Magnonic Crystal with Two-Dimensional Periodicity as a Waveguide for Spin Waves (original) (raw)
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Magnetic superlattice with two-dimensional periodicity as a waveguide for spin waves
Physical Review B, 2010
We describe a simple method of including dissipation in the spin wave band structure of a periodic ferromagnetic composite, by solving the Landau-Lifshitz equation for the magnetization with the Gilbert damping term. We use this approach to calculate the band structure of square and triangular arrays of Ni nanocylinders embedded in an Fe host. The results show that there are certain bands and special directions in the Brillouin zone where the spin wave lifetime is increased by more than an order of magnitude above its average value. Thus, it may be possible to generate spin waves in such composites decay especially slowly, and propagate especially large distances, for certain frequencies and directions in k-space.
Spin waves in periodic magnetic structures—magnonic crystals
Journal of Magnetism and Magnetic Materials, 2001
Propagation of spin waves (SWs) through a periodic multilayered magnetic structure is analyzed. It is assumed that the structure consists of ferromagnetic layers having the same thickness but different magnetizations. The wave spectrum obtained contains forbidden zones (stop bands) in which wave propagation is prohibited. Introduction into the structure of the ferromagnetic layer with a different thickness breaks the structural symmetry and leads to a localization of the SW mode with the frequency lying in the stop band. Reflection of the wave by the structure of the finite length and transmission of the wave through the structure are also investigated. Numerical calculations of the wave dispersion and the transmission coefficients for symmetrical periodic structures as well as the structures with a defect are presented. Drawing an analogy from photonic crystals known in optics, such magnetic structures can be called one-dimensional (1-D) magnonic crystals (MCs). The possibilities of existence of the 2-D MCs are also discussed. r
Collective spin waves in a bicomponent two-dimensional magnonic crystal
Applied Physics Letters, 2012
ABSTRACT Spin waves propagating in a bicomponent magnonic crystal consisting of a two-dimensional array of alternated NiFe and Co nanodots have been investigated. The frequency dispersion of collective modes, measured by Brillouin light scattering, is compared with the band diagram obtained by numerically solving the eigenvalue problem derived from the linearized Landau-Lifshitz magnetic torque equation. It is shown that the modes which are active in Brillouin experiment are characterized by the simplest modal profiles within the NiFe dots. For such excitations, the Co dots act as mediators of dipole coupling between the NiFe dots. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4704659\]
Band Diagram of Spin Waves in a Two-Dimensional Magnonic Crystal
Physical Review Letters, 2011
The dispersion curves of collective spin-wave excitations in a magnonic crystal consisting of a square array of interacting saturated nanodisks have been measured by Brillouin light scattering along the four principal directions of the first Brillouin zone. The experimental data are successfully compared to calculations of the band diagram and of the Brillouin light scattering cross section, performed through the dynamical matrix method extended to include the dipolar interaction between the disks. We found that the fourfold symmetry of the geometrical lattice is reduced by the application of the external field and therefore equivalent directions of the first Brillouin zone are characterized by different dispersion relations of collective spin waves. The dispersion relations are explained through the introduction of a bidimensional effective wave vector that characterizes each mode in this magnonic metamaterial.
Shape Dependent High Frequency Spin-Wave Dynamics in Nanoscale Magnonic Crystals
Journal of Magnetism and Magnetic Materials, 2019
Efficient tunability of magnetization dynamics in two-dimensional circular and triangularshaped Ni80Fe20 antidots arranged in hexagonal lattice is demonstrated using a combination of all-electrical and all-optical detection techniques. A broad band of modes is observed for both the lattices. A strong variation in the spin-wave spectra is obtained with the strength and orientation of the bias magnetic field. A crossover between two higher frequency branches is observed with the variation of bias magnetic field strength in circular antidot lattice, whereas no such crossover is observed in the triangular antidot lattice. In addition, the spin-wave modes in both lattices show strong six-fold anisotropic behaviour presumably due to the variation of internal field distribution originating from a combination of the lattice arrangement and the shape of the antidots as a function of the bias magnetic field orientation. Micromagnetic simulations qualitatively reproduce the experimentally observed spin-wave modes and the simulated mode profiles reveal the presence of extended and quantized standing spin-wave modes in these lattices. Also, some lower frequency localized edge modes, obtained in the triangular antidot lattice due to the asymmetric demagnetized regions at sharp corners, are not observed in the circular antidot lattice. These observations are significant for large tunability and anisotropic propagation of spin waves in GHz frequency magnetic devices.
Anisotropic spin waves in two-dimensional triangular shaped bi-component magnonic crystal
Journal of Magnetism and Magnetic Materials, 2019
Bi-component magnonic crystals with a strong dipole-exchange interaction across the interface of the constituent magnetic elements have shown promising potentials in magnonics and magnon-spintronics. Here, we have reported an all-optical investigation of spin wave dynamics in an array of periodically arranged bi-component magnonic crystal in the form of triangular shaped Ni 80 Fe 20 nanoelements embedded in Co 50 Fe 50 matrix using time-resolved magneto-optical Kerr effect magnetometry. The spin wave spectra obtained from the sample reveal a broad band of spin wave modes where they possess a strong and systematic bias magnetic field tunability which is crucial for active control over such system in device applications. Further, the spin wave modes show a six-fold and a four-fold rotational anisotropy with the bias field orientation due to combined effects of element shape and lattice symmetry. Micromagnetic simulations reproduce the experimental results qualitatively where the simulated mode profiles unravel the spatial distribution of spin wave frequencies inside both constituent elements while the internal magnetic fields play a crucial role for the observed tunability of spin wave dynamics. Development of such magnetically coupled embedded magnetic nanostructures can pave a new pathway in designing the future magnonic devices and faster microwave communication systems.
Magnetostatic spin waves in nanoelements
Physica B-condensed Matter, 2004
The relaxation of magnetostatic spin waves in a square NiFe nano-element (100×100×20 nm3) has been simulated by micromagnetic finite element modeling after the excitation by a rotational field of μ0H=0.2 T with various frequencies between 1 and 16 GHz. The micromagnetic simulations are based on the Landau–Lifshitz–Gilbert equation of motion with a Gilbert damping parameter α=0.02. The relaxation after switching off the external field led to a damped oscillation of the magnetization, which is related to changes of the exchange and magnetostatic field energies of the system. Finally, depending on the frequency of the rotating field “C-” and “S-” domain configurations were observed after approximately 10 ns. The different inhomogeneous magnetostatic and exchange field strength values inside the square for the “C-” and “S-” state lead to different frequencies of the magnetostatic spin-wave modes, such as about 4.5 GHz for the C-state and 3 GHz for the S-state, respectively.
Physical Review B, 2010
The Brillouin light-scattering technique has been applied to study collective spin waves in a dense array of dipolarly coupled Ni 80 Fe 20 stripes of alternating widths, during the magnetization reversal process. Both the saturated "ferromagnetic" state, where the magnetizations of wide and narrow stripes are parallel, and the "antiferromagnetic" state, characterized by an antiparallel alignment of the static magnetization in adjacent stripes, have been analyzed. The experimental data provide strong evidence of sustained collective excitations in the form of Bloch waves with permitted and forbidden magnonic energy bands. The measured frequencies as a function of the exchanged wave vector have been satisfactorily reproduced by numerical simulations which enabled us to calculate the spatial profiles of the Bloch waves, showing that some of the modes are preferentially localized in either the wide or the narrow stripes. We estimated the expected light-scattering cross section for each mode at different magnetic ground states, achieving a good agreement with the measured intensities. The alternating-width stripes system studied here represents a one-dimensional artificial magnonic crystal with a complex base and can be considered as a model system for reprogrammable dynamical response, where the band structure of collective spin waves can be tailored by changing the applied magnetic field.
Brillouin scattering of light by spin waves in ferromagnetic nanorods
2012
We report the investigations of spin wave modes of arrays of Ni and Co nanorods using Brillouin light scattering. We have revealed the significant influence of spin wave modes along the nanorod axis in contrast to infinite magnetic nanowires. Unusual optical properties featuring an inverted Stokes/anti-Stokes asymmetry of the Brillouin scattering spectra have been observed. The spectrum of spin wave modes in the nanorod array has been calculated and compared with the experiment. Experimental observations are explained in terms of a combined numerical-analytical approach taking into account both the low aspect ratio of individual magnetic nanorods and dipolar magnetic coupling between the nanorods in the array. The optical studies of spin-wave modes in nanorod metamaterials with low aspect ratio nanorods have revealed new magnetic and magneto-optical properties compared to continuous magnetic films or infinite magnetic nanowires. Such magnetic artificial materials are important class of active metamaterials needed for prospective data storage and signal processing applications.