Control of spin-wave excitations in deterministic fractals

Swoboda, Christian; Martens, M.; Meier, Guido

doi:10.1103/physrevb.91.064416

Cited by 14 publications

(9 citation statements)

References 43 publications

(91 reference statements)

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“…Various physical processes in nano-and microfractals, such as plasmonic wave propagation (Ng et al, 2014), spin-wave excitations (Swoboda et al, 2015) and self-assembly of fractal macromolecules (Newkome et al, 2006), can be related to the fractal structure.…”

Section: Introductionmentioning

confidence: 99%

Scattering from surface fractals in terms of composing mass fractals

et al. 2017

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We argue that a finite iteration of any surface fractal can be composed of mass-fractal iterations of the same fractal dimension. Within this assertion, the scattering amplitude of surface fractal is shown to be a sum of the amplitudes of composing mass fractals. Various approximations for the scattering intensity of surface fractal are considered. It is shown that small-angle scattering (SAS) from a surface fractal can be explained in terms of power-law distribution of sizes of objects composing the fractal (internal polydispersity), provided the distance between objects is much larger than their size for each composing mass fractal. The power-law decay of the scattering intensity $I(q) \propto q^{D_{\mathrm{s}}-6}$, where $2 < D_{\mathrm{s}} < 3$ is the surface fractal dimension of the system, is realized as a non-coherent sum of scattering amplitudes of three-dimensional objects composing the fractal and obeying a power-law distribution $d N(r) \propto r^{-\tau} dr$, with $D_{\mathrm{s}}=\tau-1$. The distribution is continuous for random fractals and discrete for deterministic fractals. We suggest a model of surface deterministic fractal, the surface Cantor-like fractal, which is a sum of three-dimensional Cantor dusts at various iterations, and study its scattering properties. The present analysis allows us to extract additional information from SAS data, such us the edges of the fractal region, the fractal iteration number and the scaling factor.Comment: Corrected and extended copy, 15 pages, 12 figure

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Section: Introductionmentioning

confidence: 99%

Scattering from surface fractals in terms of composing mass fractals

et al. 2017

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“…For spin waves of longer wavelength, the same magnonic crystal will represent an effectively continuous medium with properties defined not only by those of the constituent magnetic materials but also details of the geometrical and micromagnetic structure. Magnonic crystals therefore represent a class of metamaterials, often referred to as "magnonic metamaterials", [73][74][75][76][77][78] which also includes systems that are not periodic, such as magnonic quasi-crystals [79][80][81][82][83][84][85] and (when considered from the point of view of their dynamic properties) magnetic composites. [86][87][88][89][90][91][92][93] The nature of the interlayer magnetization boundary conditions has crucial consequences for the scattering of spin waves from interfaces between regions with different magnetic properties.…”

Section: Introductionmentioning

confidence: 99%

Formation of the band spectrum of spin waves in 1D magnonic crystals with different types of interfacial boundary conditions

Kruglyak¹,

Davies²,

Tkachenko³

et al. 2017

J. Phys. D: Appl. Phys.

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We report a theoretical study of the spin-wave band spectrum of magnonic crystals formed by stacking thin-film magnetic layers, with general assumptions about the properties of the interfaces between the layers. The use of the Barnaś-Mills magnetization boundary conditions has enabled us to systematically trace the origin of the magnonic band gaps in the spin-wave spectrum of such systems. We find that the band gaps are a ubiquitous attribute of a weakened interlayer coupling and a finite interface anisotropy (pinning). The band gaps in such systems represent a legacy of the discrete spinwave spectrum of the individual magnetic layers periodically stacked to form the magnonic crystal rather than result from Bragg scattering. At the same time, magnonic crystals with band gaps due to the Bragg scattering can be described by natural boundary conditions (i.e. those maintaining continuity of the magnetization direction across the whole sample). We generalize our conclusions to systems beyond thin-film magnonic crystals and propose magnonic crystals based on the ideas of graded-index magnonics and those formed by Fano resonances as a possible way to circumvent the discovered issues.

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“…Early works on magnetic fractals were focused on diluted antiferromagnets, where the magnetic ions can form a percolating structure that is a statistical fractal [32]. Recently, the spinwave spectra in square-based ferromagnetic Sierpinski carpet structures were also reported [33,34]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Precessional dynamics of geometrically scaled magnetostatic spin waves in two-dimensional magnonic fractals

et al. 2022

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The control of spin waves in periodic magnetic structures has facilitated the realization of many functional magnonic devices, such as band stop filters and magnonic transistors, where the geometry of the crystal structure plays an important role. Here, we report on the magnetostatic mode formation in an artificial magnetic structure, going beyond the crystal geometry to a fractal structure, where the mode formation is related to the geometric scaling of the fractal structure. Specifically, the precessional dynamics was measured in samples with structures going from simple geometric structures toward a Sierpinski carpet and a Sierpinski triangle. The experimentally observed evolution of the precessional motion could be linked to the progression in the geometric structures that results in a modification of the demagnetizing field. Furthermore, we have found sets of modes at the ferromagnetic resonance frequency that form a scaled spatial distribution following the geometric scaling. Based on this, we have determined the two conditions for such mode formation to occur. One condition is that the associated magnetic boundaries must scale accordingly, and the other condition is that the region where the mode occurs must not coincide with the regions for the edge modes. This established relationship between the fractal geometry and the mode formation in magnetic fractals provides guiding principles for their use in magnonics applications.

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Control of spin-wave excitations in deterministic fractals

Cited by 14 publications

References 43 publications

Scattering from surface fractals in terms of composing mass fractals

Scattering from surface fractals in terms of composing mass fractals

Formation of the band spectrum of spin waves in 1D magnonic crystals with different types of interfacial boundary conditions

Precessional dynamics of geometrically scaled magnetostatic spin waves in two-dimensional magnonic fractals

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