Magnetic Characterization of Direct-Write Free-Form Building Blocks for Artificial Magnetic 3D Lattices

Three-dimensional magnetic nanotextures with high-order vorticity in soft magnetic wireframes

Additive nanotechnology enable curvilinear and three-dimensional (3D) magnetic architectures with tunable topology and functionalities surpassing their planar counterparts. Here, we experimentally reveal that 3D soft magnetic wireframe structures resemble compact manifolds and accommodate magnetic textures of high order vorticity determined by the Euler characteristic, χ. We demonstrate that self-standing magnetic tetrapods (homeomorphic to a sphere; χ = + 2) support six surface topological solitons, namely four vortices and two antivortices, with a total vorticity of + 2 equal to its Euler characteristic. Alternatively, wireframe structures with one loop (homeomorphic to a torus; χ = 0) possess equal number of vortices and antivortices, which is relevant for spin-wave splitters and 3D magnonics. Subsequent introduction of n holes into the wireframe geometry (homeomorphic to an n-torus; χ < 0) enables the accommodation of a virtually unlimited number of antivortices, which suggests their usefulness for non-conventional (e.g., reservoir) computation. Furthermore, complex stray-field topologies around these objects are of interest for superconducting electronics, particle trapping and biomedical applications.

Magnetic characterization techniques and micromagnetic simulations of magnetic nanostructures: from zero to three dimensions

The investigation of the magnetic characteristics of magnetic nanostructures (MNs) in various dimensions is a crucial direction of research in nanomagnetism, with MNs belonging to various dimensions exhibiting magnetic properties related to their geometry. A better understanding of these magnetic properties is required for MN manipulation. The primary tools for researching MNs are magnetic characterisation techniques with great spatial resolution and spin sensitivity. Micromagnetic simulation is another technique that minimises experimental costs, while providing information on the magnetic structure and magnetic behaviour, and has enormous potential for predicting, validating, and extending the magnetic characterisation results. This review first looks at the progress of research into quantitatively characterising the magnetic properties of low-dimensional (including 0D, 1D, and 2D) and 3D MNs in two directions: magnetic characterisation techniques and micromagnetic simulations, with a particular emphasis on the potential for future applications of these techniques. Single magnetic characterization techniques, single micromagnetic simulations, or a mix of both are utilised in these research studies to investigate MNs in a variety of dimensions. How the magnetic characterisation techniques and micromagnetic simulations can be better applied to MNs in various dimensions is then outlined. This discussion has significant application potential for low-dimensional and 3D MNs.

Additive Manufacturing of Co3Fe Nano-Probes for Magnetic Force Microscopy

Magnetic force microscopy (MFM) is a powerful extension of atomic force microscopy (AFM), which mostly uses nano-probes with functional coatings for studying magnetic surface features. Although well established, additional layers inherently increase apex radii, which reduce lateral resolution and also contain the risk of delamination, rendering such nano-probes doubtful or even useless. To overcome these limitations, we now introduce the additive direct-write fabrication of magnetic nano-cones via focused electron beam-induced deposition (FEBID) using an HCo₃Fe(CO)₁₂ precursor. The study first identifies a proper 3D design, confines the most relevant process parameters by means of primary electron energy and beam currents, and evaluates post-growth procedures as well. That way, highly crystalline nano-tips with minimal surface contamination and apex radii in the sub-15 nm regime are fabricated and benchmarked against commercial products. The results not only reveal a very high performance during MFM operation but in particular demonstrate virtually loss-free behavior after almost 8 h of continuous operation, thanks to the all-metal character. Even after more than 12 months of storage in ambient conditions, no performance loss is observed, which underlines the high overall performance of the here-introduced FEBID-based Co₃Fe MFM nano-probes.

Fundamentals of Curvilinear Ferromagnetism: Statics and Dynamics of Geometrically Curved Wires and Narrow Ribbons

Low-dimensional magnetic architectures including wires and thin films are key enablers of prospective ultrafast and energy efficient memory, logic, and sensor devices relying on spin-orbitronic and magnonic concepts. Curvilinear magnetism emerged as a novel approach in material science, which allows tailoring of the fundamental anisotropic and chiral responses relying on the geometrical curvature of magnetic architectures. Much attention is dedicated to magnetic wires of Möbius, helical, or DNA-like double helical shapes, which act as prototypical objects for the exploration of the fundamentals of curvilinear magnetism. Although there is a bulk number of original publications covering fabrication, characterization, and theory of magnetic wires, there is no comprehensive review of the theoretical framework of how to describe these architectures. Here, theoretical activities on the topic of curvilinear magnetic wires and narrow nanoribbons are summarized, providing a systematic review of the emergent interactions and novel physical effects caused by the curvature. Prospective research directions of curvilinear spintronics and spin-orbitronics are discussed, the fundamental framework for curvilinear magnonics are outlined, and mechanically flexible curvilinear architectures for soft robotics are introduced.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Focused-Electron-Beam Engineering of 3D Magnetic Nanowires

Focused-electron-beam-induced deposition (FEBID) is the ultimate additive nanofabrication technique for the growth of 3D nanostructures. In the field of nanomagnetism and its technological applications, FEBID could be a viable solution to produce future high-density, low-power, fast nanoelectronic devices based on the domain wall conduit in 3D nanomagnets. While FEBID has demonstrated the flexibility to produce 3D nanostructures with almost any shape and geometry, the basic physical properties of these out-of-plane deposits are often seriously degraded from their bulk counterparts due to the presence of contaminants. This work reviews the experimental efforts to understand and control the physical processes involved in 3D FEBID growth of nanomagnets. Co and Fe FEBID straight vertical nanowires have been used as benchmark geometry to tailor their dimensions, microstructure, composition and magnetism by smartly tuning the growth parameters, post-growth purification treatments and heterostructuring.

High-Fidelity 3D Nanoprinting of Plasmonic Gold Nanoantennas

The direct-write fabrication of freestanding nanoantennas for plasmonic applications is a challenging task, as demands for overall morphologies, nanoscale features, and material qualities are very high. Within the small pool of capable technologies, three-dimensional (3D) nanoprinting via focused electron beam-induced deposition (FEBID) is a promising candidate due to its design flexibility. As FEBID materials notoriously suffer from high carbon contents, the chemical postgrowth transfer into pure metals is indispensably needed, which can severely harm or even destroy FEBID-based 3D nanoarchitectures. Following this challenge, we first dissect FEBID growth characteristics and then combine individual advantages by an advanced patterning approach. This allows the direct-write fabrication of high-fidelity shapes with nanoscale features in the sub-10 nm range, which allow a shape-stable chemical transfer into plasmonically active Au nanoantennas. The here-introduced strategy is a generic approach toward more complex 3D architectures for future applications in the field of 3D plasmonics.

Writing 3D Nanomagnets Using Focused Electron Beams

Focused electron beam induced deposition (FEBID) is a direct-write nanofabrication technique able to pattern three-dimensional magnetic nanostructures at resolutions comparable to the characteristic magnetic length scales. FEBID is thus a powerful tool for 3D nanomagnetism which enables unique fundamental studies involving complex 3D geometries, as well as nano-prototyping and specialized applications compatible with low throughputs. In this focused review, we discuss recent developments of this technique for applications in 3D nanomagnetism, namely the substantial progress on FEBID computational methods, and new routes followed to tune the magnetic properties of ferromagnetic FEBID materials. We also review a selection of recent works involving FEBID 3D nanostructures in areas such as scanning probe microscopy sensing, magnetic frustration phenomena, curvilinear magnetism, magnonics and fluxonics, offering a wide perspective of the important role FEBID is likely to have in the coming years in the study of new phenomena involving 3D magnetic nanostructures.

Focused Electron Beam-Based 3D Nanoprinting for Scanning Probe Microscopy: A Review

Scanning probe microscopy (SPM) has become an essential surface characterization technique in research and development. By concept, SPM performance crucially depends on the quality of the nano-probe element, in particular, the apex radius. Now, with the development of advanced SPM modes beyond morphology mapping, new challenges have emerged regarding the design, morphology, function, and reliability of nano-probes. To tackle these challenges, versatile fabrication methods for precise nano-fabrication are needed. Aside from well-established technologies for SPM nano-probe fabrication, focused electron beam-induced deposition (FEBID) has become increasingly relevant in recent years, with the demonstration of controlled 3D nanoscale deposition and tailored deposit chemistry. Moreover, FEBID is compatible with practically any given surface morphology. In this review article, we introduce the technology, with a focus on the most relevant demands (shapes, feature size, materials and functionalities, substrate demands, and scalability), discuss the opportunities and challenges, and rationalize how those can be useful for advanced SPM applications. As will be shown, FEBID is an ideal tool for fabrication / modification and rapid prototyping of SPM-tipswith the potential to scale up industrially relevant manufacturing.

Temperature-Dependent Growth Characteristics of Nb- and CoFe-Based Nanostructures by Direct-Write Using Focused Electron Beam-Induced Deposition

Focused electron and ion beam-induced deposition (FEBID/FIBID) are direct-write techniques with particular advantages in three-dimensional (3D) fabrication of ferromagnetic or superconducting nanostructures. Recently, two novel precursors, HCo3Fe(CO)12 and Nb(NMe3)2(N-t-Bu), were introduced, resulting in fully metallic CoFe ferromagnetic alloys by FEBID and superconducting NbC by FIBID, respectively. In order to properly define the writing strategy for the fabrication of 3D structures using these precursors, their temperature-dependent average residence time on the substrate and growing deposit needs to be known. This is a prerequisite for employing the simulation-guided 3D computer aided design (CAD) approach to FEBID/FIBID, which was introduced recently. We fabricated a series of rectangular-shaped deposits by FEBID at different substrate temperatures between 5 °C and 24 °C using the precursors and extracted the activation energy for precursor desorption and the pre-exponential factor from the measured heights of the deposits using the continuum growth model of FEBID based on the reaction-diffusion equation for the adsorbed precursor.

Diameter modulation of 3D nanostructures in focused electron beam induced deposition using local electric fields and beam defocus

Focused electron beam induced deposition (FEBID) is a leading nanolithography technique in terms of resolution and the capability for three-dimensional (3D) growth of functional nanostructures. However, FEBID still presents some limitations with respect to the precise control of the dimensions of the grown nano-objects as well as its use on insulating substrates. In the present work, we overcome both limitations by employing electrically-biased metal structures patterned on the surface of insulating substrates. Such patterned metal structures serve for charge dissipation and also allow the application of spatially-dependent electric fields. We demonstrate that such electric fields can dramatically change the dimensions of the growing 3D nanostructures by acting on the primary electron beam and the generated secondary electrons. In the performed experiments, the diameter of Pt-C and W-C vertical nanowires grown on quartz, MgO and amorphous SiO₂ is tuned by application of moderate voltages (up to 200 V) on the patterned metal microstructures during growth, achieving diameters as small as 50 nm. We identify two competing effects arising from the generated electric fields: a slight change in the primary beam focus point and a strong action on the secondary electrons. Beam defocus is exploited to achieve the in situ modulation of the diameter of 3D FEBID structures during growth.

High Volume-Per-Dose and Low Resistivity of Cobalt Nanowires Grown by Ga+ Focused Ion Beam Induced Deposition

The growth of ferromagnetic nanostructures by means of focused-Ga+-beam-induced deposition (Ga+-FIBID) using the Co2(CO)8 precursor has been systematically investigated. The work aimed to obtain growth conditions allowing for the simultaneous occurrence of high growth speed, good lateral resolution, low electrical resistivity, and ferromagnetic behavior. As a first result, it has been found that the competition between deposition and milling that is produced by the Ga+ beam is a limiting factor. In our working conditions, with the maximum available precursor flux, the maximum deposit thickness has been found to be 65 nm. The obtained volumetric growth rate is at least 50 times higher than in the case of deposition by focused-electron-beam-induced deposition. The lateral resolution of the deposits can be as good as 50 nm while using Ga+-beam currents lower than 10 pA. The high metallic content of the as-grown deposits gives rise to a low electrical resistivity, within the range 20-40 µΩ·cm. Magnetic measurements confirm the ferromagnetic nature of the deposits at room temperature. In conclusion, the set of obtained results indicates that the growth of functional ferromagnetic nanostructures by Ga+-FIBID while using the Co2(CO)8 precursor is a viable and competitive technique when compared to related nanofabrication techniques.

Three-Dimensional Nanothermistors for Thermal Probing

Accessing the thermal properties of materials or even full devices is a highly relevant topic in research and development. Along with the ongoing trend toward smaller feature sizes, the demands on appropriate instrumentation to access surface temperatures with high thermal and lateral resolution also increase. Scanning thermal microscopy is one of the most powerful technologies to fulfill this task down to the sub-100 nm regime, which, however, strongly depends on the nanoprobe design. In this study, we introduce a three-dimensional (3D) nanoprobe concept, which acts as a nanothermistor to access surface temperatures. Fabrication of nanobridges is done via 3D nanoprinting using focused electron beams, which allows direct-write fabrication on prestructured, self-sensing cantilever. As individual branch dimensions are in the sub-100 nm regime, mechanical stability is first studied by a combined approach of finite-element simulation and scanning electron microscopy-assisted in situ atomic force microscopy (AFM) measurements. After deriving the design rules for mechanically stable 3D nanobridges with vertical stiffness up to 50 N m^-1, a material tuning approach is introduced to increase mechanical wear resistance at the tip apex for high-quality AFM imaging at high scan speeds. Finally, we demonstrate the electrical response in dependence of temperature and find a negative temperature coefficient of -(0.75 ± 0.2) 10^-3 K^-1 and sensing rates of 30 ± 1 ms K^-1 at noise levels of ±0.5 K, which underlines the potential of our concept.

Impact of Electron-Beam Heating during 3D Nanoprinting

An artifact limiting the reproduction of three-dimensional (3D) designs using nanoprinting has been quantified. Beam-induced heating was determined through complementary experiments, models, and simulations to affect the deposition rate during the 3D nanoprinting of mesh objects using focused electron beam induced deposition (FEBID). The mesh objects are constructed using interconnected nanowires. During nanowire growth, the beam interaction driving deposition also causes local heating. The temperature at the beam impact region progressively rises as thermal resistance increases with nanowire growth. Heat dissipation resembles the classical mode of heat transfer from extended surfaces; heat must flow through the mesh object to reach the substrate sink. Simulations reveal that beam heating causes an increase in the rate of precursor desorption at the BIR, causing a concomitant decrease in the deposition rate, overwhelming an increase in the deposition rate driven by thermally enhanced precursor surface diffusion. Temperature changes as small as 10 K produce noticeable changes in deposit geometry; nanowires appear to deflect and curve toward the substrate because the vertical growth rate decreases. The 3D FEBID naturally ensues from the substrate surface upward, inducing a vertical temperature gradient along the deposit. Simulations, experiments, temperature-controlled studies, and process current monitoring all confirm the cause of nanowire distortion as beam-induced heating while also revealing the rate-determining physics governing the final deposit shape.

Pattern generation for direct-write three-dimensional nanoscale structures via focused electron beam induced deposition

Fabrication of three-dimensional (3D) nanoarchitectures by focused electron beam induced deposition (FEBID) has matured to a level that highly complex and functional deposits are becoming available for nanomagnetics and plasmonics. However, the generation of suitable pattern files that control the electron beam's movement, and thereby reliably map the desired target 3D structure from a purely geometrical description to a shape-conforming 3D deposit, is nontrivial. To address this issue we developed several writing strategies and associated algorithms implemented in C++. Our pattern file generator handles different proximity effects and corrects for height-dependent precursor coverage. Several examples of successful 3D nanoarchitectures using different precursors are presented that validate the effectiveness of the implementation.

Direct-write of free-form building blocks for artificial magnetic 3D lattices

By the fabrication of periodically arranged nanomagnetic systems it is possible to engineer novel physical properties by realizing artificial lattice geometries that are not accessible via natural crystallization or chemical synthesis. This has been accomplished with great success in two dimensions in the fields of artificial spin ice and magnetic logic devices, to name just two. Although first proposals have been made to advance into three dimensions (3D), established nanofabrication pathways based on electron beam lithography have not been adapted to obtain free-form 3D nanostructures. Here we demonstrate the direct-write fabrication of freestanding ferromagnetic 3D nano-architectures. By employing micro-Hall sensing, we have determined the magnetic stray field generated by our free-form structures in an externally applied magnetic field and we have performed micromagnetic and macro-spin simulations to deduce the spatial magnetization profiles in the structures and analyze their switching behavior. Furthermore we show that the magnetic 3D elements can be combined with other 3D elements of different chemical composition and intrinsic material properties.

Magnetic Characterization of Direct-Write Free-Form Building Blocks for Artificial Magnetic 3D Lattices

Three-dimensional (3D) nanomagnetism, where spin configurations extend into the vertical direction of a substrate plane allow for more complex, hierarchical systems and the design of novel magnetic effects. As an important step towards this goal, we have recently demonstrated the direct-write fabrication of freestanding ferromagnetic 3D nano-architectures of ferromagnetic CoFe in shapes of nano-tree and nano-cube structures by means of focused electron beam induced deposition. Here, we present a comprehensive characterization of the magnetic properties of these structures by local stray-field measurements using a high-resolution micro-Hall magnetometer. Measurements in a wide range of temperatures and different angles of the externally applied magnetic field with respect to the surface plane of the sensor are supported by corresponding micromagnetic simulations, which explain the overall switching behavior of in part rather complex magnetization configurations remarkably well. In particular, the simulations yield coercive and switching fields that are in good quantitative correspondence with the measured coercive and switching fields assuming a bulk metal content of 100 at % consisting of bcc Co 3 Fe. We show that thermally-unstable magnetization states can be repetitively prepared and their lifetime controlled at will, a prerequisite to realizing dynamic and thermally-active magnetic configurations if the building blocks are to be used in lattice structures.