Dr. Szymon Mieszczak
- Tel: +48 61 829 5073
- Loc: wing G, second floor, room 294
- Email: szymon.mieszczak@amu.edu.pl
Scientific degrees
PhD in physics – 2022
MSc in physics – 2017
Research interests
Keywords: spin waves, magnonic crystals, magnonic quasicrystal, magnonic waveguides, spin wave localization
Projects
1. | Szymon Mieszczak Anderson localization of spin waves in magnonic nanostructures 2020 - 2021, (NCN Etiuda, No. 2020/36/T/ST3/00542, budget: 150 264 PLN). @misc{Mieszczak2021, title = {Anderson localization of spin waves in magnonic nanostructures}, author = {Szymon Mieszczak}, url = {https://projekty.ncn.gov.pl/index.php?projekt_id=475240}, year = {2021}, date = {2021-12-01}, abstract = {The long-standing paradigm is that computation, data processing, etc. needs to be done by the electric circuit, i.e. it is based on the transport of electrons. The Moore's law refers to the empirical rule which states that the number of transistors in a microchip doubles every two years. This statement approaching the end of the road because of the fundamental bottlenecks of physical origin. Therefore, the further miniaturization of microprocessors is questionable. It naturally raises the question, what next? The prospective solution can be found by the studies in the field of solid state physics. In order to encode, process and transmit information at the nanoscale, other fundamental characteristics of particles, in addition to the electric charge, can be used. We can use the intrinsic angular momentum of the particle -- the spin. In ferromagnetic materials, spins and related magnetic moments interact with each other in quantum manner (by the so-called exchange interaction) or classically (by a dipole coupling between magnetic moments). The interacting magnetic moments perform an oscillatory and coherent motion. Thanks to this they can transmit information in the form of the so-called spin wave. Over the last few decades, a new field of research and technology has emerged – magnonics, which is focused on the spin wave propagation in magnetic nanostructures. Spin waves allow high frequency signals to be transmitted at the nanoscale. In magnonics, the nanostructured magnetic material are used to control the spin waves. The modifications of the geometry of the system or its static magnetic configuration take place on a scale from several dozen to several hundred nanometers, corresponding to the length of the spin wavelength. The materials modified in this way have completely new properties. Particularly noteworthy are magnetic systems with the periodic pattering – so called magnonic crystals, where in certain frequency ranges (in so-called frequency gaps) the propagation of spin waves is forbidden. Research on spin waves in naostructures, including the magnonic crystals, is developing intensively thanks to new experimental techniques as well as the increasing computing power, which in turn has allowed the numerical research on more complex systems. This has enabled many fascinating effects and new phenomena on spin waves to be discovered, opening the way to the numerous applications in the field of information processing. These include typical applications such as transistors and logic gateways, working according the principles of the Boolean computing. However, the waves (including spin waves) can be used for analog processing of the information encoded in wave’s amplitude and phase. The general advantage of this type of calculation is that the results of certain operations on signals in waveform can be obtained in real time. A good example is the Fourier transform of signals or the solution of inhomogenious differential equations, where the inhomogeneous part and the solution are treated as input and output signals. Spin waves are characterized by a number of unique properties such as anisotropic propagation, easily accessible nonlinear dynamics and the ability to control by means of a magnetic field or by the interactions with other types of waves: elastic waves and electromagnetic waves. Our research are focused on the analysis of spin waves dynamics in one-dimensional magnonic crystals made of ferromagnetic stripes where the disorder has been introduced. It can be done by random change of size or modification of material parameters of these strips. The research hypothesis is based on a common-sense observation that controlling the disturbances of the structure allows for modification of the frequency spectrum of spin waves and control of their location in the magnetic structure. In particular, we intend to show that the introduction of disorder may lead to the so-called Anderson location of spin waves in the system of coupled ferromagnetic stripes. }, howpublished = {2020}, note = {NCN Etiuda, No. 2020/36/T/ST3/00542, budget: 150 264 PLN}, keywords = {}, pubstate = {published}, tppubtype = {misc} } The long-standing paradigm is that computation, data processing, etc. needs to be done by the electric circuit, i.e. it is based on the transport of electrons. The Moore's law refers to the empirical rule which states that the number of transistors in a microchip doubles every two years. This statement approaching the end of the road because of the fundamental bottlenecks of physical origin. Therefore, the further miniaturization of microprocessors is questionable. It naturally raises the question, what next? The prospective solution can be found by the studies in the field of solid state physics. In order to encode, process and transmit information at the nanoscale, other fundamental characteristics of particles, in addition to the electric charge, can be used. We can use the intrinsic angular momentum of the particle -- the spin. In ferromagnetic materials, spins and related magnetic moments interact with each other in quantum manner (by the so-called exchange interaction) or classically (by a dipole coupling between magnetic moments). The interacting magnetic moments perform an oscillatory and coherent motion. Thanks to this they can transmit information in the form of the so-called spin wave. Over the last few decades, a new field of research and technology has emerged – magnonics, which is focused on the spin wave propagation in magnetic nanostructures. Spin waves allow high frequency signals to be transmitted at the nanoscale. In magnonics, the nanostructured magnetic material are used to control the spin waves. The modifications of the geometry of the system or its static magnetic configuration take place on a scale from several dozen to several hundred nanometers, corresponding to the length of the spin wavelength. The materials modified in this way have completely new properties. Particularly noteworthy are magnetic systems with the periodic pattering – so called magnonic crystals, where in certain frequency ranges (in so-called frequency gaps) the propagation of spin waves is forbidden. Research on spin waves in naostructures, including the magnonic crystals, is developing intensively thanks to new experimental techniques as well as the increasing computing power, which in turn has allowed the numerical research on more complex systems. This has enabled many fascinating effects and new phenomena on spin waves to be discovered, opening the way to the numerous applications in the field of information processing. These include typical applications such as transistors and logic gateways, working according the principles of the Boolean computing. However, the waves (including spin waves) can be used for analog processing of the information encoded in wave’s amplitude and phase. The general advantage of this type of calculation is that the results of certain operations on signals in waveform can be obtained in real time. A good example is the Fourier transform of signals or the solution of inhomogenious differential equations, where the inhomogeneous part and the solution are treated as input and output signals. Spin waves are characterized by a number of unique properties such as anisotropic propagation, easily accessible nonlinear dynamics and the ability to control by means of a magnetic field or by the interactions with other types of waves: elastic waves and electromagnetic waves. Our research are focused on the analysis of spin waves dynamics in one-dimensional magnonic crystals made of ferromagnetic stripes where the disorder has been introduced. It can be done by random change of size or modification of material parameters of these strips. The research hypothesis is based on a common-sense observation that controlling the disturbances of the structure allows for modification of the frequency spectrum of spin waves and control of their location in the magnetic structure. In particular, we intend to show that the introduction of disorder may lead to the so-called Anderson location of spin waves in the system of coupled ferromagnetic stripes. |
Publications
2022 |
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6. | Szymon Mieszczak, Maciej Krawczyk, Jarosław W. Kłos Spin-wave localization on phasonic defects in a one-dimensional magnonic quasicrystal Phys. Rev. B, 106 , pp. 064430, 2022. @article{PhysRevB.106.064430, title = {Spin-wave localization on phasonic defects in a one-dimensional magnonic quasicrystal}, author = {Szymon Mieszczak and Maciej Krawczyk and Jarosław W. Kłos}, url = {https://link.aps.org/doi/10.1103/PhysRevB.106.064430}, doi = {10.1103/PhysRevB.106.064430}, year = {2022}, date = {2022-08-25}, journal = {Phys. Rev. B}, volume = {106}, pages = {064430}, publisher = {American Physical Society}, abstract = {We report on the evolution of the spin-wave spectrum under structural disorder introduced intentionally into a one-dimensional magnonic quasicrystal. We study theoretically a system composed of ferromagnetic strips arranged in a Fibonacci sequence. We considered several stages of disorder in the form of phasonic defects, where different rearrangements of strips are introduced. By transition from the quasiperiodic order towards disorder, we show a gradual degradation of spin-wave fractal spectra and closing of the frequency gaps. In particular, the phasonic defects lead to the disappearance of the van Hove singularities at the frequency gap edges by moving modes into the frequency gaps and creating new modes inside the frequency gaps. These modes disperse and eventually can close the gap, with increasing disorder levels. The work reveals how the presence of disorder modifies the intrinsic spin-wave localization existing in undefected magnonic quasicrystals. The paper contributes to the knowledge of magnonic Fibonacci quasicrystals and opens the way to study of the phasonic defects in two-dimensional magnonic quasicrystals.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We report on the evolution of the spin-wave spectrum under structural disorder introduced intentionally into a one-dimensional magnonic quasicrystal. We study theoretically a system composed of ferromagnetic strips arranged in a Fibonacci sequence. We considered several stages of disorder in the form of phasonic defects, where different rearrangements of strips are introduced. By transition from the quasiperiodic order towards disorder, we show a gradual degradation of spin-wave fractal spectra and closing of the frequency gaps. In particular, the phasonic defects lead to the disappearance of the van Hove singularities at the frequency gap edges by moving modes into the frequency gaps and creating new modes inside the frequency gaps. These modes disperse and eventually can close the gap, with increasing disorder levels. The work reveals how the presence of disorder modifies the intrinsic spin-wave localization existing in undefected magnonic quasicrystals. The paper contributes to the knowledge of magnonic Fibonacci quasicrystals and opens the way to study of the phasonic defects in two-dimensional magnonic quasicrystals. |
5. | Szymon Mieszczak, Jarosław W. Kłos Interface modes in planar one-dimensional magnonic crystals Scientific Reports, 12 (1), pp. 11335, 2022, ISSN: 2045-2322. @article{mieszczak_interface_2022, title = {Interface modes in planar one-dimensional magnonic crystals}, author = {Szymon Mieszczak and Jarosław W. Kłos}, url = {https://www.nature.com/articles/s41598-022-15328-x}, doi = {10.1038/s41598-022-15328-x}, issn = {2045-2322}, year = {2022}, date = {2022-07-05}, urldate = {2022-07-11}, journal = {Scientific Reports}, volume = {12}, number = {1}, pages = {11335}, abstract = {We present the concept of Zak phase for spin waves in planar magnonic crystals and discuss the existence condition of interface modes localized on the boundary between two magnonic crystals with centrosymmetric unit cells. Using the symmetry criterion and analyzing the logarithmic derivative of the Bloch function, we study the interface modes and demonstrate the bulk-to-edge correspondence. Our theoretical results are verified numerically and extended to the case in which one of the magnonic crystals has a non-centrosymmetric unit cells. We show that by shifting the unit cell, the interface modes can traverse between the band gap edges. Our work also investigate the role of the dipolar interaction, by comparison the systems both with exchange interaction only and combined dipolar-exchange interactions.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present the concept of Zak phase for spin waves in planar magnonic crystals and discuss the existence condition of interface modes localized on the boundary between two magnonic crystals with centrosymmetric unit cells. Using the symmetry criterion and analyzing the logarithmic derivative of the Bloch function, we study the interface modes and demonstrate the bulk-to-edge correspondence. Our theoretical results are verified numerically and extended to the case in which one of the magnonic crystals has a non-centrosymmetric unit cells. We show that by shifting the unit cell, the interface modes can traverse between the band gap edges. Our work also investigate the role of the dipolar interaction, by comparison the systems both with exchange interaction only and combined dipolar-exchange interactions. |
4. | A V Chumak, P Kabos, M Wu, C Abert, C Adelmann, A O Adeyeye, J Akerman, F G Aliev, A Anane, A Awad, C H Back, A Barman, G E W Bauer, M Becherer, E N Beginin, V A S V Bittencourt, Y M Blanter, P Bortolotti, I Boventer, D A Bozhko, S A Bunyaev, J J Carmiggelt, R R Cheenikundil, F Ciubotaru, S Cotofana, G Csaba, O V Dobrovolskiy, C Dubs, M Elyasi, K G Fripp, H Fulara, I A Golovchanskiy, C Gonzalez-Ballestero, Piotr Graczyk, D Grundler, Paweł Gruszecki, G Gubbiotti, K Guslienko, A Haldar, S Hamdioui, R Hertel, B Hillebrands, T Hioki, A Houshang, C -M Hu, H Huebl, M Huth, E Iacocca, M B Jungfleisch, G N Kakazei, A Khitun, R Khymyn, T Kikkawa, M Kloui, O Klein, Jarosław W. Kłos, S Knauer, S Koraltan, M Kostylev, Maciej Krawczyk, I N Krivorotov, V V Kruglyak, D Lachance-Quirion, S Ladak, R Lebrun, Y Li, M Lindner, R Macedo, S Mayr, G A Melkov, Szymon Mieszczak, Y Nakamura, H T Nembach, A A Nikitin, S A Nikitov, V Novosad, J A Otalora, Y Otani, A Papp, B Pigeau, P Pirro, W Porod, F Porrati, H Qin, Bivas Rana, T Reimann, F Riente, O Romero-Isart, A Ross, A V Sadovnikov, A R Safin, E Saitoh, G Schmidt, H Schultheiss, K Schultheiss, A A Serga, S Sharma, J M Shaw, D Suess, O Surzhenko, Krzysztof Szulc, T Taniguchi, M Urbanek, K Usami, A B Ustinov, T van der Sar, S van Dijken, V I Vasyuchka, R Verba, Viola S Kusminskiy, Q Wang, M Weides, M Weiler, S Wintz, S P Wolski, X Zhang Advances in Magnetics Roadmap on Spin-Wave Computing IEEE Trans. Magn., 58 (6), pp. 1-72, 2022, ISSN: 1941-0069. @article{9706176, title = {Advances in Magnetics Roadmap on Spin-Wave Computing}, author = {A V Chumak and P Kabos and M Wu and C Abert and C Adelmann and A O Adeyeye and J Akerman and F G Aliev and A Anane and A Awad and C H Back and A Barman and G E W Bauer and M Becherer and E N Beginin and V A S V Bittencourt and Y M Blanter and P Bortolotti and I Boventer and D A Bozhko and S A Bunyaev and J J Carmiggelt and R R Cheenikundil and F Ciubotaru and S Cotofana and G Csaba and O V Dobrovolskiy and C Dubs and M Elyasi and K G Fripp and H Fulara and I A Golovchanskiy and C Gonzalez-Ballestero and Piotr Graczyk and D Grundler and Paweł Gruszecki and G Gubbiotti and K Guslienko and A Haldar and S Hamdioui and R Hertel and B Hillebrands and T Hioki and A Houshang and C -M Hu and H Huebl and M Huth and E Iacocca and M B Jungfleisch and G N Kakazei and A Khitun and R Khymyn and T Kikkawa and M Kloui and O Klein and Jarosław W. Kłos and S Knauer and S Koraltan and M Kostylev and Maciej Krawczyk and I N Krivorotov and V V Kruglyak and D Lachance-Quirion and S Ladak and R Lebrun and Y Li and M Lindner and R Macedo and S Mayr and G A Melkov and Szymon Mieszczak and Y Nakamura and H T Nembach and A A Nikitin and S A Nikitov and V Novosad and J A Otalora and Y Otani and A Papp and B Pigeau and P Pirro and W Porod and F Porrati and H Qin and Bivas Rana and T Reimann and F Riente and O Romero-Isart and A Ross and A V Sadovnikov and A R Safin and E Saitoh and G Schmidt and H Schultheiss and K Schultheiss and A A Serga and S Sharma and J M Shaw and D Suess and O Surzhenko and Krzysztof Szulc and T Taniguchi and M Urbanek and K Usami and A B Ustinov and T van der Sar and S van Dijken and V I Vasyuchka and R Verba and Viola S Kusminskiy and Q Wang and M Weides and M Weiler and S Wintz and S P Wolski and X Zhang}, doi = {10.1109/TMAG.2022.3149664}, issn = {1941-0069}, year = {2022}, date = {2022-02-07}, journal = {IEEE Trans. Magn.}, volume = {58}, number = {6}, pages = {1-72}, abstract = {Magnonics addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operation in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors, which covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with the Boolean digital data, unconventional approaches, such as neuromorphic computing, and the progress toward magnon-based quantum computing. This article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of current challenges and the outlook of further development for each research direction.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Magnonics addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operation in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility with CMOS are just a few of many advantages offered by magnons. Although magnonics is still primarily positioned in the academic domain, the scientific and technological challenges of the field are being extensively investigated, and many proof-of-concept prototypes have already been realized in laboratories. This roadmap is a product of the collective work of many authors, which covers versatile spin-wave computing approaches, conceptual building blocks, and underlying physical phenomena. In particular, the roadmap discusses the computation operations with the Boolean digital data, unconventional approaches, such as neuromorphic computing, and the progress toward magnon-based quantum computing. This article is organized as a collection of sub-sections grouped into seven large thematic sections. Each sub-section is prepared by one or a group of authors and concludes with a brief description of current challenges and the outlook of further development for each research direction. |
2021 |
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3. | Jarosław W. Kłos, Igor L. Lyubchanskii, Maciej Krawczyk, Paweł Gruszecki, Szymon Mieszczak, Justyna Rychły, Yuliya S. Dadoenkova, Nataliya N. Dadoenkova Magnonics and Confinement of Light in Photonic–Magnonic Crystals, in Optomagnonic Structures Almpanis, Evangelos (Ed.): Chapter 2, pp. 79–134, World Scientific Publishing, Singapure, 2021, ISBN: 978-981-122-005-0. @inbook{opto-mag, title = {Magnonics and Confinement of Light in Photonic–Magnonic Crystals, in Optomagnonic Structures}, author = {Jarosław W. Kłos and Igor L. Lyubchanskii and Maciej Krawczyk and Paweł Gruszecki and Szymon Mieszczak and Justyna Rychły and Yuliya S. Dadoenkova and Nataliya N. Dadoenkova}, editor = {Evangelos Almpanis}, doi = {10.1142/9789811220050_0002}, isbn = {978-981-122-005-0}, year = {2021}, date = {2021-02-08}, pages = {79–134}, publisher = {World Scientific Publishing}, address = {Singapure}, chapter = {2}, abstract = {We discuss the spin-wave confinement in the magnetic components of magnetophotonic structures. In the initial sections of the chapter, we describe the principles of magnetization dynamics, including both the exchange and dipolar interactions. We showed that the spin-wave spectrum in confined geometry is determined not only by the spatial constraints but is also strongly influenced by non-local demagnetizing effects. In addition, we analyze the localization of light in the regions of spin-wave confinement, which can strengthen the magneto–optical interaction. Such enhancement can be potentially realized in photonic–magnonic crystals, where the light localization in magnetic components of the structure results from the periodicity and the spin waves co-exist with electromagnetic waves. The final sections are devoted to the Faraday effect and Goos–Hänchen effect in photonic–magnonic crystals.}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } We discuss the spin-wave confinement in the magnetic components of magnetophotonic structures. In the initial sections of the chapter, we describe the principles of magnetization dynamics, including both the exchange and dipolar interactions. We showed that the spin-wave spectrum in confined geometry is determined not only by the spatial constraints but is also strongly influenced by non-local demagnetizing effects. In addition, we analyze the localization of light in the regions of spin-wave confinement, which can strengthen the magneto–optical interaction. Such enhancement can be potentially realized in photonic–magnonic crystals, where the light localization in magnetic components of the structure results from the periodicity and the spin waves co-exist with electromagnetic waves. The final sections are devoted to the Faraday effect and Goos–Hänchen effect in photonic–magnonic crystals. |
2. | Nandan K. P. Babu, Aleksandra Trzaskowska, Piotr Graczyk, Grzegorz Centała, Szymon Mieszczak, Hubert Głowiński, Miłosz Zdunek, Sławomir Mielcarek, Jarosław W. Kłos Nano Lett., 21 (2), pp. 946-951, 2021. @article{doi:10.1021/acs.nanolett.0c03692, title = {The Interaction between Surface Acoustic Waves and Spin Waves: The Role of Anisotropy and Spatial Profiles of the Modes}, author = {Nandan K. P. Babu and Aleksandra Trzaskowska and Piotr Graczyk and Grzegorz Centała and Szymon Mieszczak and Hubert Głowiński and Miłosz Zdunek and Sławomir Mielcarek and Jarosław W. Kłos}, url = {https://doi.org/10.1021/acs.nanolett.0c03692}, doi = {10.1021/acs.nanolett.0c03692}, year = {2021}, date = {2021-01-01}, journal = {Nano Lett.}, volume = {21}, number = {2}, pages = {946-951}, abstract = {The interaction between different types of wave excitation in hybrid systems is usually anisotropic. Magnetoelastic coupling between surface acoustic waves and spin waves strongly depends on the direction of the external magnetic field. However, in the present study we observe that even if the orientation of the field is supportive for the coupling, the magnetoelastic interaction can be significantly reduced for surface acoustic waves with a particular profile in the direction normal to the surface at distances much smaller than the wavelength. We use Brillouin light scattering for the investigation of thermally excited phonons and magnons in a magnetostrictive CoFeB/Au multilayer deposited on a Si substrate. The experimental data are interpreted on the basis of a linearized model of interaction between surface acoustic waves and spin waves.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The interaction between different types of wave excitation in hybrid systems is usually anisotropic. Magnetoelastic coupling between surface acoustic waves and spin waves strongly depends on the direction of the external magnetic field. However, in the present study we observe that even if the orientation of the field is supportive for the coupling, the magnetoelastic interaction can be significantly reduced for surface acoustic waves with a particular profile in the direction normal to the surface at distances much smaller than the wavelength. We use Brillouin light scattering for the investigation of thermally excited phonons and magnons in a magnetostrictive CoFeB/Au multilayer deposited on a Si substrate. The experimental data are interpreted on the basis of a linearized model of interaction between surface acoustic waves and spin waves. |
2020 |
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1. | Szymon Mieszczak, Oksana Busel, Paweł Gruszecki, Andriy N Kuchko, Jarosław W. Kłos, Maciej Krawczyk Anomalous Refraction of Spin Waves as a Way to Guide Signals in Curved Magnonic Multimode Waveguides Physical Review Applied, 13 (5), pp. 054038, 2020, ISSN: 2331-7019. @article{mieszczak_anomalous_2020, title = {Anomalous Refraction of Spin Waves as a Way to Guide Signals in Curved Magnonic Multimode Waveguides}, author = {Szymon Mieszczak and Oksana Busel and Paweł Gruszecki and Andriy N Kuchko and Jarosław W. Kłos and Maciej Krawczyk}, url = {https://link.aps.org/doi/10.1103/PhysRevApplied.13.054038}, doi = {10.1103/PhysRevApplied.13.054038}, issn = {2331-7019}, year = {2020}, date = {2020-01-01}, urldate = {2021-05-04}, journal = {Physical Review Applied}, volume = {13}, number = {5}, pages = {054038}, abstract = {We present a method for efficient spin-wave guiding within the magnonic nanostructures. Our technique is based on the anomalous refraction in the metamaterial flat slab. The gradual change of the material parameters (saturation magnetization or magnetic anisotropy) across the slab allows tilting the wavefronts of the transmitted spin waves and controlling the refraction. Numerical studies of the spin-wave refraction are preceded by the analytical calculations of the phase shift acquired by the spin wave due to the change of material parameters in a confined area. We demonstrate that our findings can be used to guide the spin waves smoothly in curved waveguides, even through sharp bends, without reflection and scattering between different waveguide’s modes, preserving the phase, the quantity essential for wave computing.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present a method for efficient spin-wave guiding within the magnonic nanostructures. Our technique is based on the anomalous refraction in the metamaterial flat slab. The gradual change of the material parameters (saturation magnetization or magnetic anisotropy) across the slab allows tilting the wavefronts of the transmitted spin waves and controlling the refraction. Numerical studies of the spin-wave refraction are preceded by the analytical calculations of the phase shift acquired by the spin wave due to the change of material parameters in a confined area. We demonstrate that our findings can be used to guide the spin waves smoothly in curved waveguides, even through sharp bends, without reflection and scattering between different waveguide’s modes, preserving the phase, the quantity essential for wave computing. |