The automotion of spin textures, where geometrical gradients are exploited to propagate localized magnetic states without the need of external stimuli, is a promising phenomenon for fast, low-power transmission of magnetic information, as previously demonstrated in planar nanowire systems [1]. Here, we show that automotion is an attractive mechanism in 3D nanowire circuits for the vertical interconnectivity of functional magnetic planes, alternative to the standard current-based spintronic effects normally employed to move spin textures. To showcase this new approach, we have prototyped 3D spiral nanowires by a combination of 3D-printing Focused Electron Beam Induced Deposition and physical vapor deposition methods [2, 3]. The magnetic devices (Fig. 1) are made of Permalloy and are 3 Î¼m tall, 150 nm wide, presenting curvature gradients of 0.09 Î¼m-2. Due to the high directionality of the physical deposition process, they have average thickness gradients of -5.3nm/Î¼m; this very large thickness gradient results to be the dominating mechanism responsible for 3D domain wall automotion, as micromagnetic simulations indicate. We have directly imaged the automotion of domain walls in the 3D spirals using â€œshadowâ€ X-ray photoelectron microscopy [4]. In these experiments, we nucleate a pair of domain walls at different locations within the spirals using external magnetic fields, and directly observe the evolution of the system as the field is reduced until reaching zero value (Fig. 2). The experiments show the successful automotion of the walls along the 3D interconnectors, and its competition with the intrinsic pinning present in the devices at localized regions. This work thus proposes and successfully demonstrates the automotion of spin textures as a viable effect to create 3D interconnected magnetic devices [5].

Domain Wall Automotion for Three Dimensional Magnetic Interconnectivity

Bringing nanomagnetism into the third dimension is of growing interest due to many advantages that three-dimensional (3D) structures provide. The introduction of 3D geometrical effects such as curvature and chirality1, as well as the high density and enhanced device connectivity, lead to many opportunities for new physics and applications2,3. When we combine this promising field of 3D nanomagnetism with the well-established field of spintronics, a number of proposals ranging from the ultra-high-density 3D racetrack memory4 to 3D interconnected memristors for neuromorphic computing5 appear. However, before we can fully exploit the promise of 3D spintronics, significant advances in both the integration of 3D nanomagnets into 2D microelectronic circuits，and the understanding of the influence of a 3D geometry on the magnetotransport properties, are required. The implementation of 3D nanomagnetic circuits faces great challenges regarding the fabrication of a 3D nanostructure and its interconnectivity to the electronic components. Until recently, most magnetotransport experiments have concerned cylindrical nanowires, with complex micromanipulations needed to electrically contact them6. In this work, we employ 3D nano-printing capabilities provided by Focused Electron Beam Induced Deposition (FEBID)7, to directly fabricate a high-quality 3D Cobalt nanobridge with well-defined leads on pre-synthesized electrical contacts (Figure 1a). The SEM image shown in Figure 1b demonstrates the successful integration of this complex, high-aspect-ratio 3D nanostructure onto lithographically patterned electrodes. This printed 3D nanomagnetic circuit allows four-probe transport measurements with which we can probe the magnetotransport properties of the 3D nanostructure - and determine the influence of the three-dimensionality on these properties. To fully characterise the magnetotransport (MT) properties of the 3D magnetic nanobridge, we measured MT hysteresis loops for fields applied in different directions in three-dimensions (Figure 2a, b). These magnetotransport measurements, in combination with macrospin and finite element simulations, reveal that the three-dimensional structure of the nanobridge directly affects the magnetotransport in several ways. Firstly, the non-collinear current path in the 3D geometry results in a complex superposition of different MT effects, leading to an unusual angular dependence of well-known effects such as the Anomalous Hall effect. Secondly, we also identify a significant angular-dependence of the magnetoelectric signal due to the magnon magnetoresistance. This strong angular dependence occurs due to the strong influence of the demagnetising field within the non-collinear regions of the 3D geometry, highlighting the importance of magnetostatics in 3D nanostructures8. These new insights into the influence of a 3D geometry on the magnetotransport effects reported in this work provide the basis for the future study of new spintronic effects in 3D magnetic nanostructures, as well as the realization of 3D spintronic technologies. This methodology shown here combining FEBID 3D printing and standard planar lithography can be extended to more complicated geometries and other materials, opening the door to the fundamental study of new phenomena that exploit the interplay between 3D geometry and magnetotransport and may find applications in the future of areas such as magnonics, frustrated magnetic systems, and magnetic neural networks.

**References:**

 (1) R. Streubel, P. Fischer and F. Kronast, J Phys D Appl Phys., Vol. 49, p.363001(2016) (2) A. Fernández-Pacheco, R. Streubel and O. Fruchart, Nat Commun., Vol. 8, p.15756 (2017) (3) P. Fischer, D. Sanz-Hernández and R. Streubel, Apl Mater., Vol. 8, p.15756 (2017) (4) S. Parkin, M. Hayashi and L. Thomas, Science., Vol. 320, p.190-194 (2008) (5) A. May, M. Hunt and A. Berg, Commun Phys., Vol. 2, p.13 (2019) (6) M. Schöbitz, A. Riz and S. Martin, Phys Rev Lett ., Vol. 123, p.217201 (2019) (7) L. Skoric, D. Sanz-Hernández and F. Meng, Nano Lett ., Vol. 20, p.184-191 (2019) (8) F. Meng, C. Donnelly and C. Abert, Arxiv., arXiv:2011.09199 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f82793d4777c5e628b8b37e46d66e2d7.jpg)
Fig.1 (a) 3D nano-printing of the bridge via Focused Electron Beam Induced Deposition (FEBID) on pre-patterned electrical contacts. (b) The SEM image of the as-fabricated nanomagnetic circuit. (c) Four-probe magnetotransport measurement configuration. (d) The SEM image of the top view of the nanobridge.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba14c1bac15d9b830f10e775d14b93fe.jpg)
Fig.2 (a) The schematic shows how the field was applied relative to the 3D nanobridge, θ is the angle between the applied field and the substrate (b) Magnetotransport hysteresis loop obtained from -4 T to 4 T and 4 T to -4 T for each field angle θ, from θ = 0° to θ = 90° (from violet to red).

 Non-planar geometrical effects on the magnetoelectrical signal in a 3D nanomagnetic circuit

The extension of nanomagnetism to three dimensions is proposed as an exciting route to study new physical effects, such as the emergence of new spin textures and magneto-chiral phenomena, with the prospective of being exploited in future technologies [1,2]. Whereas a significant amount of work has been so far devoted to simulating 3D nanostructures, its fabrication and characterization has proven to be very challenging, and very few of these systems have been experimentally investigated. Our group has been recently developing new fabrication and characterization methods specifically tailored for the study of 3D nanostructures, which made it possible to control the advanced motion of domain walls in 3D straight nanowires [3,4]. Here, we will present recent advances in this realm, which now enable us to create and probe nanomagnets with more complex 3D geometries. First, we will present recent work dedicated to the 3D printing of nanomagnets using Focused Electron Beam Induced Deposition (FEBID). Based on the effective FEBID continuum model [5] and proximity effect corrections, we have developed an algorithm with the capability of modelling the deposition and defining beam scanning patterns for arbitrary 3D geometries [6]. The algorithm performance has been demonstrated in different electron microscopes and precursor gases, allowing us to create 3D nanomagnets with a wide range of geometries directly from CAD files (see Fig. 1). Complementing nanofabrication, we will present a new Kerr magneto-optical setup with the ability to probe 3D magnetic nanostructures, by exploiting the dark-field MOKE (dfMOKE), a technique that we have recently developed [3]. The unprecedented flexibility of the system to characterize these newly accessible 3D geometries will be demonstrated, thanks to the combination of mobile optics and full-3D vector magnetic fields (see Fig. 2).References: [1] Fernández-Pacheco, A. et al. Nat. Commun. 8, 15756 (2017). [2] Streubel, R. et al. J. Phys. D. Appl. Phys. 49, 363001 (2016). [3] Sanz-Hernández, D. et al. ACS Nano 11, 11066–11073 (2017). [4] Sanz-Hernández, D. et al. Nanomaterials 8, 483 (2018). [5] Toth, M., Lobo, C., Friedli, V., Szkudlarek, A. & Utke, I. Beilstein J. Nanotechnol. 6, 1518–1540 (2015). [6] Skoric, L. et al. Nano Lett. 20, 184–191 (2020). 

Advanced fabrication and magnetometry of nanostructures with complex 3D geometries

MOA: Nanocomposite Magnetic Materials

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Domain Wall Automotion for Three Dimensional Magnetic Interconnectivity

Non-planar geometrical effects on the magnetoelectrical signal in a 3D nanomagnetic circuit

Advanced fabrication and magnetometry of nanostructures with complex 3D geometries

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