFM3 phases are also investigated.

Excitation of spin waves by a current-driven magnetic nanocontact in a perpendicularly magnetized waveguide

It is demonstrated both analytically and numerically that the properties of spin wave modes excited by a current-driven nanocontact of length $L$ in a quasi-one-dimensional magnetic waveguide magnetized by a perpendicular bias magnetic field ${H}_{e}$ are qualitatively different from the properties of spin waves excited by a similar nanocontact in a two-dimensional unrestricted magnetic film (``free layer''). In particular, there is an optimum nanocontact length ${L}_{\mathrm{opt}}$ corresponding to the minimum critical current of the spin wave excitation. This optimum length is determined by the magnitude of ${H}_{e}$, the exchange length, and the Gilbert dissipation constant of the waveguide material. Also, for $L<{L}_{\mathrm{opt}}$ the wavelength \ensuremath{\lambda} (and the wave number $k$) of the excited spin wave can be controlled by the variation of ${H}_{e}$ (\ensuremath{\lambda} decreases with the increase of ${H}_{e}$), while for $L>{L}_{\mathrm{opt}}$ the wave number $k$ is fully determined by the contact length $L$ ($k\ensuremath{\sim}1/L$), similar to the case of an unrestricted two-dimensional free layer.

Characterization of magnetostatic surface spin waves in magnetic thin films: evaluation for microelectronic applications

The authors have investigated the possibility of utilizing spin waves for inter- and intra-chip communications, and as logic elements using both simulations and experimental techniques. Through simulations it has been shown that the decay lengths of magnetostatic spin waves are affected most by the damping parameter, and least by the exchange stiffness constant. The damping and dispersion properties of spin waves limit the attenuation length to several tens of microns. Thus, we have ruled out the possibility of inter-chip communications via spin waves. Experimental techniques for the extraction of the dispersion relationship have also been demonstrated, along with experimental demonstrations of spin wave interference for amplitude modulation. The effectiveness of spin wave modulation through interference, along with the capability of determining the spin wave dispersion relationships electrically during manufacturing and testing phase of chip production may pave the way for using spin waves in analog computing wherein the circuitry required for performing similar functionality becomes prohibitive.

Spin-wave propagation and transformation in a thermal gradient

The influence of a thermal gradient on the propagation properties of externally excited dipolar spin waves in a magnetic insulator waveguide is investigated. It is shown that spin waves propagating towards a colder region along the magnetization direction continuously reduce their wavelength. The wavelength increase of a wave propagating into a hotter region was utilized to realize its decomposition in the partial waveguide modes which are reflected at different locations. This influence of temperature on spin-wave properties is mainly caused by a change in the saturation magnetization and yields promising opportunities for the manipulation of spin waves in spin-caloritronic applications.

Quantum coherence in spin-torque nano-oscillators

We study the quantum coherence properties of spin waves in a ferromagnetic thin film driven by a dc current in a spin-torque nano-oscillator. We show that if the current barely exceeds the threshold value the driven magnon states are not coherent and exhibit pronounced thermal noise. Only when the current exceeds the threshold value by a certain amount that depends on the material parameters and temperature of the nanostructure the microwave oscillation will exhibit quantum coherence.

Field dependence of collective spin modes in transversely magnetized stripes with homogeneous and alternating width

Brillouin light scattering is used to study the spin-wave properties of arrays of closely spaced magnetic stripes with both homogeneous and alternating width, thickness of 30 nm, and edge-to-edge spacing of 55 nm. Experiments are performed with both the transferred wave vector and the applied magnetic field in the direction transverse to the length of the stripes, i.e., in the hard magnetization direction. When the transverse applied field is decreased from a relatively large value (0.15 T) down to zero, the overall direction of the stripe magnetization gradually switches from the transverse to the preferred longitudinal orientation, as confirmed by the shape of the Kerr hysteresis loops. The measured frequencies were compared to numerical calculations obtained for Permalloy stripe arrays by a microscopic dipole-exchange theory. A good overall agreement is achieved between experiment and theory, thanks to the inclusion of the dynamical interstripe dipolar coupling.

Spinwave propagation in lossless cylindrical magnonic waveguides

Spinwave propagation in clad cylindrical magnonic waveguides is investigated under linear approximation. With the assumption of no magnetic damping, characteristic equation to determine the bound spinwave modes has been obtained based on the structural and magnetic properties of the waveguides. The study is then applied to homogenous magnetic nanowires with no cladding. Spinwave characteristics and properties, such as the dispersion relationship and group velocity, can be described analytically.

Nano-optics with spin waves at microwave frequencies

With the recent development in nanoscale patterning techniques, the potential of practical applications of nanometer-size structures for signal processing has been growing continuously. Experimental findings on the manipulation of optical signals in nanostructures have recently given rise to a widely addressed scientific area—subwavelength nano-optics. Here, we demonstrate that spin waves in microscopic ferromagnetic film structures represent a superb object for realization of the principles of nano-optics in the microwave frequency range. We show experimentally that by using the unique properties of spin waves, one can easily channelize, split, and manipulate submicrometer-width spin-wave beams propagating in microscopic magnetic-film waveguides.