# 16. Computation in 3D nanomagnetic systems

Markus Becherer¹ and Jack Gartside²

¹ Department of Electrical Engineering, Technical University of Munich (TUM), Munich, Germany

² Blackett Laboratory, Imperial College London, London, United Kingdom

## Status

In 2012, about a decade ago, NAND Flash technology for solid-state mass storage devices became 3D. It came with relaxed constraints regarding bit area but simultaneously at the cost of increased fabrication complexity in transistor vertical stacking. Nevertheless, by 'simply' exploiting 3D stacking (hard-disc drives, compact discs, and Blu-rays remain stuck in 2D), a 100X improvement in 'areal density' has been achieved. Now, reaching the end of Moore's law of scaling, it is up to computing devices to follow this trend. While true 3D integration into mainstream MOS technology for general-purpose (digital) computing is not getting off the ground and, even worse, electrical losses in the complex wiring of modern ICs are increasingly proving to be a bottleneck, magnetic computing schemes with physically non-volatile state variables are promising. Computing in memory or memory as a computer, whatever you want. To give one example, perpendicular Nanomagnetic Logic, a 3D computing scheme for Boolean computation, offers intrinsically non-volatile computational states via stacked nanomagnets, as exemplified in figure 30. Local engineering with ion beams 'tunes' the properties of the individual magnet, lateral dipolar magnetic fields provide next-neighbor computing capability, while vertical coupling fields enable signal transitions, and a global magnetic field clock provides switching power and synchronization [185, 186]. A complete set of Boolean logic devices has been demonstrated, and validated system-level simulations suggest atto-joule dissipation per bit operation at CMOS-competitive data throughput. However, it is not the order-of-magnitude improvement we might be looking for, so as always, it is hard to beat CMOS where it is best: in high-performance digital computing. Still, for magnetic Boolean logic, there are some clear pathways following the approach of migrating similar to memory architectures from 2D to 3D, as mentioned above.

The other computing paradigm that is currently generating much attention amongst magnetism researchers is neuromorphic computing, a rapidly developing field that aims to draw inspiration from biological or neural network architectures to circumvent the increasing restrictions that thermodynamics, finite transistor size, and the von Neumann memory-processor bottleneck place on conventional CMOS digital Boolean logic.

Recent years have seen an explosion in the number and variety of magnetic neuromorphic computation schemes, from spin-torque nano oscillators to skyrmion systems and artificial spin ice nanoarrays. However, all existing schemes are 2D, with no real forays of magnetic neuromorphic technology into 3D. This gives us somewhat of a blank canvas with which to

write this roadmap, which is both freeing and challenging. The challenge being that we would like to identify routes forward which harness benefits that are uniquely available by moving magnetic systems into the third dimension and avoid the more generic advantages of 3D systems such as increased density, which are not specific to magnetic systems and appear in other 3D systems e.g. electrical & optical devices. Identifying such unique benefits of 3D nanomagnetic architectures before they have been demonstrated is a challenge, but an interesting one and we hope a somewhat valuable exercise.

## Current and future challenges

A primary driver of neuromorphic computing is reaching the energy efficiency of biological brains. A human brain consumes around 20 W, while multi-GPU machine learning rigs regularly consume kW to MW. A huge part of this biological efficiency comes from the massively parallel interconnections of neuronal architectures. The human brain has hundreds to thousands of synapses per neuron depending on the region, allowing operations by a single neuron to efficiently inform many parallel subsequent operations at no additional energy cost. Existing computation is performed sequentially, with either repeated computations or repeated memory-processor shuttling operations generating huge additional energy costs.

Biologically-high degrees of interconnectivity are only remotely possible with the geometric freedoms of a 3D system. We said we would try to resist the temptation of highlighting generic advantages of 3D, and increased parallel connectivity arguably touches on the generic appeal of increased areal density in 3D systems. Indeed, we are already seeing efforts to exploit this in 3D memristive crossbar arrays. However, nanofabricating conductive multilayer 3D interconnects between functional elements is still technologically challenging, and comes with additional Ohmic losses and thermodynamic challenges from increasingly dense wiring.

Something uniquely magnetic is exploiting the benefits of free-space dipolar coupling. Recently the effective strength of both static and dynamic components of dipolar coupling has shown capacity for substantial enhancement in 3D structures. While dipolar coupling has limited range, it is passive, natively 3D, and can couple both magnetostatic energy landscapes and GHz spin-waves/magnons. Functional designs such as the magnonic half-adder from the Chumak & Pirro group show the strong potential of such dipolar interconnects in 2D [184], migrating such designs to 3D offers unique benefits to magnetic computing that are not available in memristive or photonic architectures, the leading competing approaches. While the dipolar interaction may be thought of as somewhat weak relative to exchange coupling, recent work has shown that 3D architectures may be used to greatly enhance the effective intensity of dynamic dipolar coupling, with dipolar non-local ultrastrong magnon-magnon coupling demonstrated in a multilayered artificial spin ice [187] (figure 31(a)).

A key factor defining the versatility and computing power of neuromorphic systems is the range of available states.
<figure><img src="image_40.png" /><figcaption>**Figure 30.** (a) Nanomagnetic digital gates are stacked in the end-of-line technology of CMOS chips and powered/synchronized by a magnetic field. (b) Ion-beam engineering to control domain reversal and domain-wall motion for signal routing is applied in a 3D stack. (c) A highly permeable cladding combined with meander-like copper wires provides the magnetic field-clock. Reprinted from [185], Copyright (2016), with permission from Elsevier.</figcaption></figure>

Recent work has shown that enriching the magnetic state space greatly enhances computing ability [188, 189]. An attractive benefit of 3D magnetic systems is their expanded microstate spaces, including 3D-specific states. Examples include distinct bulk & surface magnon states [23], strongly-coupled hybrid chiral-collinear states [187], 3D solitons, and memristor-like multi-level states. Exploiting these states for enhanced neuromorphic computation is an enticing future direction. Gaining precise control over such expanded microstate spaces, both magnetostatically and in the magnon/spin-wave regime is a key future challenge for the field.

**Advances in science and technology to meet challenges**

In 3D nanomagnetic logic technology, care was taken not to connect each logic gate by electrical wires. The number of electrical I/O devices is orders of magnitude lower than the

number of magnetic field-coupled gates. This comes at the cost that only a global magnetic field clock, integrated on-chip, could generate the needed bipolar field amplitudes for clocking in the two-digit MHz range. No efficient on-chip clock generator has yet been demonstrated, even if concepts can be adopted from on-chip inductors where soft-magnetic materials are applied for field concentration. However, it is an unsolved question: How can sandwiched computing elements be fed with electrical I/O structures and simultaneously clocked by a global magnetic field without significant interference (i.e. generated induction voltages)? Nanomagnetic logic relies on billions of simple binary ‘states’ laid out in vertically stacked planar geometry and coupled by local dipolar coupling fields for computation. Simple switches interconnected with inherent nonvolatility.

By contrast, neuromorphic systems draw their computing power from the complexity and rich state spaces of their functional elements. A distribution, stochastic or tailored, of functional elements may be engineered to produce usefully
<figure><img src="image_41.png" /><figcaption>**Figure 31.** 3D nanomagnetic systems and field-free writing approaching. (a) Multilayered systems comprising strongly dipolar-coupled magnetic nanoelements may offer benefits for 3D magnetic computing, allowing information exchange and physical interaction between discrete nanoelements via the intrinsic dipolar field, with both static and GHz dynamic components. This may be a route to reducing or avoiding huge amounts of electrical interconnects in 3D nanostructures. Reproduced from [187]. **CC BY 4.0.** (b) All-optical magnetic writing of nanostructures. 3D nanomagnetic systems require state control mechanisms that match the complexity of the 3D geometries if they are to be utilised as computing platforms. Mechanisms to write any nanomagnetic element, whether as a binary digital state or neuromorphic neuronal ‘weight’ are essential, particularly attractive if they avoid attaching electrical connections to every nanoelement. All-optical writing offers an appealing route forwards here, and has recently been demonstrated in 2D nanostructures. Reproduced with permission from [191]. **CC BY-NC 4.0.** (c) Promising examples of 3D nanomagnetic architectures which should be explored for neuromorphic computing schemes include densely connected nanowire networks such as the example here from reproduced from [23]. **CC BY 4.0.** Such systems offer both longer-range dipolar and strong short-range exchange coupling and the ability to host spin-waves/magnons which have been demonstrated as attractive potential information carriers in a host of 2D nanomagnetic neuromorphic computing schemes recently. The laser light here represents the two-photon lithography used to write the geometric structure, using such a voxel-focused laser with 3D spatial control could be an appealing future route towards 3D all-optical nanomagnetic writing similar to that shown in (b), albeit with technological challenges to be overcome.</figcaption></figure>

distinct responses from non-unique spatially distributed inputs, with greater potential density and diversity of these functional elements. Here, the challenge is to identify & engineer synergetic combinations of these functional elements such that computational power is maximised without overly-complicating fabrication, state-control and readout.

However, global magnetic field protocols (whether as clock or data-input) place limitations on both digital and neuromorphic schemes. Gaining enhanced field-free control of magnetic systems is a crucial future challenge for the field. Promising state-control solutions are being developed, including spin-wave [190] and all-optical [191] switching (figure 31(b)). These methodologies will require future refinement to tailor them 3D systems. While such field-free state control approaches are being studied in the lab, an appealing route to explore is all-optical magnetic writing using the spatial 3D laser control afforded by two-photon lithography systems such as those used in [23] and [2]. If these systems are already present in labs fabricating these 3D structures, enabling them to also provide proof-of-concept magnetic state reconfigurability is worth exploring (figure 31(c)).

Alongside state control, neuromorphic algorithms & training must be advanced to meet the challenges of complex 3D state spaces. Stochastic p-bit approaches are promising here, with designs harnessing non-local dipolar coupling of particular interest for 3D systems [192]. ‘Digital-twin’ and neuralODE models of 3D systems could play an increasingly important role here allowing a data-driven approach to modelling the complex 3D dynamics. However, it is prudent that such data-driven ‘digital twin’ models performed using neural

networks are supported and confirmed by methods which have knowledge of the magnetic physics, such as micromagnetic simulation or analytical modelling.

Readout techniques must also be advanced to meet the challenges of dense 3D state spaces. Frequency-domain approaches are promising, capable of resolving some of the novel 3D states and behaviours [23] without requiring direct access to the hard-to-probe interior of 3D systems. We have seen 3D systems increase the frequency range across which modes are distributed [186, 188], which is great for resolving distinct states and enhancing neuromorphic computation—but detection electronics will need to match these advances and develop low-power broadband detection.

## Concluding remarks

Monolithic fabrication of digital computing devices with 3D stacked nanomagnets is, in principle, similar to magnetic memory technologies and can naturally be integrated into the back-end-of-line of a CMOS process. Even though a complete set of devices has been demonstrated, there is a need for complex circuits, simultaneous integration of field-clocking structures, electrical transducers for I/O, and system-level benchmarking for real-world computing scenarios. Stochasticity of the magnetic states is likely to be one of the biggest hurdles since, in contrast to memory devices, every computing element must function reliably—memory is more forgiving.
Neuromorphic, fault-tolerant computing methods seem
to offer routes around this stochasticity, particularly p-bit
systems. Here, enhanced state-control, spatially distributed
readout, and maturity of neuromorphic algorithms to match
the enhanced complexity of 3D systems are likely to be the
largest challenges in coming years.

Perhaps an interesting approach may be the development of
‘hybrid’ systems integrating deterministic Boolean magnetic
logic with neuromorphic elements, implementing tradition-
ally power-hungry digital-to-analog and analog-to-digital con-
version via magnetic physics and offering crucial interfacing
between neuromorphic processing and conventional CMOS
systems via magnetic physics. It is unlikely that any computing
system will be purely neuromorphic, and maintaining efficient
compatibility with surrounding CMOS hardware is crucial to

increase the prospects of industrial uptake of 3D magnetic
computing technologies.

Acknowledgments

MB was supported by the German Research Foundation (DFG)—Project Numbers 114933698, 229838035, and 403505866.

JCG was supported by EPSRC Grant EP/X015661/1,
the Royal Academy of Engineering Research Fellowships,
and the EPSRC ECR International Collaboration Grant
‘Three-Dimensional Multilayer Nanomagnetic Arrays
for Neuromorphic Low-Energy Magnonic Processing’
EP/Y003276/1.
# 17. 3D magnetic memory

Teruo Ono

Kyoto University, Kyoto, Japan

## Status

Figure 32 shows a conceptual diagram of the memory hierarchy in computers and other devices. It is well known that high-speed memories such as SRAM and DRAM are expensive and volatile memories with low recording density, while SSD and HDD are inexpensive non-volatile memories with high recording density. But there is a serious problem of triple-digit speed gap between DRAM and SSD. What is needed is a 3D, high-capacity memory that is as fast as DRAM.

The so-called ‘race-track memory’ proposed by IBM [20], which is based on the operating principle of current-driven magnetic DW motion [193], is expected to become a high-speed 3D large-capacity memory. The 3D nature of the memory allows for a large amount of information per transistor, and the high-speed spin dynamics of the magnetic material makes it a high-speed memory.

Although the reduction of the threshold current density and the fast motion of the magnetic DW have been demonstrated, 3D race-track memory has not yet been demonstrated. The two problems that need to be solved to realize 3D race-track memory are how to precisely control the magnetic wall position and how to fabricate a 3D structure. As a 3D structure to complete the magnetic wall position control, a 3D magnetic memory using artificial ferromagnetic materials as shown in figure 33 has been proposed [194]. Each column has an alternating overlapping structure of a recording layer (green), which has large magnetic anisotropy and is responsible for bit recording, and a magnetic DW layer (yellow), which has no magnetic anisotropy and acts as an artificial DW layer. Simulations have confirmed that this 3D magnetic memory offers both high DW position controllability, thermal stability, and low power consumption [194, 195].

## Current and future challenges

A major challenge is how to fabricate a 3D structure like figure 33(a). Considering the aspect ratio problem of micro-fabrication even in the current 2D MRAM, it seems to be an extremely difficult task to fabricate a 3D structure like figure 33(a) with the currently available microfabrication

technology. A possible solution is to first fabricate nanoholes to ensure a columnar structure, and then electrodeposit artificial ferromagnets inside the nanoholes. Using the latest technology developed for 3D NAND flash memory, it is possible to fabricate high aspect ratio nanohole arrays of tens of nanometers in diameter and several microns in length. The technology to create nanowires in such nanoholes by electrodeposition has already been established [196]. In fact, free-standing, interconnected metallic nanowire networks have been fabricated by electrodeposition into polycarbonate membranes that have been ion-tracked at multiple angles [197]. Such 3D interconnected magnetic nanowire networks can be expected to be integrated multistate memristors. To date, only field-assisted current-driven DW motion has been demonstrated in electrodeposited nanowires [198]. Therefore, current-driven DW motion in electrodeposited nanowires is another major challenge.

## Advances in science and technology to meet challenges

In addition to the electrodeposition in nanoholes described above, several other techniques are being developed to fabricate 3D structures. For example, by using two-photon lithography followed by thin film deposition and direct writing by FEBID, 3D magnetic structures of almost arbitrary shape can be fabricated [6].

To realize 3D magnetic memory, in addition to the fabrication of 3D structures, technologies to visualize 3D structures at the nanoscale are required. In particular, a technology is needed to visualize not only the physical structure but also the magnetic structure at the nanoscale in three dimensions. The 3D magnetic tomography technique based on x-ray magnetic circular dichroism, combined with sample rotation control and a graphics processing unit to reconstruct spin structures inside bulk materials, is a promising technology of this kind [60].

In 3D magnetic memory, information is transported by DW motion, and figure 33 assumes that the DWs are driven by electric current. However, current is accompanied by Joule heating, which is a problem in terms of power consumption. Recently, a method to drive the magnetic wall by transferring the magnon angular momentum to the DW has been demonstrated [199]. The energy required to drive the DW is orders of magnitude less than that reported for metallic systems.
<figure><img src="image_42.png" /><figcaption>**Figure 32.** Conceptual diagram of memory configuration of computers.</figcaption></figure>

<figure><img src="image_43.png" /><figcaption>**Figure 33.** (a) Illustration of the vertical DW motion memory with artificial ferromagnets. Left panel: Memory array with vertically arranged word line and bit line. The columns within the array are the multi-bit memory cells constructed with artificial ferromagnets. Right panel: Detailed structure of a column. (b) Data writing scheme: A current is applied to the bottom electrode to invert the magnetization direction of layer 1 by spin-orbit torque. A DW is then generated in layer 3. The current is then passed through the column to shift this DW up to any DW layer. The next information is then written by inverting the magnetization direction of layer1 by applying a current to the bottom electrode. By repeating this operation, any bit sequence can be stored in the column. (c) Readout can be done in batches by reading out the information at the top MTJ while shifting all DWs upwards with a current. Reproduced from [194]. CC BY 4.0.</figcaption></figure>

## Concluding remarks

With the commercialization of spin-transfer MRAM as an embedded memory, expectations for magnetic memory as a

high-speed nonvolatile memory are rising. The development of high-speed, large-capacity 3D nonvolatile memory is essential for the future development of the information society. The key to the development of 3D magnetic memory will be the use
of new materials such as artificial ferromagnets, artificial anti-ferromagnets, and artificial ferrimagnets, and the use of novel device fabrication techniques such as electrodeposition, two-photon lithography followed by thin film deposition, and direct writing by FEBID.

**Acknowledgments**

Teruo Ono was supported by JST, CREST (Grant Number JP MJCR21C1), Japan. Figure 32 is courtesy of Prof. Yota Takamura.
## 18. 3D spintronics

Paolo Bortolotti<fnref n="1" /> and Amalio Fernández-Pacheco<fnref n="2" />

### Status

The expansion of nanomagnetism to three dimensions provides unique opportunities for the development of 3D spintronic technologies. Planar spintronic sensors and classical magnetic memories are made by thin film and standard lithography methods, restricting their functionality to the substrate plane. The usage of new spintronic devices, where the magnetic state is not confined to a single plane, will open a new era in spintronics, boosting storage and processing capacities, as well as device interconnectivity. It also has the potential to creating radically new computing architectures, driven by effects emerging with the change of dimensionality [6]. The paradigm shift of moving to 3D already initiated by CMOS [200], appears now on the hard disk drive industry roadmaps [201] and will strongly benefit emerging areas such as in-memory and neuromorphic computing (see section 16).

A natural way to go into 3D is via the usage of magnetic nanowires (see figures 34(a)–(c)). The vertical racetrack memory is arguably the most iconic 3D spintronic device ever proposed (see section 17). Serving as an inspiration, many efforts are focused on exploring new effects associated to 3D motion of magnetic textures e.g. DWs, skyrmions..., and recently magnons (section 15), via nanowire conduits. The most widespread approach followed so far to successful realize complex 3D nanowire circuits consists of the 3D printing of nonmagnetic scaffolds by FEBID or two-photon polymerization (see sections 1 and 2), followed by thin film deposition. These approaches are reaching a high maturity level [4] and can be extended to complex multilayered materials with functional interfaces. In particular, in-built gradients can induce strong automation of spin textures, a new mechanism proposed to unidirectionally interconnect spintronic devices located at different levels [145]. FEBID-written ferromagnetic 3D nano-bridges can connect planar circuits and present unconventional magnetotransport angular dependences, result of the complex magnetostatic vector fields present in a 3D geometry [10].

An alternative approach to direct 3D printing for the creation of 3D DW nanowire devices has been recently demonstrated, where a free-standing film is obtained by using an underlayer which dissolves in water, and can be positioned on top of pre-patterned substrates with humps of different radii. Using this methodology, synthetic antiferromagnet-based racetrack devices show a comparable performance to planar devices for moderate hump heights, demonstrating robust DW out-of-the-substrate motion at high speeds and low critical current densities [11].

### Current and future challenges

Direct-write lithography methods as described above can create circuits with arbitrary shapes, thanks to recently developed computational tools that enable 3D printing with nanoscale resolution (see sections 1 and 2) and [4]. However, these prototyping techniques, invaluable to investigate new physical phenomena, are not yet mature for high-throughput applications, and their integration with standardized lithography methods by the microelectronics industry will be very challenging. Multi-beam electron tools and patterning under cryogenic conditions, as well as advanced optical methods enabling multi-beam parallel patterning will improve speeds and could be a route to overcome related technical challenges. The introduction of cutting-edge spintronic materials (antiferromagnets, chiral ultra-thin multilayers...) into circuits with complex 3D geometries faces great challenges, but also incredible opportunities. Curved conduits with emerging magnetic energies are a first step in this direction (sections 3 and 11). Recent developments in chemical thin film deposition of ferromagnetic metals, and their integration in 3D scaffolds, is a promising future avenue. Chemical methods also provide fine control over the composition and microstructure of materials during growth, which combined with new methods for the patterning of 3D templates could create networks of highly interconnected nanowires. See sections 1, 14, and 15 for further details.

Beyond spintronic devices based on new patterning methodologies, a seemingly more direct and robust path for 3D magnetic computing consists of employing multilayered heterostructures (figure 34(d)), building upon the developments over decades of GMR and TMR based, sensing and memory devices (section 6). New schemes for 3D magnetic sensing based on spin-orbit torques in standard geometries have been already demonstrated [204]. The exploitation of shape anisotropy instead of PMA is one of the first realizations of pseudo-3D spintronic devices to achieve sub-20 nm MRAM devices [205]. A key aspect for real 3D functionality concerns the vertical motion of magnetic bits from one layer to the next, exploiting interlayer interactions [202]. Extending these ideas to current-driven schemes e.g. for memory applications (section 17), overcoming negative effects in miniaturization due to strong magnetostatic interactions for large number of layers, and the continuum degradation of thin film properties for stacks based on hundreds of layers, are challenges ahead. Fine tuning of individual energies for each film on a magnetic stack can be also exploited for the formation of topological spin textures spanning across multiple layers, from coupled pairs of textures such as skyrmions to improve functionality, e.g. cancel the total skyrmion Hall effect, to the realization of topological 3D textures spanning across multiple layers such as hopfions and torons/cocoons textures (see figures 34(e)–(h) and a more in depth discussion in section 9). Moving such 3D spin textures efficiently under spin currents is still to be demonstrated, and their advantage for computing with respect to planar textures, will need to be thoroughly investigated. All

<footnote n="1">¹ Laboratoire Albert Fert, CNRS, Thales and Université Paris Saclay, Palaiseau cedex, France</footnote>

<footnote n="2">² Institute of Applied Physics, TU Wien, Vienna, Austria</footnote>
<figure><img src="image_44.png" /><figcaption>**Figure 34.** Recent works related to 3D spintronic devices. (a) Ferromagnetic interconnector directly printed by FEBID. Reproduced from [10]. **CC BY 4.0.** (b) Automotion of magnetic bits in between planes using interconnectors with in-built gradients. Reproduced from [145]. **CC BY 4.0.** (c) State-of-the-art racetrack memories formed by synthetic antiferromagnets, positioned on 3D pre-patterned substrates to achieve vertical domain wall motion. Reproduced from [11]. **CC BY 4.0.** (d) Concept for MRAM with vertical magnetic bit transfer functionality. Reproduced from [202]. **CC BY 4.0.** (e)–(g) Theoretical study of current-induced motion of a Hopfion in a racetrack device. Reprinted (figure) with permission from [203], Copyright (2019) by the American Physical Society. (h) Micromagnetic simulations of a skyrmion cocoon formed along the height of ultra-thin magnetic multilayers, obtained by engineering the heterostructure energies. Reproduced from [113]. **CC BY 4.0.**</figcaption></figure>

these schemes will benefit from fundamental and technical
recent advances, included the recent discovery of chiral inter-
layer spin interactions [206], and the development of magnetic
characterisation and imaging methods; in particular, magnetic
vector tomography at nanoscale resolutions (sections 4 and 5),
key to resolve the static and dynamic vector dependence of
these devices across its depth.

**Advances in science and technology to meet
challenges**

3D spintronics is an emerging field with at the same time great
opportunities and challenges. In a first stage, except for exper-
imental works on cylindrical nanowires, the field was mostly
theoretical and computational. For several years, a variety of
new effects were predicted, from new types of DWs to non-
reciprocal motion of spin textures and magnons, emergence

of chiral interactions due to nano-curvatures, etc. Few years
ago, we entered a second phase, where experimental invest-
igations became possible. The acceleration of this progress is
very likely, due to the urgent demand for new forms of ultra-
high storage and processing devices. We are now giving first
steps in this second exciting phase, with theoretical predictions
being finally tested, and new experimental discoveries taking
place. Despite these advances, moving to higher Technology
Readiness Levels remains challenging. Today the objective is
to build novel demonstrators and confirm the expectation of
such alternative functionalities based on 3D; tomorrow, the
third phase will consist of conceiving and fabricating com-
plex 3D spintronic circuits fully profiting of both the novel
functionalities described above and the gain obtained by mov-
ing to the third dimension (see figure 35). For this to happen,
significant advances in robust, scalable manufacturing pro-
cesses will be essential. Technical breakthroughs in techniques
such as ALD and large-scale parallel multiphoton lithography
<figure><img src="image_45.png" /><figcaption>**Figure 35.** Futuristic view of a 3D spintronic multi-functional chip integrating different computing elements. This includes ultra-high data storage and memory devices, a microfluidic chip and a highly-interconnected network for efficient neuromorphic computations. Reproduced from [6]. CC BY 4.0.</figcaption></figure>

may become key drivers of this endeavour. Moreover, large clusters integrating multiple growth techniques—such as sputtering, ALD, and pulsed laser deposition—along with in-situ characterization methods, will play a crucial role. When combined with robotics and AI for e.g. automated diagnostics, these advances will enable the engineering of new, complex 3D spintronic devices.

## Concluding remarks

3D spintronics, under the common umbrella of creating new spintronic devices with 3D functionality has several flavours, from 3D circuits with complex geometries, to magnetic multilayered based devices with magnetic functionality across the whole space, including 3D topological textures. Today Spintronics is bridging the gap with the microelectronic industry by conceiving new spin-chip integrating spins and CMOS [207]. Tomorrow, by giving access to the third dimension, complex circuits with completely novel functionalities and huge gain in performances will be achieved.

## Data availability statement

No new data were created or analysed in this study.

## Acknowledgments

This work was supported by the European Community under the Horizon 2020 Program, Contract Nos. 101001290 (3DNANOMAG) and 101070417 (SPIDER).

## ORCID iDs

Gianluca Gubbiotti https://orcid.org/0000-0002-7006-0370

Anjan Barman https://orcid.org/0000-0002-4106-5658

Sam Ladak https://orcid.org/0000-0002-0275-0927

Cristina Bran https://orcid.org/0000-0001-8571-5846

Dirk Grundler https://orcid.org/0000-0002-4966-9712

Michael Huth https://orcid.org/0000-0001-7415-465X

Harald Plank https://orcid.org/0000-0003-1112-0908

Georg Schmidt https://orcid.org/0000-0002-4151-6543

Sebastiaan van Dijken https://orcid.org/0000-0001-6372-2252

Robert Streubel https://orcid.org/0000-0003-4783-892X

Oleksandr Dobrovoloskiy https://orcid.org/0000-0002-7895-8265

Valerio Scagnoli https://orcid.org/0000-0002-8116-8870

Laura Heyderman https://orcid.org/0000-0003-3843-6611

Claire Donnelly https://orcid.org/0000-0002-9942-2419

Olav Hellwig https://orcid.org/0000-0002-1351-5623

Lorenzo Fallarino https://orcid.org/0000-0002-5181-5272

M Benjamin Jungfleisch https://orcid.org/0000-0001-8204-3677

Alan Farhan https://orcid.org/0000-0002-2384-2249

Nicolò Maccaferri https://orcid.org/0000-0002-0143-1510

Paolo Vavassori https://orcid.org/0000-0002-4735-6640

Peter Fischer https://orcid.org/0000-0002-9824-9343

Riccardo Tomasello https://orcid.org/0000-0002-9218-5633

Giovanni Finocchio https://orcid.org/0000-0002-1043-3876

Rodolphe Clérac https://orcid.org/0000-0001-5429-7418

Roberta Sessoli https://orcid.org/0000-0003-3783-2700

Denys Makarov https://orcid.org/0000-0002-7177-4308

Denis D Sheka https://orcid.org/0000-0001-7311-0639

Maciej Krawczyk https://orcid.org/0000-0002-0870-717X

Rodolfo Gallardo https://orcid.org/0000-0002-4495-5592

Pedro Landeros https://orcid.org/0000-0002-0927-1419

Massimiliano d'Aquino https://orcid.org/0000-0002-5321-5772

Riccardo Hertel https://orcid.org/0000-0002-0646-838X

Philipp Pirro https://orcid.org/0000-0002-0163-8634

Florin Ciubotaru https://orcid.org/0000-0002-7088-2075

Markus Becherer https://orcid.org/0000-0002-1291-8877

Jack Gartside https://orcid.org/0000-0002-7044-7399

Teruo Ono https://orcid.org/0000-0002-9629-0633

Paolo Bortolotti https://orcid.org/0000-0002-0892-0368

Amalio Fernández-Pacheco https://orcid.org/0000-0002-3862-8472

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