Half-hedgehog spin textures in sub-100 nm soft magnetic nanodots

Chiral spin-transfer torque induced by curvature gradient

This work analyzes the propagation of a transverse domain wall (DW) under the action of an electric current along a nanowire with a curvature gradient. Our results evidence that the curvature gradient induces a chiral spin-transfer torque (CSTT) whose effect on the DW dynamics depends on the direction along which the DW points, evidencing a curvature-induced non-reciprocity in the current-driven DW motion. The origin of the CSTT is explained in terms of a position-dependent effective field associated with the DW profile and the electric current direction. This current-driven chiral effect is responsible for direction-dependent reinforcing or blocking the DW propagation. The emergence of curvature-induced chiral spin transport is a phenomenon to consider when designing spintronic devices.

Stability and Spin Waves of Skyrmion Tubes in Curved FeGe Nanowires

In this work, we investigate the influence of curvature on the dynamic susceptibility in FeGe nanowires, both curved and straight, hosting a skyrmionic tube texture under the action of an external bias field, using micromagnetic simulations. Our results demonstrate that both the resonance frequencies and the number of resonant peaks are highly dependent on the curvature of the system. To further understand the nature of the spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases, describing the differences among resonance modes observed. The ability to control the dynamic properties and frequencies of these nanostructures underscores their potential application in frequency-selective magnetic devices.

Long-Term Performance of Magnetic Force Microscopy Tips Grown by Focused Electron Beam Induced Deposition

High-resolution micro- and nanostructures can be grown using Focused Electron Beam Induced Deposition (FEBID), a direct-write, resist-free nanolithography technology which allows additive patterning, typically with sub-100 nm lateral resolution, and down to 10 nm in optimal conditions. This technique has been used to grow magnetic tips for use in Magnetic Force Microscopy (MFM). Due to their high aspect ratio and good magnetic behavior, these FEBID magnetic tips provide several advantages over commercial magnetic tips when used for simultaneous topographical and magnetic measurements. Here, we report a study of the durability of these excellent candidates for high-resolution MFM measurements. A batch of FEBID-grown magnetic tips was subjected to a systematic analysis of MFM magnetic contrast for 30 weeks, using magnetic storage tape as a test specimen. Our results indicate that these FEBID magnetic tips operate effectively over a long period of time. The magnetic signal was well preserved, with a maximum reduction of 60% after 21 weeks of recurrent use. No significant contrast degradation was observed after 30 weeks in storage.

Field-Driven Magnetic Phase Diagram and Vortex Stability in Fe Nanometric Square Prisms

In this work, we deal with the zero temperature hysteretic properties of iron (Fe) quadrangular nanoprisms and the size conditions underlying magnetic vortex states formation. Different aspect ratios of a square base prism of thickness t with free boundary conditions were considered in order to summarize our results in a proposal of a field-driven magnetic phase diagram where such vortex states are stable along the hysteresis loops. To do that, a Hamiltonian consisting of exchange, magnetostatic, Zeeman and cubic anisotropy energies was considered. The time dynamics at each magnetic field step was performed by solving the time-dependent Landau-Lifshitz-Gilbert differential equation. The micromagnetic simulations were performed using the Ubermag package based on the Object Oriented Micromagnetic Framework (OOMMF). Circular magnetic textures were also characterized by means of topological charge calculations. The aspect ratio dependencies of the coercive force, nucleation and annihilation fields are also analyzed. Computations agree with related experimental observations and other micromagnetic calculations.

3D quasi-skyrmions in thick cylindrical and dome-shape soft nanodots

Magnetic skyrmions are widely attracting researchers due to fascinating physics and novel applications related to their non-trivial topology. Néel skyrmions have been extensively investigated in magnetic systems with Dzyaloshinskii-Moriya interaction (DMI) and/or perpendicular magnetic anisotropy. Here, by means of micromagnetic simulations and analytical calculations, we show that 3D quasi-skyrmions of Néel type, with topological charge close to 1, can exist as metastable states in soft magnetic nanostructures with no DMI, such as in Permalloy thick cylindrical and dome-shaped nanodots. The key factor responsible for the stabilization of DMI-free is the interplay of the exchange and magnetostatic energies in the nanodots. The range of geometrical parameters where the skyrmions are found is wider in magnetic dome-shape nanodots than in their cylindrical counterparts. Our results open the door for a new research line related to the nucleation and stabilization of magnetic skyrmions in a broad class of nanostructured soft magnetic materials.

The Bloch point 3D topological charge induced by the magnetostatic interaction

A hedgehog or Bloch point is a point-like 3D magnetization configuration in a ferromagnet. Regardless of widely spread treatment of a Bloch point as a topological defect, its 3D topological charge has never been calculated. Here, applying the concepts of the emergent magnetic field and Dirac string, we calculate the 3D topological charge (Hopf index) of a Bloch point and show that due to the magnetostatic energy contribution it has a finite, non-integer value. Thus, Bloch points form a new class of hopfions-3D topological magnetization configurations. The calculated Bloch point non-zero gyrovector leads to important dynamical consequences such as the appearance of topological Hall effect.

Magnetic Functionalization of Scanning Probes by Focused Electron Beam Induced Deposition Technology

The fabrication of nanostructures with high resolution and precise control of the deposition site makes Focused Electron Beam Induced Deposition (FEBID) a unique nanolithography process. In the case of magnetic materials, apart from the FEBID potential in standard substrates for multiple applications in data storage and logic, the use of this technology for the growth of nanomagnets on different types of scanning probes opens new paths in magnetic sensing, becoming a benchmark for magnetic functionalization. This work reviews the recent advances in the integration of FEBID magnetic nanostructures onto cantilevers to produce advanced magnetic sensing devices with unprecedented performance.

Skyrmion Formation in Nanodisks Using Magnetic Force Microscopy Tip

We demonstrated numerically the skyrmion formation in ultrathin nanodisks using a magnetic force microscopy tip. We found that the local magnetic field generated by the magnetic tip significantly affects the magnetization state of the nanodisks and leads to the formation of skyrmions. Experimentally, we confirmed the influence of the local field on the magnetization states of the disks. Micromagnetic simulations explain the evolution of the magnetic state during magnetic force microscopy scanning and confirm the possibility of skyrmion formation. The formation of the horseshoe magnetic domain is a key transition from random labyrinth domain states into the skyrmion state. We showed that the formation of skyrmions by the magnetic probe is a reliable and repetitive procedure. Our findings provide a simple solution for skyrmion formation in nanodisks.

Evidence of Skyrmion-Tube Mediated Magnetization Reversal in Modulated Nanowires

Magnetic nanowires, conceived as individual building blocks for spintronic devices, constitute a well-suited model to design and study magnetization reversal processes, or to tackle fundamental questions, such as the presence of topologically protected magnetization textures under particular conditions. Recently, a skyrmion-tube mediated magnetization reversal process was theoretically reported in diameter modulated cylindrical nanowires. In these nanowires, a vortex nucleates at the end of the segments with larger diameter and propagates, resulting in a first switching of the nanowire core magnetization at small fields. In this work, we show experimental evidence of the so-called Bloch skyrmion-tubes, using advanced Magnetic Force Microscopy modes to image the magnetization reversal process of FeCoCu diameter modulated nanowires. By monitoring the magnetic state of the nanowire during applied field sweeping, a detected drop of magnetic signal at a given critical field unveils the presence of a skyrmion-tube, due to mutually compensating stray field components. That evidences the presence of a skyrmion-tube as an intermediate stage during the magnetization reversal, whose presence is related to the geometrical dimensions of the cylindrical segments.

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.

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.