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This article discusses the physical and mathematical background of phase contrast imaging with in‑line electron holography from a physics rather than a microscopy perspective and showcases the strength of non‑iterative and iterative approaches by application to magnetism research. A comprehensive derivation of magnetic and electric phase shift due to electromagnetic interaction with matter and electron wave propagation is presented as the foundation for phase retrieval algorithms based on the transport‑of‑intensity equation and Gerchberg–Saxton—an iterative exit wave reconstruction algorithm. The strength and potential of both algorithms are highlighted by experimental and numerical quantitative comparison using non‑collinear spin textures. Although the focus of this work is on magnetism research, the indifference of the exit wave reconstruction to the origin of the phase shift ensures applicability to study spatial variations in both electric and spin distributions in quantum, energy, and magnetic materials. 

Abstract We study the effect of strain on the magnetic properties and magnetization configurations in nanogranular Fe_xGe ${}_{1-x}$films ( $x=0.53\pm 0.05$) with and without B20 FeGe nanocrystals surrounded by an amorphous structure. Relaxed films on amorphous silicon nitride membranes reveal a disordered skyrmion phase while films near and on top of a rigid substrate favor ferromagnetism and an anisotropic hybridization of Fedlevels and spin-polarized Gespband states. The weakly coupled topological states emerge at room temperature and become more abundant at cryogenic temperatures without showing indications of pinning at defects or confinement to individual grains. These results demonstrate the possibility to control magnetic exchange and topological magnetism by strain and inform magnetoelasticity-mediated voltage control of topological phases in amorphous quantum materials. 

Abstract The transition from planar to three-dimensional (3D) magnetic nanostructures represents a significant advancement in both fundamental research and practical applications, offering vast potential for next-generation technologies like ultrahigh-density storage, memory, logic, and neuromorphic computing. Despite being a relatively new field, the emergence of 3D nanomagnetism presents numerous opportunities for innovation, prompting the creation of a comprehensive roadmap by leading international researchers. This roadmap aims to facilitate collaboration and interdisciplinary dialogue to address challenges in materials science, physics, engineering, and computing. The roadmap comprises eighteen sections, roughly divided into three blocks. The first block explores the fundamentals of 3D nanomagnetism, focusing on recent trends in fabrication techniques and imaging methods crucial for understanding complex spin textures, curved surfaces, and small-scale interactions. Techniques such as two-photon lithography and focused electron beam-induced deposition enable the creation of intricate 3D architectures, while advanced imaging methods like electron holography and synchrotron x-ray tomography provide nanoscale spatial resolution for studying magnetization dynamics in three dimensions. Various 3D magnetic systems, including coupled multilayer systems, artificial spin-ice, magneto-plasmonic systems, topological spin textures, and molecular magnets are discussed. The second block introduces analytical and numerical methods for investigating 3D nanomagnetic structures and curvilinear systems, highlighting geometrically curved architectures, interconnected nanowire systems, and other complex geometries. Finite element methods are emphasized for capturing complex geometries, along with direct frequency domain solutions for addressing magnonic problems. The final block focuses on 3D magnonic crystals and networks, exploring their fundamental properties and potential applications in magnonic circuits, memory, and spintronics. Computational approaches using 3D nanomagnetic systems and complex topological textures in 3D spintronics are highlighted for their potential to enable faster and more energy-efficient computing. 

Abstract We study the influence of defects in Co/Pt multilayers on the room-temperature magnetization reversal and relaxation mechanisms via angle-dependent magnetic viscosity and coercive field measurements. The data reveal a transition from pinning-dominated domain wall propagation to a sequence of pinning-dominated and uniform switching, with increasing tilt away from the normal direction. The leading role of the dendritic domain wall propagation in the nanogranular exchange-coupled films is corroborated by the scaling of relaxation times, the angular dependence of the coercive field, and Kerr microscopy. 

A chiral 3D coordination compound, [Gd 2 (L) 2 (ox) 2 (H 2 O) 2 ], arranged around a dinuclear Gd unit has been characterized by X-ray photoemission and X-ray absorption measurements in the context of density functional theory studies. Core level photoemission of the Gd 5p multiplet splittings indicates that spin orbit coupling dominates over j–J coupling evident in the 5p core level spectra of Gd metal. Indications of spin–orbit coupling are consistent with the absence of inversion symmetry due to the ligand field. Density functional theory predicts antiferromagnet alignment of the Gd 2 dimers and a band gap of the compound consistent with optical absorption. 

Abstract Metal-organic decomposition epitaxy is an economical wet-chemical approach suitable to synthesize high-quality low-spin-damping films for resonator and oscillator applications. This work reports the temperature dependence of ferromagnetic resonances and associated structural and magnetic quantities of yttrium iron garnet nanofilms that coincide with single-crystal values. Despite imperfections originating from wet-chemical deposition and spin coating, the quality factor for out-of-plane and in-plane resonances approaches 600 and 1000, respectively, at room temperature and 40 GHz. These values increase with temperature and are 100 times larger than those offered by commercial devices based on complementary metal-oxide semiconductor voltage-controlled oscillators at comparable production costs. 

Abstract Adding Fe₃O₄nanoparticles to composites of [Fe(Htrz)₂(trz)](BF₄) spin-crossover polymer and polyaniline (PANI) drives a phase separation of both and restores the molecular structure and cooperative effects of the spin-crossover polymer without compromising the increased conductivity gained through the addition of PANI. We observe an increased on-off ratio for the DC conductivity owing to an enlarged off state resistivity and a 20 times larger AC conductivity of the on state compared with DC values. The Fe₃O₄nanoparticles, primarily confined to the [Fe(Htrz)₂(trz)](BF₄) phase, are ferromagnetically coupled to the local moment of the spin-crossover molecule suggesting the existence of an exchange interaction between both components. 

Few-layered HfS₃nanoribbons exhibit n-type conductivity and a large photoresponse to visible light. The photocurrent strongly depends on the polarization direction of the excitation laser due to the highly anisotropic quasi-1D crystal structure of HfS₃.