Spin-wave phase inverter upon a single nanodefect

Local modification of magnetic properties of nanoelements is a key to design future-generation magnonic devices, in which information is carried and processed via spin waves. One of the biggest challenges here is to fabricate simple and miniature phase-controlling elements with broad tunability. Here, we successfully realize such spin-wave phase shifter upon a single nanogroove milled by focused ion beam in a Co-Fe microsized magnonic waveguide. By varying the groove depth and the in-plane bias magnetic field we continuously tune the spin-wave phase and experimentally evidence a complete phase inversion. The microscopic mechanism of the phase shift is based on the combined action of the nanogroove as a geometrical defect and the lower spin-wave group velocity in the waveguide under the groove where the magnetization is reduced due to the incorporation of Ga ions during the ion-beam milling. The proposed phase shifter can easily be on-chip integrated with spin-wave logic gates and other magnonic devices. Our findings are crucial for designing nano-magnonic circuits and for the development of spin-wave nano-optics.Comment: 8 pages, 6 figure

Transitivity of implicative aBE algebras

We prove that every implicative aBE algebra satisfies the transitivity property. This means that every implicative aBE algebra is a Tarski algebra, and thus is also a commutative BCK algebra

Remagnetization and magnetization dynamics in complex magnetic textures, from antidots lattice to nanodots

Wydział FizykiLokalne zaburzenie uporządkowania magnetycznego, które może rozprzestrzeniać się w postaci fali w materiale magnetycznym, zostało przewidziane przez Blocha w 1929 roku i nazwane falą spinową. Periodycznie strukturyzowane układy magnoniczne są sztucznymi ośrodkami o okresowo modulowanych właściwościach magnetycznych, zwane kryształami magnonicznymi. W takich strukturach można znaleźć skomplikowane tekstury magnetyczne takie jak domeny magnetyczne, worteksy czy skyrmiony. Skyrmion jest kwazicząsteczką, charakteryzującą się tzw. ładunkiem topologicznym, będącą możliwie najmniejszym i jednocześnie stabilnym zakłóceniem jednorodnego namagnesowania. W ramach pracy doktorskiej autor zaprezentował pięć publikacji naukowych zawierających wyniki badań: procesów przemagnesowania, rezonansu ferromagnetycznego, propagacji fal spinowych w strukturalizowanych materiałach ferromagnetycznych; stabilizacji skyrmionów w nanokropkach magnetycznych w których możliwe jest istnienie dwóch stanów skyrmionowych (skyrmionu o małej i dużej średnicy) o zbliżonych poziomach energetycznych; badania możliwości formowania skyrmionów w sieci kwadratowej dziur w trakcie procesu przemagnesowania; badania sieci dziur w wielowarstwach ferromagnetycznych z prostopadłą anizotropią, w których zaobserwowano skomplikowaną teksturę magnetyczną. W ostatnim rozdziale doktoratu autor zaprezentował podsumowanie, plany badawcze oraz krótkie zestawienie innych osiągnięć naukowych.Bloch predicted a disturbance in the local magnetic order which can propagate in a magnetic material in a form of wave in 1929. It named as a spin wave since it is related to a collective excitation of the spins in ferromagnetic media. Magnonic crystals are artificial magnetic media with periodically modulated magnetic properties in space, well known as a structure where spin waves band structure consists of intervals of allowed bands of spin-wave frequencies and forbidden band gaps, making them structures with interesting properties. Magnetic skyrmions are solitonic magnetisation textures, whose stability is protected by their topology. In this thesis, the author presents the results of studying the static and dynamic properties of the complex ferromagnetic structures and unique skyrmion properties. The author studied magnetisation textures in patterned thin films during the remagnetisation process. In the next step, he studied the ferromagnetic resonance and characteristic of propagating spin-waves in the same structures. Then, he started investigations of skyrmion stabilisation in nanodisc and skyrmion nucleation process in antidot lattice during the remagnetisation process. Finally, he analysed the complex magnetic textures in patterned multilayers with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction.Various parts of the presented thesis were supported by the Polish National Science Centre (NCN), Ministry of Science and Higher Education (MNiSW), and European Union Horizon 2020 and other: 1. NCN PRELUDIUM 14, Grant No. 2018/31/N/ST7/03918 (PI), 2. NCN SONATA BIS 2 (2013-2018), Grant No. 2012/07/ST3/00538. 3. EU Horizon 2020 project MagIC Grant No. 644348, 4. Scholarship founded by Adam Mickiewicz University Foundation, 5. Scholarship founded by dr Jan Kulczyk Foundation, 6. OPUS11 (2017-2019), Grant No. 2016/21/B/ST3/00452, 7. OPUS9 (2016-2019), Grant No. 2015/17/B/ST3/00118, 8. "Premia na Horyzoncie" - MNiSW Grant No. 328712/PnH/2016, 9. National Scholarship Program of the Slovak Republic funded by the Ministry of Education, Science, Research, and Sport of the Slovak Republic (two scholarships in 2016/2017 and 2017/2018), 10. The simulations were partially performed at the Poznan Supercomputing and Networking Center (Grant No. 398)

The reproducing kernel of the Fourier symmetric Sobolev space

By showing the unitarity of the Bargmann transform between the Fourier symmetric Sobolev space $\mathcal{H}$ consisting of functions $f\in L^2(\mathbb{R})$ such that $\| f \|^2_{\mathcal{H}} = \int_{\mathbb{R}} |f(x)|^2(1+x^2) dx + \int_{\mathbb{R}} |\hat{f}(\xi)|^2(1+\xi^2) d\xi < \infty$ and the corresponding Fock space, we find an orthonormal basis of $\mathcal{H}$. This allows us to find the reproducing kernel of $\mathcal{H}$, which is expected to be useful in e.g. the area of Fourier interpolation

On Traczyk's BCK-sequences

BCK-sequences and n-commutative BCK-algebras were introduced by T. Traczyk, together with two related problems. The first one, whether BCK-sequences are always prolongable. The second one, if the class of all n-commutative BCK-algebras is characterised by one identity. W. A. Dudek proved that the answer to the former question is positive in some special cases, e.g. when BCK-algebra is linearly ordered. T. Traczyk showed that the answer to the latter is affirmative for n = 1, 2. Nonetheless, by providing counterexamples, we proved that the answers to both those open problems are negative