Magnetism in three-dimensionally curved geometries

Bending and twisting of two-dimensional structures into three-dimensional (3D) space can modify conventional or help discover novel functionalities in electronic, photonic, plasmonic or magnetic devices. In their recent JPhysD review article, “Magnetism in curved geometries”, Denys Makarov and co-authors discuss the emerging peculiarities in geometrically curved magnetic thin films:

These two-dimensional extended thin films are either conformally transformed into tubes, ‘Swiss rolls’ or helices, or applied to a curvature, e.g. spherical or cylindrically curved templates (see figure). The new fundamental effects in these objects are driven by the interplay between object geometry and topology of the magnetic (sub-)system. The recent developments, ranging from theoretical predictions to fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, and their characterization using integral means as well as advanced tomography approaches, are in the focus of this review.

Family of curved magnetic architectures and emergent fundamental effects.

Family of curved magnetic architectures and emergent fundamental effects. Cylindrical surfaces: Part of the image is reprinted with permission from [1]. Copyright (2015), Rights managed by Nature Publishing Group. Magnetic helices: (left panel) is reprinted with permission from [2]. Copyright (2014) American Chemical Society. (right panel) is reprinted with permission from [3]. Copyright (2011) by the American Physical Society. Spherical surfaces: (left image) is reprinted with permission from [4]. Copyright (2012) by the American Physical Society. (right image) is reprinted with permission from [5]. Copyright (2012) American Chemical Society. Massless domain walls: image is reprinted with permission from [6]. Copyright (2010) by the American Physical Society. Vortex domain wall: image is reprinted from [7] with the permission of AIP Publishing. Magnetization dynamics: image is reprinted from [8] with the permission of AIP Publishing.

Theoretical works predict a curvature-induced effective anisotropy and effective Dzyaloshinskii-Moriya interaction resulting in a vast of novel effects including magnetochiral effects (chirality symmetry breaking) and topologically-induced magnetization patterning. On the experimental side, the remarkable development of nanotechnology, e.g. preparation of high-quality extended thin films and nanowires as well as the potential to arbitrarily reshape those architectures after their fabrication, has granted first insights into the fundamental properties of 3D shaped magnetic objects. Optimizing magnetic and structural properties of these novel 3D architectures demands new investigation methods, particularly those based on vector tomographic imaging. Magnetic neutron tomography and electron-based 3D imaging, such as electron holography and vector field electron tomography, are well-established techniques to investigate macroscopic and nanoscopic samples, respectively. At the mesoscale, the curved objects e.g. Swiss rolls can be investigated using the novel method of magnetic soft X-ray tomography.

In spite of experimental challenges to address the appealing theoretical predictions of curvature-induced effects, those 3D magnetic architectures have already proven their application potential for life sciences, targeted delivery, realization of 3D spin-wave filters, and magneto-encephalography devices, to name just a few. To this end, the initially fundamental topic of magnetism in curved geometries strongly benefited from contributions by the application-oriented community, which among others explore the shapeability aspect of the curved magnetic thin films. These activities resulted in the development of shapeable magnetoelectronics [9], including flexible, printable, stretchable and even imperceptible magnetic field sensorics.

The balance between fundamental and applied stimuli to the topic of magnetism in curved geometries is quite unique and triggered the development of new theoretical methods and novel fabrication/ characterization techniques. This synergy will enable us to exceed the exploratory stage of research and paves the way towards novel device concepts, where the geometry of a magnetic thin film will play a decisive role in determining the device performance.

About the authors

Robert Streubel received his Diplom (2011) from TU Dresden and his Doctor (2015) from TU Chemnitz. After working at the IFW Dresden as Ph.D. student, he moved as a postdoctoral researcher to the Materials Sciences Division at Lawrence Berkeley National Laboratory. His research interests include three-dimensional curved magnetic geometries, their fabrication and characterization utilizing X-rays and electrons, as well as non-collinear spin textures and strain-engineering for structural and magnetic tailoring.

Peter Fischer is Acting Division Director and staff scientist at the Materials Sciences Division at Lawrence Berkeley National Laboratory, and Adjunct Professor of Physics at the University of California Santa Cruz. His research interest is in nanomagnetism and spin dynamics. He has pioneered x-ray spectromicroscopy techniques using polarized x-rays that allow him to image magnetic textures and their dynamics with high spatial and temporal resolution. His recent interest is to expand these techniques into 3-dimensional nanomagnetic system that provide increased functionality and complexity. He is Fellow of the American Physical Society (2014) and Fellow of the IEEE (2014).

Florian Kronast is head of the Photoemission Electron Microscopy (PEEM) group at Helmholtz-Zentrum für Materialien und Energie, Berlin, Germany. His research interests include magnetic imaging and photoelectron spectroscopy, as well as magnetization dynamics in thin films and nanostructures.

Volodymyr P. Kravchuk is a senior researcher in Bogolyubov Institute for Theoretical Physics of National Academy of Sciences of Ukraine. Scientific interests are in physics of topologically nontrivial magnetization structures (domain walls, magnetic vortices, skyrmions) in nanomagnets. The recent interests are focused on curvilinear low-dimensional magnetic systems — curvilinear films and nanowires.

Denis D. Sheka is a Professor of Theoretical Physics at the Taras Shevchenko National University of Kyiv (Ukraine). His research interests include nonlinear phenomena, topological and curvature effects in nanomagnets.

Yuri Gaididei is a head of the department “Theory of nonlinear processes in condensed media” at the Bogolyubov institute for theoretical physics (Kiev,Ukraine). His research interest is in nonlinear condensed matter physics. His recent interest to study nonlinear excitations and pattern formation in systems with complicated and flexible geometry.

Oliver G. Schmidt is Director of the Institute for Integrative Nanosciences at the Leibniz IFW Dresden, Germany, and holds a full Professorship for Material Systems for Nanoelectronics at the TU Chemnitz, Germany. His interdisciplinary activities bridge several research fields in the nanosciences, ranging from photonics and magnetoelectronics to energy storage, robotics and biomedical applications. He has received several awards: the Otto-Hahn Medal from the Max-Planck-Society in 2000, the Philip-Morris Research Award in 2002 and the Carus-Medal from the German Academy of Natural Scientists Leopoldina in 2005. In 2011, he became Honorary Professor at Fudan University, Shanghai, China, and he received the International Dresden Barkhausen Award 2013 for his work on “Materials, Architectures and Integration of Nanomembranes”.

Denys Makarov is head of the ERC group “Shapeable magnetoelectronics” and head of the research group “Intelligent materials and devices” at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Germany. His work is influential for the topic of magnetism on curved surfaces and opened up new research field of spintronics on flexible, bendable and stretchable surfaces.


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The Figure is not under the above licence, and is as follows: Family of curved magnetic architectures and emergent fundamental effects. Cylindrical surfaces: Part of the image is reprinted with permission from [1]. Copyright (2015), Rights managed by Nature Publishing Group. Magnetic helices: (left panel) is reprinted with permission from [2]. Copyright (2014) American Chemical Society. (right panel) is reprinted with permission from [3]. Copyright (2011) by the American Physical Society. Spherical surfaces: (left image) is reprinted with permission from [4]. Copyright (2012) by the American Physical Society. (right image) is reprinted with permission from [5]. Copyright (2012) American Chemical Society. Massless domain walls: image is reprinted with permission from [6]. Copyright (2010) by the American Physical Society. Vortex domain wall: image is reprinted from [7] with the permission of AIP Publishing. Magnetization dynamics: image is reprinted from [8] with the permission of AIP Publishing.

[1] Streubel R, Kronast F, Fischer P, Parkinson D, Schmidt O G and Makarov D 2015 Nat. Comms 6 7612 © Nature Publishing Group

[2] Phatak C, Liu Y, Gulsoy E B, Schmidt D, Franke-Schubert E and Petford-Long A 2014 Nano Letters 14 759–764 © American Chemical Society

[3] Smith E J, Makarov D, Sanchez S, Fomin V M and Schmidt O G 2011 Phys. Rev. Lett. 107 (9) 097204 © American Physical Society

[4] Kravchuk V P, Sheka D D, Streubel R, Makarov D, Schmidt O G and Gaididei Y 2012 Phys. Rev. B 85 (14) 144433 © American Physical Society

[5] Baraban L, Makarov D, Streubel R, Mönch I, Grimm D, Sanchez S and Schmidt O G 2012 ACS Nano 6 3383–3389 © American Chemical Society

[6] Yan M, Kákay A, Gliga S and Hertel R 2010 Phys. Rev. Lett. 104 057201 © American Physical Society

[7] Otálora J, López-López J, Vargas P and Landeros P 2012 Appl. Phys. Lett. 100 072407 © AIP Publishing

[8] Sloika M I, Kravchuk V P, Sheka D D and Gaididei Y 2014 Appl. Phys. Lett. 104 252403 © AIP Publishing

[9] Makarov D, Melzer M, Karnaushenko D and Schmidt O G 2016 Appl. Phys. Rev. 3 011101



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