Curvature-induced effects in magnetic nanostructures

• Applicants: Professor Dr. Michael Huth; Dr. Attila Kakay; Dr. Denys Makarov
• Subject Area: Experimental Condensed Matter Physics
• Term: from 2020 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 444929866

• Final Report Year: 2025

Final Report Abstract

The behaviour of any physical system is determined by its order parameter, whose distribution is governed by the geometry of the physical space - its dimensionality and curvature. Extending 2D structures into 3D space has become a general trend in multiple disciplines, providing means to modify conventional functionalities or launch novel ones by tailoring the curvature and 3D shape of magnetic thin films and nanowires. The main objective of this project was to adapt novel routes for fabricating geometrically curved magnetic shells at the low micrometer and sub-µm scale, as well as to characterize complex magnetic states and their dynamics both experimentally and using micromagnetic simulations. The methodologies and outcomes achieved in this project have significantly advanced the capabilities of focussed electron beam induced deposition (FEBID) for 3D nanofabrication and functional material synthesis. From fast growth simulations to site-selective heterostructures, and from precursor parameter refinement to magnetic excitation studies, the results obtained not only address fundamental questions but also open avenues for practical applications in magnetics and magnonics. We identified that conventional micromagnetic simulations are ill-suited for investigating spin waves in FEBID-created waveguides with curved shells. We addressed this challenge by developing a finite-element dynamic-matrix approach, which allows for direct comparison of simulations with standard ferromagnetic resonance or time-resolved synchrotron measurements. The suite of numerical methods has been released as the open-source micromagnetic modeling software package TetraX, which is used by several research groups as a primary numerical tool to study spin-wave dynamics. We combined theory, simulations and experimental explorations to demonstrate constraints imposed by the topology of an object (sphere, torus, N-torus) on the vector field of magnetization. We applied FEBID to prepare magnetic wireframes homotopic to a sphere and N-torus hosting magnetic vortices and antivortices. We identified that in 3D geometries, the prevailing type of magnetic solitons is antivortices, which cannot annihilate upon interaction. Hence, they are attractive for implementation of reservoir, neuromorphic and magnonic-based computing. Furthermore, we validated the concept of nonlocal chiral symmetry break and demonstrated its difference to the known local chiral effects like Dzyaloshinskii–Moriya interaction (DMI). In contrast to the DMI leading to a twist of a texture, nonlocal chiral symmetry break allows to deform the texture, enables textures with multiple magnetochiral parameters and leads to their coupling. These results are summarized in 46 publications and presented as 27 talks. Our achievements pave the way for follow-up projects to further explore the broader implications of curvature-induced phenomena in 3D nanostructures.

Link to the final report

https://doi.org/10.34657/23702

Publications

• New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures. Advanced Materials, 34(3).
  Makarov, Denys; Volkov, Oleksii M.; Kákay, Attila; Pylypovskyi, Oleksandr V.; Budinská, Barbora & Dobrovolskiy, Oleksandr V.
  
• Spin-wave eigenmodes in direct-write 3D nanovolcanoes. Applied Physics Letters, 118(13).
  Dobrovolskiy, O. V.; Vovk, N. R.; Bondarenko, A. V.; Bunyaev, S. A.; Lamb-Camarena, S.; Zenbaa, N.; Sachser, R.; Barth, S.; Guslienko, K. Y.; Chumak, A. V.; Huth, M. & Kakazei, G. N.
  
• Curvilinear Micromagnetism. Topics in Applied Physics. Springer International Publishing.
  Makarov, Denys & Sheka, Denis D.
  
• 3D Magnonic Conduits by Direct Write Nanofabrication. Nanomaterials, 13(13), 1926.
  Lamb-Camarena, Sebastian; Porrati, Fabrizio; Kuprava, Alexander; Wang, Qi; Urbánek, Michal; Barth, Sven; Makarov, Denys; Huth, Michael & Dobrovolskiy, Oleksandr V.
  
• Site-Selective Chemical Vapor Deposition on Direct-Write 3D Nanoarchitectures. ACS Nano, 17(5), 4704-4715.
  Porrati, Fabrizio; Barth, Sven; Gazzadi, Gian Carlo; Frabboni, Stefano; Volkov, Oleksii M.; Makarov, Denys & Huth, Michael
  
• Three-dimensional magnetic nanotextures with high-order vorticity in soft magnetic wireframes. Nature Communications, 15(1).
  Volkov, Oleksii M.; Pylypovskyi, Oleksandr V.; Porrati, Fabrizio; Kronast, Florian; Fernandez-Roldan, Jose A.; Kákay, Attila; Kuprava, Alexander; Barth, Sven; Rybakov, Filipp N.; Eriksson, Olle; Lamb-Camarena, Sebastian; Makushko, Pavlo; Mawass, Mohamad-Assaad; Shakeel, Shahrukh; Dobrovolskiy, Oleksandr V.; Huth, Michael & Makarov, Denys
  
• 2025 roadmap on 3D nanomagnetism. Journal of Physics: Condensed Matter, 37(14), 143502.
  Gubbiotti, Gianluca; Barman, Anjan; Ladak, Sam; Bran, Cristina; Grundler, Dirk; Huth, Michael; Plank, Harald; Schmidt, Georg; van Dijken, Sebastiaan; Streubel, Robert; Dobrovoloskiy, Oleksandr; Scagnoli, Valerio; Heyderman, Laura; Donnelly, Claire; Hellwig, Olav; Fallarino, Lorenzo; Jungfleisch, M. Benjamin; Farhan, Alan; Maccaferri, Nicolò ... & Fernández-Pacheco, Amalio