Three dimensional magnetic systems promise significant opportunities for applications, for example providing higher density devices and new functionality associated with complex topology and greater degrees of freedom [1,2]. For the experimental realisation of these new properties, appropriate characterisation techniques are required to determine both the three-dimensional magnetic structure, and its response to external stimuli. In this talk, I will describe our recent progress in the development of new capabilities for the imaging of three-dimensional magnetic systems, and their dynamic behaviour. For three-dimensional magnetic imaging, we have developed X-ray magnetic nanotomography [3]. By measuring high resolution 2D XMCD projections [4] of the sample for many angles about a dual rotation axis experimental setup, and combing these with a new iterative reconstruction algorithm [5], we determine the complex three-dimensional magnetic patterns within the bulk of a micrometre-sized soft magnetic pillar with 100 nm spatial resolution, as shown in Figure 1. The internal magnetic configuration reveals a complex network of topological magnetic features such as vortices, antivortices and domain walls and, at the crossing points of these structures, we observe the presence of Bloch point singularities [3]. The identification, and interpretation, of nanoscale topological objects within the complex reconstructed magnetic configurations – that consist of millions of pixels – represents a significant challenge. To address this, we have recently implemented calculations of the magnetic vorticity [6,7], a vector that represents the flux of the skyrmion number density, and thus encodes the topology of the magnetic configuration. In this way, not only can we locate and identify the presence of topological structures (Figure 1e,f), but we gain new insights into 3D magnetic solitons, leading to the first observation of magnetic vortex rings [7], as shown in Figure 1g. Lastly, in addition to the static magnetic configuration, the dynamic response of the 3D magnetic configuration to excitations is key to our understanding of both fundamental physics, and applications. With our recent development of X-ray magnetic laminography [8,9] (Figure 2), it is now possible to determine the magnetisation dynamics of a three-dimensional magnetic system [8]. In this way, we have been able to map the dynamics of a magnetic microdisc in response to the excitation of a 500 MHz magnetic field, revealing the motion of vortex domain walls within the bulk of the structure, as well as mapping the coherent rotation modes of the magnetisation in three dimensions (Figure 2c,d), with spatial and temporal resolutions of 50 nm and 70 ps, respectively. These new experimental capabilities of X-ray magnetic imaging open the door to the elucidation of complex three-dimensional magnetic structures, and their dynamic behaviour.

**References:**

[1] A. Fernández-Pacheco, et al., “Three-dimensional nanomagnetism” Nat. Comm. 8, 15756 (2017) [2] C. Donnelly & V. Scagnoli, “Imaging three-dimensional magnetic systems with X-rays” J. Phys. D: Cond. Matt. (2019). [3] C. Donnelly et al., “Three-dimensional magnetization structures revealed with X-ray vector nanotomography” Nature 547, 328 (2017). [4] C. Donnelly et al., “High-resolution hard x-ray magnetic imaging with dichroic ptychography” PRB 94, 064421 (2016). [5] C. Donnelly et al., “Tomographic reconstruction of a three-dimensional magnetization vector field” NJP 20, 083009 (2018). [6] N. R. Cooper, “Propagating magnetic vortex rings in ferromagnets.” PRL. 82, 1554 (1999). [7] C. Donnelly et al., “Experimental observation of vortex rings in a bulk magnet” Nat. Phys. (2020) [8] C. Donnelly et al., “Time-resolved imaging of three-dimensional nanoscale magnetization dynamics”, Nat. Nano. 15, 356 (2020). [9] K. Witte et al., “From 2D STXM to 3D Imaging: Soft X-ray Laminography of Thin Specimens”, Nano Lett. 20, 1305 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0e2d9057483d2b7b45d4d6c5b16ede99.jpg)
Figure 1. X-ray magnetic tomography of a GdCo micropillar (a) reveals a complex internal magnetic configuration. A horizontal slice (b) contains a number of vortices (c) and antivortices (d). Through calculations of the magnetic vorticity vector, we can identify the presence of topological structures (e) and magnetisation singularities (f) within the bulk of the micropillar. By plotting the magnetic vorticity, we identify magnetic vortex rings of circulating vorticity (g). a-d are reproduced from [3], and e-g are reproduced from [8].

![](https://assets.underline.io/uploads/markdown_image/1/image/72ea02148e85a8623efddf043a46be9a.jpg)
Figure 2 Pump-probe X-ray magnetic laminography (a) allows for the mapping of the magnetization dynamics of a magnetic microdisc (b) with spatial and temporal resolutions on the order of nanometers and picoseonds, respectively. Coherent rotation modes of the magnetization are shown for a cross section (c) and a lower slice of the structure containing vortex domain walls (d). a-d reproduced from [8].

Imaging 3D magnetic configurations with X-rays

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

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Winner of the Best Student Presentation Award:  ***JI-05 - Non-planar geometrical effects on the magnetoelectrical signal in a 3D nanomagnetic circuit***

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Imaging 3D magnetic configurations with X-rays

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

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