On the Formulation of the Exchange Field in the Landau-Lifshitz Equation for Spin-Wave Calculation in Magnonic Crystals

We investigate the properties of a photonic-magnonic crystal, a complex multifunctional one-dimensional structure with magnonic and photonic band gaps in the GHz and PHz frequency ranges for spin waves and light, respectively. The system consists of periodically distributed dielectric magnetic slabs of yttrium iron garnet and nonmagnetic spacers with an internal structure of alternating TiO2 and SiO2 layers which form finite-size dielectric photonic crystals. We show that the spin-wave coupling between the magnetic layers, and thus the formation of the magnonic band structure, necessitates a nonzero in-plane component of the spin-wave wave vector. A more complex structure perceived by light is evidenced by the photonic miniband structure and the transmission spectra in which we have observed transmission peaks related to the repetition of the magnetic slabs in the frequency ranges corresponding to the photonic band gaps of the TiO2/SiO2 stack. Moreover, we show that these modes split to very high sharp (a few THz wide) subpeaks in the transmittance spectra. The proposed novel multifunctional artificial crystals can have interesting applications and be used for creating common resonant cavities for spin waves and light to enhance the mutual influence between them.

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“…The detailed discussion of different approximation important for derivation of H ex can be found in Ref. 72.…”

Section: Structurementioning

confidence: 99%

Photonic-magnonic crystals: Multifunctional periodic structures for magnonic and photonic applications

Kłos

Krawczyk

Dadoenkova

et al. 2014

Journal of Applied Physics

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“…This assumption (that the spin wave wavelength is greater than lattice constants of constituent materials) is the essence of the continuous medium approximation in magnonics, in which the natural boundary conditions (8)(9) are derived. In particular, this explains why such a continuous medium approach as the plane wave method 70,[74][75][76][77] is consistent with the natural boundary conditions (8-9) but experiences difficulties adopting the notion of the interlayer exchange coupling.…”

Section: Natural Hoffmann and Barnaś-mills Forms Of Magnetizatimentioning

confidence: 99%

Magnetization boundary conditions at a ferromagnetic interface of finite thickness

Kruglyak

Gorobets

et al. 2014

J. Phys.: Condens. Matter

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We develop a systematic approach by which to derive boundary conditions at an interface between two ferromagnetic materials in the continuous medium approximation. The approach treats the interface as a two-sublattice material, although the final equations connect magnetizations outside of the interface and therefore do not explicitly depend on its structure. Instead, the boundary conditions are defined in terms of some average properties of the interface, which may also have a finite thickness. In addition to the interface anisotropy and symmetric exchange coupling, this approach allows us to take into account coupling resulting from inversion symmetry breaking in the vicinity of the interface, such as the Dzyaloshinskii-Moriya antisymmetric exchange interaction. In the case of negligible interface anisotropy and Dzyaloshinskii-Moriya exchange parameters, the derived boundary conditions represent a generalization of those proposed earlier by Barnaś and Mills and are therefore named "generalized Barnaś-Mills boundary conditions". We demonstrate how one could use the boundary conditions to extract parameters of the interface via fitting of appropriate experimental data. The developed theory could be applied to modeling of both linear and non-linear spin waves, including exchange, dipole-exchange, magnetostatic, and retarded modes, as well as to calculations of nonuniform equilibrium micromagnetic configurations near the interface, with a direct impact on the research in magnonics and micromagnetism. * Corresponding author: V.V.Kruglyak@exeter.ac.uk 2

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“…The important issue is contribution of interfaces between different materials. The boundary condition problem was discussed in Reference (44), where ambiguity in the derivation of the formula for exchange field was discussed. However, for bi component magnonic crystals composed of Py and Co, the difference between proposed formulations of the exchange field is minor, due to the similar values of the exchange length.…”

Section: Plane Wave Methodsmentioning

confidence: 99%

Magnonic Crystals

Gruszecki

Krawczyk

2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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Magnonic crystals can be regarded as the magnetic counterpart of photonic crystals, with spin waves acting as information carriers. Thus, magnonic crystals are magnetic materials with periodic distribution of the constituents or periodic modulation of some magnetic parameters (e.g., saturation magnetization or magnetocrystalline anisotropy), or other parameters relevant to the propagation of spin waves (e.g., external magnetic field, film thickness, stress, or a surrounding of the homogeneous ferromagnetic film). The spin waves propagating in magnonic crystal have a form of Bloch waves, and the dispersion relation includes frequency bands allowing spin wave propagation and frequency band gaps, forbidden for spin wave propagation. By adjusting relevant parameters of the magnonic crystal or external fields, the spectrum of spin waves can be tuned and the flow of spin waves can be tailored in the way unavailable with homogeneous media. The new physical effects occurring in magnetic nanostructures with periodic pattern and prospective applications of magnonic crystals, especially in integrated microwave devices and for processing information at microwave frequencies, drive the new fields of magnonics and magnon spintronics.

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On the Formulation of the Exchange Field in the Landau-Lifshitz Equation for Spin-Wave Calculation in Magnonic Crystals

Cited by 34 publications

References 68 publications

Photonic-magnonic crystals: Multifunctional periodic structures for magnonic and photonic applications

Photonic-magnonic crystals: Multifunctional periodic structures for magnonic and photonic applications

Magnetization boundary conditions at a ferromagnetic interface of finite thickness

Magnonic Crystals

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