††thanks: Correspond to<EMAIL_ADDRESS>
# 2D Magnetic Heterostructures: Spintronics and Quantum Future

Bingyu Zhang  Department of Electrical and Computer Engineering, University of
Florida, Gainesville, Florida 32611, USA.  Pengcheng Lu  Department of
Materials Science and Engineering, University of Florida, Gainesville, Florida
32611, USA.  Roozbeh Tabrizian  Department of Electrical and Computer
Engineering, University of Florida, Gainesville, Florida 32611, USA.  Philip
X.-L. Feng  Yingying Wu  Department of Electrical and Computer Engineering,
University of Florida, Gainesville, Florida 32611, USA.

###### Abstract

The discovery of two-dimensional (2D) magnetism within atomically thin
structures derived from layered crystals has opened up a new realm for
exploring magnetic heterostructures. This emerging field provides a
foundational platform for investigating unique physical properties and
exquisite phenomena at the nanometer and molecular/atomic scales. By
engineering 2D interfaces using physical methods and selecting interlayer
interactions, we unlock the potential for extraordinary exchange dynamics.
This potential extends to high-performance and high-density magnetic memory
applications, as well as future advancements in neuromorphic and quantum
computing. This review delves into recent advances in 2D magnets, elucidates
the mechanisms behind 2D interfaces, and highlights the development of 2D
devices for spintronics and quantum information. Particular focus is placed on
2D magnetic heterostructures with topological properties, promising for a
resilient and low-error information system. Finally, we discuss the trends of
2D heterostructures for future electronics, considering the challenges and
opportunities from physics, material synthesis, and technological prospective.

##  I Introduction

The advent of 2D van der Waals (vdW) materials1; 2; 3; 4 has sparked a
revolution in the field of magnetism, primarily due to the substantial
influence of the dimensionality confinement and size effects upon spin
textures and dynamics, e.g., quantum fluctuations. These 2D layered magnetic
materials (2D magnets) have garnered immense attention, driven by both their
fundamental significance and facile integration into multi-layer
heterostructures. Ever since the experimental discovery of 2D magnets with
intrinsic magnetism in 2017, like CrI3 and Cr2Ge2Te6 5; 6, 2D magnets family
has expanded significantly over the years. Unlike ultrathin film systems grown
on a substrate (e.g., CoFeB/MgO), these 2D magnets possess a naturally layered
structures, high crystallinity, and weak coupling to any transferred
substrate. Furthermore, the reduced coordination effects7, e.g., finite size
effect, seen in ultrathin films are less pronounced in these layered magnets,
thanks to their weak interlayer interactions. Consequently, these 2D magnets
serve as tailored testbeds for exploring the pure dimensional transition of
magnetism from 3D to 2D. Additionally, these magnets exhibit high
responsivities to external stimuli, such as gate voltage, molecule adsorption,
and neighboring materials. The unique controllability of magnetism by electric
ways opens up possibilities for creating heterostructures and devices for
applications in spintronics and memory technology.

However, it is worth noting that the magnetic properties of individual 2D
magnets are typically monotonous and imperfect, which poses significant
limitations for further applications. Therefore, an effective strategy
involves modulation of their magnetism through heterostructure construction,
which can tune the electronic band structures of 2D magnets via interfacial
interactions. Artificial structures can be assembled to manipulate and enhance
their magnetism through magnetic coupling. Furthermore, these 2D magnets can
be harnessed to induce valley polarization and spin splitting in many
nonmagnetic 2D materials, such as monolayer graphene8 and topological
insulators9; 10; 11.

Based on these magnetic heterostructures, 2D spintronics is an emerging field
to realize devices such as magnetic tunneling junctions (MTJ), spin field-
effect transistors and memoristors12; 13; 14; 15. 2D spintronics has unwrapped
innovation and compelling opportunities which not only improve their
performance but also diversify the functionality of electronic devices. For
example, imprinted magnetic skyrmions can only exist at 2D interfaces16, which
can be used as parallel information storage channels. When combined with
electrical control, switch of skyrmion on/off states can be realized17; 18.
Besides, 2D magnetic heterostructures for unconventional computing is an
emerging field. One examples is for neuromorphic computing, which
traditionally employs 3D bulk materials or nonlayered thin films, and thus the
resulting device size is either difficult to scale down for high density
integration or suffering from lattice mismatch problems. The emergence of 2D
magnets offers a promising solution, as evidenced by the surge of reported 2D
heterostructures functioning as neuromorphic computing devices19; 20, as well
as using skyrmions21; 22; 23. Another area is for quantum computing, concepts
such as using 2D magnetic heterostructures with superconductors towards
topological superconductivity24; 25 and skyrmion qubits26; 27, with
scalibility, offer easy electric control and new functionality. In this
review, we will first discuss the large family of existing 2D mangets,
including ferromagnet, antiferromagnet, and multiferroics, then discuss the
multifunctionality in 2D magnetic heterostructures. Based on these
heterostructures, 2D devices for spintronics will be discussed, with a
targeting for applications in high-performance and high-density magnetic
memory, as well as neuromorphic and quantum computing.

##  II Library of 2D Magnets

The hallmark of 2D magnetism is the existence of an ordered arrangement of
magnetic moments over macroscopic length scales at any finite temperature,
with a spontaneous breaking of time-reversal symmetry. Since first discovery
in 2017, a rich collection of layered magnetic materials covering a wide
spectrum of magnetic properties has been reported, as shown in Figure 1. Many
of these materials are semiconductors with bandgaps covering the near-infrared
to the ultraviolet spectral range, whereas a few are metallic.

Ferromagnetic (FM) order exists in both layered transition metal halides and
chalcogenides, when the exchange interactions favor both intralayer and
interlayer parallel spin alignments. The Curie temperature $T_{C}$ is known as
the temperature above which the material undergoes a magnetic transition from
a ferromagnet to a paramagnet. While antiferromagnetic (AFM) materials have a
rich variety of magnetic orders, they can be broadly divided into two types:
those with intralayer FM order and interlayer AFM order, and others with
intralayer AFM order. Antiferromagnets (antiferros) are magnetic ordered, yet
with zero magnetization, making them immune to external field perturbations.
Their AFM order is established by the exchange interactions between the spins,
which produces an exchange field in the order of $10^{2}$ to $10^{3}$ T and
give rise to a THz spin precession frequency. In the following, we discuss
some magnetic materials under extensive studies, with physical properties
promising for device design.

Figure 1: Illustration of 2D magnetic materials, showing the critical
temperature and electrical properties. Arrangement is in accordance with their
magnetism, conductivity and critical temperature. Ferromagnetic and
antiferromagnetic materials are characterized by Curie and Néel temperature,
respectively. They are divided into three dashed spheres based on
conductivity: smallest (insulating), medium (semiconducting), large
(metallic). Multiferroics are highlighted by red color.

Multilayer CrI3 exhibits interlayer AFM behavior, while monolayers display FM
ordering. The atomically thin CrI3 flakes were successfully prepared by
mechanical exfoliation, and the monolayer FM properties were subsequently
demonstrated using a low-temperature microscopic magneto-optical Kerr effect
(MOKE) measurement setup6. The transition temperature $T_{C}$ for monolayer
was measured at 45 K, slightly lower than the bulk $T_{C}$ of 61 K28; 29. The
bilayer CrI3 shows AFM behaviour due to a weak AFM interlayer coupling, which
is different from monolayer. The interlayer magnetic coupling can be tuned by
external field, either magnetic or electric fields. If an out-of-plane
magnetic field is applied, with a field strength of $\sim$ 0.65 T, it can flip
the magnetization in one layer and change the bilayer from AFM to FM state.
Gate voltage applied through electric way can also help switch CrI3 between FM
and AFM states, with more energy-efficiency30.

The intrinsic ferromagnetism in 2D Cr2Ge2Te6 (CGT) layers was reported around
the same time as CrI35, and it is also revealed by MOKE microscopy under a
small stabilizing magnetic field of 0.075 T. CGT is a FM material with a band
gap around 0.8 eV31. Its electrical property was characterized with a two-
terminal resistivity of around M$\Omega$ at room temperature32, showing the
electrically resistive nature. Thus few work can be done to study its
transport properties. Additionally, CGT thin layers exhibit a thickness-
dependent $T_{C}$, from a bilayer value of about 30 K to a bulk limit of 68 K.
This thickness dependence of $T_{C}$ exists also in as-grown thin magnetic
films, which shows more pronounced dependence33.

These two materials mentioned above have relatively low $T_{C}$, with respect
to room-temperature memory device. To market application of 2D magnets in
spintronic devices, the emphasis is on developing 2D materials with stable
magnetic properties at room temperature. Among all 2D magnets, Fe-based
materials usually have higher $T_{C}$, e.g. Fe3GeTe2 (FGeT). Its itinerant
ferromagnetism was observed to persist down to the monolayer, due to its
strong perpendicular magnetic anisotropy (PMA) with a uniaxial
magnetocrystalline anisotropy constant $K_{u}$=1.46$\times 10^{7}$ erg/cm3.34
This anisotropy energy is about two or three orders of magnitude larger than
CrI3 ($K_{u}$=4.3$\times 10^{4}$ erg/cm3 at 50 K)35 and CGT ($K_{u}$=1$\times
10^{5}$ erg/cm3)36 case. In bulk FGeT, the $T_{C}$ is $200-220$ K, depending
on Fe deficiency. Although this value is diminished in atomically thin FGeT
flakes, it can be significantly elevated to reach room temperature by
employing liquid gating37, showing electrically tunable nature of these 2D
magnetism.

Another example is VSe2, with monolayer grown by molecular beam epitaxy (MBE)
method. This material has been shown to maintain its FM ordering at 330 K38.
Exceptionally, a recent discovered material Fe3GaTe2 (FGaT), with similar
crystal structure to FGeT, exhibits as an above room temperature 2D metallic
ferromagnet39. It has been demonstrated a record-high $T_{C}$ ($\sim$350-380
K) as well as a robust PMA. These outstanding magnetic properties render
Fe3GaTe2 a widely favored material for practical magnetoelectronic and
spintronic applications.

Beyond magnetic properties, these 2D magnets also provide a unique platform
for the realization of topological magnetic materials, to study the interplay
between magnetism and topology. MnBi2Te4 and its derivative compounds have
received focused attention recently for their inherent magnetic order and the
rich, robust and tunable topological phases11. MnBi2Te4 has an AFM interlayer
coupling, while a FM order exists in each single layer, with out-of-plane easy
magnetic axis. The interplay between the magnetic structure and the
topological nontrivial bands endows the materials with rich topological
phases, e.g. quantized anomalous Hall effect above 1.5 K40, which has higher
temperature than magnetically doped BST samples41. In odd-layer flakes,
quantum anomalous Hall effect was observed with quantized plateaus of Hall
resistivity as well as diminishing longitudinal resistance42, absence of any
applied magnetic fields. This is extremely promising for low-power devices
with dissipationless edge states. These materials and their heterostructures
provide a neat, simple and versatile way to fuse topological bands with
magnetic order, which are promising to help push quantum anamolous Hall effect
towards the liquid nitrogen temperature. Possession of topology contributes to
improving the performance of electronic components, by enabling high fault
tolerance with topological protection, which is a key factor desired in
quantum computing.

Additionally, 2D multiferroic materials are actively studied for their cross-
coupling effects. This class of materials exhibit multiple ferroic properties
simultaneously, including ferromagnetism, ferroelectricity, and
ferroelasticity. Multiferroics hold great promise for the development of
innovative, multifunctional devices, with enhanced device performance and
scaled down size in vdW case. The discovery of type-II multiferroic order in a
single atomic layer of the transition-metal-based layered material NiI2 was
reported recently43, which exhibits an inversion-symmetry-breaking magnetic
order and directly induces a ferroelectric (FE) polarization. Later,
intriguing in-plane electrical and magnetic anisotropies in layered
multiferroic CuCrP2S644 has generated much excitement owing to coexsitence of
antiferroelectric and antiferromagnetism, along with strong polarization-
magnetization coupling. These multiferroics enable magnetization affected by
electric field, and vice versa. This functionality has motivated fundamental
and applied research in applying multiferroics for voltage controlled magnetic
anisotropy, towards low-power switching devices.

Overall, the current main thrusts for 2D magnets search are (1) room-
temperature atomically thin magnet, for high-density and high-performance
memory; (2) FM or AFM semiconductors with a tunable band gap and a stability,
which would be an ideal platform to investigate the magneto-electric coupling
between electrons and spin; (3) exotic topological properties, like searching
for high-temperature quantum anomalous Hall insulators; (4) large-scale thin
films for device integration. Although 2D exfoliated films offer high quality
of layers, the limitation on the lateral size normally to hundreds of
micrometers still prohibits their applications in the integration level.
Efforts are working on to obtain high-quality wafer-scale 2D magnetic
heterostructures.

##  III 2D Magnetic Heterostructures and Their Interface

2D magnetic heterostructure is a material system composed of two or more
distinct layers of atomically thin magnetic materials stacked on top of each
other. These layers can have different magnetic properties or orientations.
The use of 2D magnetic heterostructures is mainly for two purposes. One is to
expand the functionality of these structures for both experimental
investigations and future practical applications. The other is, the proximity
effects within heterostructuers give rise to valuable phenomena that enhance
the magnetic properties. When combining with magnetism, the interface has even
more intriguing physics and phenomena as shown in Figure 2, compared to the
charge-based system.

Firstly, the orbital hybridization at the interface can not only induce the
exchange interaction at the interface, but also modify the electronic and
magnetic properties in adjacent layers by impacting their band structure and
orbital characters. Established orbital hybridization is a new degree of
freedom for controlling interfacial Dzyaloshinskii-Moriya interaction (DMI), a
short-range anti-symmetric exchange interaction45. Taking CGT/FGeT
heterostructure for examples, the topological Hall effect arising from
magnetic skyrmions was observed, which are due to interfacial DMI16.

Another proximity effect is exchange coupling, which refers to the interaction
between magnetic moment of different layers within the heterostructure. It’s
crucial for the applications in magnetic memory and spintronic devices, like
spin valve, MTJ and magnetic sensors based on giant magnetoresistance (GMR) or
tunneling magnetoresistance (TMR). As reported, large exchange bias observed
in a FGeT/antiferro interface46, which is tunable by magnetic field cooling.
Antiferro, with zero magnetization, shows robustness against external
perturbations and THz fast spin procession. These makes coupling to antiferro
materials extremely promising.

Figure 2: Schematic mechanisms of 2D interface in magnetic heterostructures,
including orbital hybridization, exchange coupling, lattice perturbation,
strain effect, SOC proximity and magnetoelectric effect.

Following is lattice perturbation, which distorts the crystal lattice
structure at the interface, thus tuning the magnetic behaviours. Examples
include applying electric voltages and vertical stacking to form the Moiré
lattice47. This can lead to either the control of magnetization or the
emergence of new exotic effects like Moiré skyrmions48.

Different from above mechanism, strain effect arises from mechanical
deformation, leading to the change of electronic band structures. The methods
to induce strain include lattice mismatch, utilization of flexible, patterned,
or piezoelectric/FE substrates, as well as an atomic force microscopy tip or
even the presence of bubbles at the interface during sample assembly.

Spin-orbit coupling (SOC) refers to the interaction between the spin and
orbital angular momentum of electrons across different layers within the
heterostructure. This can play an important role when 2D magnet is interfaced
with heavy metal element. An example of this is the emergence of skymions in
WTe2/FGeT heterostructure49 through SOC coupling. This SOC is also crucial to
realize spin-orbit torque (SOT) or spin-transfer torque (STT) in magnetic
random-access memory (MRAM).

The last but significant effect is the magnetoelectric effect, which occurs
when a FM layer interfaces with a FE or multiferroic layer. The magnetism of
the FM material can be switched by the electric polarization in the FE layer,
and vice versa. FE control of magnetism is particularly interesting due to its
energy-efficient and nonvolatile nature. One example is to use a thin FE
polymer to open and close the CGT magnetic loop50.

Material | Thickness (nm) | Polarization ($\mu$C/cm2) | Coercive field (MV/cm)
---|---|---|---
2D FEs | CuInP2S6 | N/A | 2.55 | 0.077
$\alpha$-In2Se3 | 5 | 2-11 | 0.2
h-BN | N/A | 0.09 | 2
Other FEs | HfxZr1-xO2 | 0.5-30 | 5-50 | 1-3
Al${}_{1-x}Sc_{x}N$ | <10 | 100-150 | 3-7
Al${}_{1-x}B_{x}N$ | 500 | >125 | 5-6
Zn${}_{1-x}Mg_{x}O$ | 500 | 25-100 | 2-3
Table 1: Comparing FE properties between different classes of 2D and thin
materials.

An alternative promising approach to generate a substantial magnetoelectric
effect involves the stacking 2D FM layer with recently emerging fluorite51;
52; 53 and wurtzite FE54; 55; 56 materials. These CMOS-compatible FE
materials, such as hafnium-dioxide, zinc-magnesium-oxide, or aluminum-
scandium-nitride, offer a unique advantage over conventional perovskites due
to their remarkable scalability, while providing very large polarization and
coercive fields57. Moreover, fluoride FEs with sub-nm thickness58; 59 and
wurtzite FEs with sub-10 nm thickness60 have been demonstrated, and their
integration with 2D materials is explored to create novel memory devices are
explored61. In comparison to 2D FEs62; 63 as shown in Table 1, these 3D yet
atomically thin materials offer one to two orders of magnitude higher
polarization, significantly amplifying magnetoelectric effects at the
interface with FMs64. Additionally, they boast coercive fields two to three
orders of magnitude higher compared to 2D FE counterparts, enabling the
attainment of higher switching voltages and improved interstate isolation,
which is desirable for memory applications.

The high-quality and seamless 2D interfaces offer a platform for introducing
new functionalities into 2D devices, thereby enabling the exploration of novel
physics and effects. Of particular interest is the pursuit of ultra-fast,
ultra-compact, and energy-efficient spintronics through precise interface
engineering. By leveraging the interface, it becomes possible to amalgamate
THz spin procession in AFM materials, nonvolatile control via 2D FEs, and
scalable configurations into a single device. This development holds
significant promise for advancing the field of spintronics in the future.

##  IV 2D Spintronics

###  IV.1 Device for Magnetic Memory

Introducing magnetic elements into memory devices provides substantial
advantages, particularly in achieving non-volatile memory functionality. The
utilization of 2D magnetic heterostructures, comprised of multiple layers of
2D materials with unique properties, takes these advantages even further. It
enhances energy efficiency, boosts data storage density, and enriches the
range of functionalities achievable within a single memory device, as shown in
Figure 3.

MTJ is a fundamental component in modern memory devices. It consists of two FM
layers separated by a thin insulating barrier. The core principle governing
MTJ operation is the TMR effect, wherein the electrical resistance of the
junction changes based on the relative alignment of magnetization in the two
FM layers. In contrast to traditional bulk ferros such as Fe3O4 and Co,
employing atomically thin layered magnets for MTJs offers the potential to
significantly enhance their TMR, since TMR heavily depends on interface
quality. Additionally, this approach relaxes the stringent lattice-matching
requirements associated with epitaxy growth and enables high-quality
integration of dissimilar materials with atomically sharp interfaces.

Among the existing 2D magnets, CrI3 stands out due to its layered AFM ordering
and relatively electrically insulating properties, making it a desirable
choice as tunnel barrier in MTJs. One spin-filter MTJ design involves a
heterostructure consisting of h-BN encapsulated graphene/CrI3/graphene
layers65. This device demonstrated remarkable TMR values of 530%, 3200%, and
19,000% for bilayer, trilayer, and four-layer CrI3 structures, respectively.
The highest value of the four-layer structure greatly exceeds typically
achieved in conventional bulk material MTJs66; 67. While MTJs based on CrI3
exhibit promising properties in TMR, it’s crucial to acknowledge their
operational constraints - cryogenic low temperature for operation and need of
magnetic fields. In response, ongoing research focuses on advancing MTJs by
employing materials suitable for room-temperature operation. A notable
candidate is FGaT, which boasts a high $T_{C}$ of 380 K, as well as operation
temperature above room temperature. This characteristic overcomes the
limitation, greatly facilitating the realization of practical spintronic
devices. A room-temperature MTJ based on a FGaT/WSe2/FGaT heterostructure was
successfully demonstrated68, showing significant TMR of 85% at room
temperature.

Spin field-effect transistor (Spin-FET) is a new type of spintronics device
towards non-volatile memory. This device utilizes the spin, rather than
charge, in the flow of electrical current, which could potentially offer non-
volatile data storage and improved performance compared with traditional FETs.
The application of a magnetic tunnel barrier in MTJ can be extended to Spin-
FETs, leading to a noval device - the spin tunnel FET, e.g. dual-gated
graphene/CrI3/graphene tunnel junctions69, with similar structure as spin-
filter MTJs. This device achieves an impressive high-to-low conductance ratio
of nearly 400% by electrical modulation of magnetization configurations.
However, it shares a common constraint with CrI3-based MTJs, requiring low
operational temperatures and magnetic fields. Despite these challenges, the
search for high-temperature semiconducting magnets holds the key to advancing
the development of this device, potentially overcoming existing limitations
and paving the way for future applications.

Utilizing SOC, SOT devices are engineered to manipulate the magnetization of a
magnetic layer by an spin-polarized current. Compared to traditional STT
devices, SOT devices are anticipated to offer superior performance like easy
stacking, operation in sub-ns writing and reading speed. Typically, a SOT
device comprises two key components: a FM layer and a non-magnetic heavy metal
(HM) layer. SOT efficiency heavily relies on the interface quality. Thus, 2D
magnets can be promising building blocks for SOT devices, like CGT, CrI3, and
FGeT with intrinsic PMA. Even in monolayer form, these materials maintain
their PMA, making them highly responsive to external stimuli. In the initial
designs of 2D magnetic SOT devices, structures like Pt/FGeT70 and Ta/CGT71
were featured, showing significant improvements in SOT switching efficiency
with the incorporation of 2D FM materials. Creating all-vdW heterostructures
can further enhance the switching efficiency. For instance, a FGeT/WSe2
heterostructure was realized72, achieving a remarkably low switching current
density of 3.90$\times 10^{6}$ A/cm2 at 150 K, which is comparable or even
better to that of conventional thin films system73; 74. Recent research
efforts have been directed towards achieving reliable vdW SOT operation at
room temperature. One work75 incorporates high $T_{C}$ FGaT to achieve room
temperature operation, with a FGaT/Pt bilayer structure. Currently, this
approach still needs a high switching current density of 1.3$\times$107 A/cm2.
Another notable approach involves a wafer-scale FGeT/Bi2Se3 layered
heterostructure76, where the topological insulator Bi2Se3 plays a crucial role
in raising the TC of FGeT to room temperature through exchange coupling. This
approach has yielded promising results, including a high damping-like SOT
efficiency of $\sim$2.69 and a notably low switching current of 2.2$\times$
106 A/cm2 at room temperature. This development marks a significant step
toward practical SOT devices for real applications.

Apart from conventional memory, Josephson junction (JJ) combines the quantum
phenomena with memory device technology, opening the door to the development
of superconducting Random Access Memories (RAMs)77. JJs are typically composed
of two superconductors (SCs) separated by a thin insulating or non-
superconducting barrier. JJ based on 2D ferro/SC heterostructure presents
unique opportunity to explore the interaction between superconductivity and
ferromagnetism. For instance, one approach involves constructing a JJ by
introducing a few-layer FM insulator, CGT, between two layers of SCs NbSe278.
This JJ demonstrates a hysteresis behavior in the critical current, which is
induced by the remanence of the magnetic barrier. Following this, another
lateral JJ emerged, composed of a FGeT, laterally interconnected between two
layered spin-singlet SCs NbSe279. This SC/ferro/SC heterostructure
successfully sustains skin Josephson supercurrents with a remarkable long-
range reach over 300 nanometers (nms).

Figure 3: Schematic of 2D magnetic heterostructures for magnetic memory.
Examples include magnetic tunneling junction (MTJ), spin-tunnel field-effect
transistor (spin-TFET), spin-orbit torque (SOT) devices and Josephson
junction.

###  IV.2 2D Magnetic Heterostructures for Neuromorphic Computing

Figure 4:  (a) Schematic of the skyrmionic synaptic device. Skyrmions
generated within 2D ferro/heaavy metal heterostructure. Bidirectional stimulus
applied on heavy metal layer inducing the spin current in FM layer. (b)
Schematic of skyrmion neuromorphic computer based on reservoir computing. Low-
dimensional voltage input applied to 2D skyrmion systems yields high-
dimensional magnetic output22. (c) Schematic of CrBr3/NbSe2 topological
superconductor. $dI/dV-V_{\textrm{bias}}$ spectrum charaterized on the NbSe2
substrate (blue), the middle of CrBr3 island (red) and the edge of CrBr3
island (green)25. (d) Schematic of skyrmion qubit concept based on magnetic
heterostructure.

Neuromorphic computing is an emerging field of artificial intelligence that
seeks to design computer systems inspired by the human brain’s neural
architecture. Owing to the atomic thickness, dangling-bond-free surfaces and
high mechanical robustness, 2D materials and heterostructures are extensively
investigated for neuromorphic computing devices, showing great promise for
high-performance artificial neurons and synapses80; 81; 82; 83; 84. The
integration of magnetic elements within 2D materials to form 2D magnetic
heterostructures takes this field a step further. These magnetic elements
provide non-volatility, longevity, and high-density information storage
capabilities. Furthermore, 2D magnetic heterostructures have the capability to
generate skyrmions16; 49, which are topological spin structures with unique
topology towards more compact, energy-efficient, fault-tolerant and resilient
neuromorphic devices23; 22; 85. Figure 4a schematics an artificial synapse
device concept based on skyrmions86. The primary component of the device is a
2D ferro/heavy metal heterostructrue, which forms a nanotrack for skyrmions
motion. The system replicating the operations of biological neurons and
synapses through the following processes: in spike transmission mode, the pre-
neuron’s spike is modulated by the synaptic device’s weight (reading through
magnetoresistance), leading to the generation of a post-synaptic spike
current. During the learning phase, a bidirectional charge current through the
heavy metal layer injects a vertical spin current in FM layer, driving the
skyrmions into (or out of) the postsynaptic region. This dynamic process
effectively adjusts the synaptic weight, closely mirroring the potentiation
and depression mechanisms observed in biological synapses. Additionally, the
resolution of the synaptic weight can be adjusted based on the nanotrack width
and the skyrmion size, which enriches the flexibility and tunibility of the
skyrmion-based synapse. Another example for the application of 2D skyrmions is
the reservoir computing22, a framework derived from recurrent neural network
theory. The essence of reservoir computing is the nonlinear transformation of
input into high-dimensional outputs. A physical system capable of implement
the reservoir part should possess both complex nonlinearity and memory effect
(or equally hysteresis) while also exhibiting short-term properties87; 88; 89.
Thus, magnetic skyrmions emerge as a promising candidate. In Figure 4b, 2D
skyrmion system performs as the "resvervoir part", nonlinearly converting the
one-dimensional time-series input $H_{\textrm{AC}}(t)$ to the linearly
independent $N$-dimensional time-series outputs $V(t)$. This design provides a
guideline for developing energy-saving and high-performance skyrmion
neuromorphic computing devices.

##  V 2D Heterostructures for Quantum Computing

2D magnetic heterostructures hold promise for quantum computing due to their
unique electronic properties, controllability, and potential for creating
novel quantum states. These interfaces can give rise to emergent quantum
phenomena, broadening the horizons for quantum information processing.
Notably, topological quantum computing benefits significantly from the
topological protection and qubit safeguarding that 2D magnet/magnetic
heterostructure can offer. An illustrative example is the observation of 2D
topological superconductivity within vdW heterostructures that combine the
ferro CrBr3 with the SC NbSe225. As Figure 4c shows, the monolayer CrBr3
island was grown on the NbSe2 layer. The $dI/dV$ spectrum was characterized at
different sites of this structure: NbSe2 substrate (blue), the middle of the
CrBr3 island (red) and the edge of the CrBr3 (green). Among them, a peak of
conductance localized at $E_{F}$ can be clearly seen for the edge of magnetic
island, which exhibits as a hallmark of topological superconductivity for this
structure. Furthermore, owing to the 2D layered structure, these edge modes
can be readily accessed and manipulated using various external stimuli,
including electrical, mechanical, and optical methods. This feature enhances
the promise of these heterostructures for integration into components of
topological quantum computing systems.

Another application of 2D magnetic heterostructures in quantum computing is
the implementation of skyrmion qubit. Unlike other proposed qubit systems such
as trapped atoms, quantum dots, and photons, magnetic skyrmions offer a
topologically protected structure that shows promise in resisting external
perturbations and faults. Moreover, skyrmion qubits hold additional potential
in addressing challenges related to control and scalability, further enhancing
their viability in quantum information processing. In Figure 4d, a skyrmion
qubit concept is illustrated, utilizing a bilayer magnetic materials
platform26. In this setup, quantum information is stored within the quantum
degree of helicity, and the logical states can be dynamically adjusted through
the manipulation of electric and magnetic fields.

##  VI Conclusions and perspectives

For decades, 2D magnetism has been a captivating subject, especially in the
context of the Mermin-Wagner-Hohenberg (MWH) theorem, which predicts that
thermal fluctuations will disrupt long-range magnetic order in 2D systems at
any finite temperature, following the isotropic Heisenberg model. Extensive
theoretical and experimental studies have been undertaken to unravel causes of
long-range ordering in 2D systems. Beyond magnetization, other physical
properties, including polarization, that may exhibit potential long-range
order within 2D systems hold the promise of pushing the limits of Moore’s law.
The inherent atomic-layer cleavability and magnetic anisotropy of 2D magnets
may help mitigate spin fluctuations in the face of short-range interactions,
thus paving the way for the emergence of 2D magnetism. While the duality in
electromagnetism remains a profound aspect of fundamental physics, the recent
discovery of 2D multiferroics further reinforces this concept, as
ferroelectricity is analogous to ferromagnetism. These discoveries pose
thought-provoking questions, such as the existence of an electric counterpart
to the MWH theorem. Considering dipole-dipole interactions, the absence of
polarization becomes a relevant consideration. Much like magnetic skyrmions
are topological whirls in magnetization, one might comtemplate the existence
of a FE equivalent.

The allure of 2D magnets extends beyond fundamental physics and into the realm
of novel device fabrication. Significant progress has been made in
comprehending their fundamental properties, and the demonstration of devices
is in its nascent stages. We have witnessed the expansion of the materials
library and glimpsed the potential device functionalities. However, achieving
integration of these materials into functional devices requires large-area
wafer-scale materials growth. Encouraging strides have been made through
techniques such as MBE and atomic layer deposition (ALD), e.g. large-scale
monolayer CrBr3 with MgO as a passivation layer from ALD 90 and wafer-scale
FGeT on Bi2Te3 from MBE20. Challenges still persist at the device level,
particularly in advancing dielectric and contact interfaces. The self-
passivated nature of monolayer 2D magnets will necessitate seeding for the
deposition of dielectrics through methods like ALD. It may lead to non-ideal
interfaces, limiting device performance compared to the best laboratory data
that employs crystalline 2D insulators like h-BN. Similar challenges are
encountered with electrical contacts, as they only partially conform to
industry specifications and have not yet reached the level of readiness
required for manufacturing. Addressing these crucial manufacturing bottlenecks
will pave the way for a significant enhancement in chip functionality,
heralding a new era of 2D magnet applications characterized by increased
device complexity.

Moreover, in the context of neuromorphic computing, a fundamental challenge
lies in improving the endurance of resistance switching. Achieving material
uniformity is essential to create massively connected device arrays capable of
mimicking the hyper-connectivity and efficiency of the brain. Computational
methods will be employed to guide experimental studies and optimize memristive
devices for maximum performance.

For using 2D magnetic heterostructures in topological quantum computing,
quantum states can benefit from topological protection, safeguarding qubits
against external perturbations and errors, in contrast to standard quantum
computing. Efforts in topological superconductivity and skyrmion qubits
present a unique opportunity to explore the interplay between topology,
magnetism, and electronic properties, potentially yielding new discoveries and
insights in physics, as well as paving the way for future quantum computing
devices.

References

## References

  * Chen et al. (2016) X. Chen, L. Wang, Y. Wu, H. Gao, Y. Wu, G. Qin, Z. Wu, Y. Han, S. Xu, T. Han, et al., 2D Materials 3, 015012 (2016).
  * Wu et al. (2016) Y. Wu, X. Chen, Z. Wu, S. Xu, T. Han, J. Lin, B. Skinner, Y. Cai, Y. He, C. Cheng, et al., Physical Review B 93, 035455 (2016).
  * Han et al. (2018) T. Han, J. Shen, N. F. Yuan, J. Lin, Z. Wu, Y. Wu, S. Xu, L. An, G. Long, Y. Wang, et al., Physical Review B 97, 060505 (2018).
  * Wu et al. (2019) Y. Wu, J. J. He, T. Han, S. Xu, Z. Wu, J. Lin, T. Zhang, Y. He, and N. Wang, Physical Review B 99, 121406 (2019).
  * Gong et al. (2017) C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, et al., Nature 546, 265 (2017).
  * Huang et al. (2017a) B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, et al., Nature 546, 270 (2017a).
  * Wang et al. (2020a) M.-C. Wang, C.-C. Huang, C.-H. Cheung, C.-Y. Chen, S. G. Tan, T.-W. Huang, Y. Zhao, Y. Zhao, G. Wu, Y.-P. Feng, et al., Annalen Der Physik 532, 1900452 (2020a).
  * Wu et al. (2020a) Y. Wu, G. Yin, L. Pan, A. J. Grutter, Q. Pan, A. Lee, D. A. Gilbert, J. A. Borchers, W. Ratcliff, A. Li, et al., Nature Electronics 3, 604 (2020a).
  * Pan et al. (2022) Q. Pan, Y. Liu, H. Wu, P. Zhang, H. Huang, C. Eckberg, X. Che, Y. Wu, B. Dai, Q. Shao, et al., Advanced Electronic Materials 8, 2200003 (2022).
  * Yang et al. (2020) C.-Y. Yang, L. Pan, A. J. Grutter, H. Wang, X. Che, Q. L. He, Y. Wu, D. A. Gilbert, P. Shafer, E. Arenholz, et al., Science Advances 6, eaaz8463 (2020).
  * Wang et al. (2020b) K. L. Wang, Y. Wu, C. Eckberg, G. Yin, and Q. Pan, MRS Bulletin 45, 373 (2020b).
  * Grollier et al. (2020) J. Grollier, D. Querlioz, K. Camsari, K. Everschor-Sitte, S. Fukami, and M. D. Stiles, Nature Electronics 3, 360 (2020).
  * Lin et al. (2019) X. Lin, W. Yang, K. L. Wang, and W. Zhao, Nature Electronics 2, 274 (2019).
  * Wang et al. (2020c) K. L. Wang, Y. Wu, C. Eckberg, G. Yin, and Q. Pan, MRS Bulletin 45, 373 (2020c).
  * Sierra et al. (2021) J. F. Sierra, J. Fabian, R. K. Kawakami, S. Roche, and S. O. Valenzuela, Nature Nanotechnology 16, 856 (2021).
  * Wu et al. (2022a) Y. Wu, B. Francisco, Z. Chen, W. Wang, Y. Zhang, C. Wan, X. Han, H. Chi, Y. Hou, A. Lodesani, et al., Advanced Materials 34, 2110583 (2022a).
  * Zhou et al. (2021) Y. Zhou, R. Mansell, and S. van Dijken, Applied Physics Letters 118 (2021).
  * Bhattacharya et al. (2020) D. Bhattacharya, S. A. Razavi, H. Wu, B. Dai, K. L. Wang, and J. Atulasimha, Nature Electronics 3, 539 (2020).
  * Kim et al. (2020) H. H. Kim, S. Jiang, B. Yang, S. Zhong, S. Tian, C. Li, H. Lei, J. Shan, K. F. Mak, and A. W. Tsen, Advanced Materials 32, 1905433 (2020).
  * Wang et al. (2020d) C.-Y. Wang, C. Wang, F. Meng, P. Wang, S. Wang, S.-J. Liang, and F. Miao, Advanced Electronic Materials 6, 1901107 (2020d).
  * Felser and Parkin (2022) C. Felser and S. Parkin, MRS Bulletin 47, 600 (2022).
  * Yokouchi et al. (2022) T. Yokouchi, S. Sugimoto, B. Rana, S. Seki, N. Ogawa, Y. Shiomi, S. Kasai, and Y. Otani, Science Advances 8, eabq5652 (2022).
  * Song et al. (2020) K. M. Song, J.-S. Jeong, B. Pan, X. Zhang, J. Xia, S. Cha, T.-E. Park, K. Kim, S. Finizio, J. Raabe, et al., Nature Electronics 3, 148 (2020).
  * Palacio-Morales et al. (2019) A. Palacio-Morales, E. Mascot, S. Cocklin, H. Kim, S. Rachel, D. K. Morr, and R. Wiesendanger, Science Advances 5, eaav6600 (2019).
  * Kezilebieke et al. (2020) S. Kezilebieke, M. N. Huda, V. Vaňo, M. Aapro, S. C. Ganguli, O. J. Silveira, S. Głodzik, A. S. Foster, T. Ojanen, and P. Liljeroth, Nature 588, 424 (2020).
  * Psaroudaki and Panagopoulos (2021) C. Psaroudaki and C. Panagopoulos, Physical Review Letters 127, 067201 (2021).
  * Xia et al. (2023) J. Xia, X. Zhang, X. Liu, Y. Zhou, and M. Ezawa, Physical Review Letters 130, 106701 (2023).
  * McGuire et al. (2015) M. A. McGuire, H. Dixit, V. R. Cooper, and B. C. Sales, Chemistry of Materials 27, 612 (2015).
  * Dillon Jr and Olson (1965) J. Dillon Jr and C. Olson, Journal of Applied Physics 36, 1259 (1965).
  * Huang et al. (2018) B. Huang, G. Clark, D. R. Klein, D. MacNeill, E. Navarro-Moratalla, K. L. Seyler, N. Wilson, M. A. McGuire, D. H. Cobden, D. Xiao, et al., Nature Nanotechnology 13, 544 (2018).
  * Hao et al. (2018) Z. Hao, H. Li, S. Zhang, X. Li, G. Lin, X. Luo, Y. Sun, Z. Liu, and Y. Wang, Science Bulletin 63, 825 (2018).
  * Xing et al. (2017) W. Xing, Y. Chen, P. M. Odenthal, X. Zhang, W. Yuan, T. Su, Q. Song, T. Wang, J. Zhong, S. Jia, et al., 2D Materials 4, 024009 (2017).
  * Zhang et al. (2019) X. Zhang, Y. Lao, J. Sklenar, N. S. Bingham, J. T. Batley, J. D. Watts, C. Nisoli, C. Leighton, and P. Schiffer, APL Materials 7 (2019).
  * León-Brito et al. (2016) N. León-Brito, E. D. Bauer, F. Ronning, J. D. Thompson, and R. Movshovich, Journal of Applied Physics 120 (2016).
  * Richter et al. (2018) N. Richter, D. Weber, F. Martin, N. Singh, U. Schwingenschlögl, B. V. Lotsch, and M. Kläui, Physical Review Materials 2, 024004 (2018).
  * Liu et al. (2019) Y. Liu, C. Petrovic, et al., Physical Review Materials 3, 014001 (2019).
  * Deng et al. (2018) Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, et al., Nature 563, 94 (2018).
  * Bonilla et al. (2018) M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan, and M. Batzill, Nature Nanotechnology 13, 289 (2018).
  * Zhang et al. (2022) G. Zhang, F. Guo, H. Wu, X. Wen, L. Yang, W. Jin, W. Zhang, and H. Chang, Nature Communications 13, 5067 (2022).
  * Liu et al. (2020) C. Liu, Y. Wang, H. Li, Y. Wu, Y. Li, J. Li, K. He, Y. Xu, J. Zhang, and Y. Wang, Nature Materials 19, 522 (2020).
  * Pan et al. (2020) L. Pan, A. Grutter, P. Zhang, X. Che, T. Nozaki, A. Stern, M. Street, B. Zhang, B. Casas, Q. L. He, et al., Advanced Materials 32, 2001460 (2020).
  * Deng et al. (2020) Y. Deng, Y. Yu, M. Z. Shi, Z. Guo, Z. Xu, J. Wang, X. H. Chen, and Y. Zhang, Science 367, 895 (2020).
  * Song et al. (2022) Q. Song, C. A. Occhialini, E. Ergeçen, B. Ilyas, D. Amoroso, P. Barone, J. Kapeghian, K. Watanabe, T. Taniguchi, A. S. Botana, et al., Nature 602, 601 (2022).
  * Wang et al. (2023a) X. Wang, Z. Shang, C. Zhang, J. Kang, T. Liu, X. Wang, S. Chen, H. Liu, W. Tang, Y.-J. Zeng, et al., Nature Communications 14, 840 (2023a).
  * Zhu et al. (2022a) L. Zhu, L. Zhu, X. Ma, X. Li, and R. A. Buhrman, Communications Physics 5, 151 (2022a).
  * Wu et al. (2022b) Y. Wu, W. Wang, L. Pan, and K. L. Wang, Advanced Materials 34, 2105266 (2022b).
  * Yang et al. (2023) B. Yang, Y. Li, H. Xiang, H. Lin, and B. Huang, Nature Computational Science 3, 314 (2023).
  * Tong et al. (2018) Q. Tong, F. Liu, J. Xiao, and W. Yao, Nano Letters 18, 7194 (2018).
  * Wu et al. (2020b) Y. Wu, S. Zhang, J. Zhang, W. Wang, Y. L. Zhu, J. Hu, G. Yin, K. Wong, C. Fang, C. Wan, et al., Nature Communications 11, 3860 (2020b).
  * Liang et al. (2023) S. Liang, T. Xie, N. A. Blumenschein, T. Zhou, T. Ersevim, Z. Song, J. Liang, M. A. Susner, B. S. Conner, S.-J. Gong, et al., Nature Electronics 6, 199 (2023).
  * Böscke et al. (2011) T. Böscke, J. Müller, D. Bräuhaus, U. Schröder, and U. Böttger, Applied Physics Letters 99 (2011).
  * Muller et al. (2012) J. Muller, T. S. Boscke, U. Schroder, S. Mueller, D. Brauhaus, U. Bottger, L. Frey, and T. Mikolajick, Nano Letters 12, 4318 (2012).
  * Mikolajick et al. (2014) T. Mikolajick, S. Müller, T. Schenk, E. Yurchuk, S. Slesazeck, U. Schröder, S. Flachowsky, R. van Bentum, S. Kolodinski, P. Polakowski, et al., Advances in Science and Technology 95, 136 (2014).
  * Fichtner et al. (2019) S. Fichtner, N. Wolff, F. Lofink, L. Kienle, and B. Wagner, Journal of Applied Physics 125 (2019).
  * Hayden et al. (2021) J. Hayden, M. D. Hossain, Y. Xiong, K. Ferri, W. Zhu, M. V. Imperatore, N. Giebink, S. Trolier-McKinstry, I. Dabo, and J.-P. Maria, Physical Review Materials 5, 044412 (2021).
  * Ferri et al. (2021) K. Ferri, S. Bachu, W. Zhu, M. Imperatore, J. Hayden, N. Alem, N. Giebink, S. Trolier-McKinstry, and J.-P. Maria, Journal of Applied Physics 130 (2021).
  * Kim et al. (2023) K.-H. Kim, I. Karpov, R. H. Olsson III, and D. Jariwala, Nature Nanotechnology pp. 1–20 (2023).
  * Cheema et al. (2022a) S. S. Cheema, N. Shanker, S.-L. Hsu, Y. Rho, C.-H. Hsu, V. A. Stoica, Z. Zhang, J. W. Freeland, P. Shafer, C. P. Grigoropoulos, et al., Science 376, 648 (2022a).
  * Cheema et al. (2022b) S. S. Cheema, N. Shanker, C.-H. Hsu, A. Datar, J. Bae, D. Kwon, and S. Salahuddin, Advanced Electronic Materials 8, 2100499 (2022b).
  * Wang et al. (2020e) D. Wang, J. Zheng, P. Musavigharavi, W. Zhu, A. C. Foucher, S. E. Trolier-McKinstry, E. A. Stach, and R. H. Olsson, IEEE Electron Device Letters 41, 1774 (2020e).
  * Liu et al. (2021) X. Liu, D. Wang, K.-H. Kim, K. Katti, J. Zheng, P. Musavigharavi, J. Miao, E. A. Stach, R. H. Olsson III, and D. Jariwala, Nano Letters 21, 3753 (2021).
  * Guan et al. (2020) Z. Guan, H. Hu, X. Shen, P. Xiang, N. Zhong, J. Chu, and C. Duan, Advanced Electronic Materials 6, 1900818 (2020).
  * Wang et al. (2023b) C. Wang, L. You, D. Cobden, and J. Wang, Nature Materials pp. 1–11 (2023b).
  * Dmitriyeva et al. (2021) A. Dmitriyeva, V. Mikheev, S. Zarubin, A. Chouprik, G. Vinai, V. Polewczyk, P. Torelli, Y. Matveyev, C. Schlueter, I. Karateev, et al., ACS Nano 15, 14891 (2021).
  * Song et al. (2018) T. Song, X. Cai, M. W.-Y. Tu, X. Zhang, B. Huang, N. P. Wilson, K. L. Seyler, L. Zhu, T. Taniguchi, K. Watanabe, et al., Science 360, 1214 (2018).
  * Ikeda et al. (2008) S. Ikeda, J. Hayakawa, Y. Ashizawa, Y. Lee, K. Miura, H. Hasegawa, M. Tsunoda, F. Matsukura, and H. Ohno, Applied Physics Letters 93 (2008).
  * Parkin et al. (2004) S. S. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes, M. Samant, and S.-H. Yang, Nature Materials 3, 862 (2004).
  * Zhu et al. (2022b) W. Zhu, S. Xie, H. Lin, G. Zhang, H. Wu, T. Hu, Z. Wang, X. Zhang, J. Xu, Y. Wang, et al., Chinese Physics Letters 39, 128501 (2022b).
  * Jiang et al. (2019) S. Jiang, L. Li, Z. Wang, J. Shan, and K. F. Mak, Nature Electronics 2, 159 (2019).
  * Alghamdi et al. (2019) M. Alghamdi, M. Lohmann, J. Li, P. R. Jothi, Q. Shao, M. Aldosary, T. Su, B. P. Fokwa, and J. Shi, Nano Letters 19, 4400 (2019).
  * Ostwal et al. (2020) V. Ostwal, T. Shen, and J. Appenzeller, Advanced Materials 32, 1906021 (2020).
  * Shin et al. (2022) I. Shin, W. J. Cho, E.-S. An, S. Park, H.-W. Jeong, S. Jang, W. J. Baek, S. Y. Park, D.-H. Yang, J. H. Seo, et al., Advanced Materials 34, 2101730 (2022).
  * Xie et al. (2022) H. Xie, X. Chen, Q. Zhang, Z. Mu, X. Zhang, B. Yan, and Y. Wu, Nature Communications 13, 5744 (2022).
  * Kang and Shin (2021) D. H. Kang and M. Shin, Scientific Reports 11, 22842 (2021).
  * Li et al. (2023) W. Li, W. Zhu, G. Zhang, H. Wu, S. Zhu, R. Li, E. Zhang, X. Zhang, Y. Deng, J. Zhang, et al., arXiv preprint arXiv:2304.10718 (2023).
  * Wang et al. (2023c) H. Wang, H. Wu, J. Zhang, Y. Liu, D. Chen, C. Pandey, J. Yin, D. Wei, N. Lei, S. Shi, et al., Nature Communications 14, 5173 (2023c).
  * Semenov et al. (2019) V. K. Semenov, Y. A. Polyakov, and S. K. Tolpygo, IEEE Transactions on Applied Superconductivity 29, 1 (2019).
  * Ai et al. (2021) L. Ai, E. Zhang, J. Yang, X. Xie, Y. Yang, Z. Jia, Y. Zhang, S. Liu, Z. Li, P. Leng, et al., Nature Communications 12, 6580 (2021).
  * Hu et al. (2023) G. Hu, C. Wang, S. Wang, Y. Zhang, Y. Feng, Z. Wang, Q. Niu, Z. Zhang, and B. Xiang, Nature Communications 14, 1779 (2023).
  * Tong et al. (2021) L. Tong, Z. Peng, R. Lin, Z. Li, Y. Wang, X. Huang, K.-H. Xue, H. Xu, F. Liu, H. Xia, et al., Science 373, 1353 (2021).
  * Huh et al. (2020) W. Huh, D. Lee, and C.-H. Lee, Advanced Materials 32, 2002092 (2020).
  * Wang et al. (2022) L. Wang, X. Shen, Z. Gao, J. Fu, S. Yao, L. Cheng, and X. Lian, Journal of Materials Science 57, 4915 (2022).
  * Yan et al. (2022) X. Yan, J. H. Qian, V. K. Sangwan, and M. C. Hersam, Advanced Materials 34, 2108025 (2022).
  * Tian et al. (2021) C. Tian, L. Wei, Y. Li, and J. Jiang, Current Applied Physics 31, 182 (2021).
  * Yu et al. (2020) Z. Yu, M. Shen, Z. Zeng, S. Liang, Y. Liu, M. Chen, Z. Zhang, Z. Lu, L. You, X. Yang, et al., Nanoscale Advances 2, 1309 (2020).
  * Huang et al. (2017b) Y. Huang, W. Kang, X. Zhang, Y. Zhou, and W. Zhao, Nanotechnology 28, 08LT02 (2017b).
  * Du et al. (2017) C. Du, F. Cai, M. A. Zidan, W. Ma, S. H. Lee, and W. D. Lu, Nature Communications 8, 2204 (2017).
  * Nakane et al. (2021) R. Nakane, A. Hirose, and G. Tanaka, Physical Review Research 3, 033243 (2021).
  * Milano et al. (2022) G. Milano, G. Pedretti, K. Montano, S. Ricci, S. Hashemkhani, L. Boarino, D. Ielmini, and C. Ricciardi, Nature Materials 21, 195 (2022).
  * Galbiati et al. (2020) M. Galbiati, V. Zatko, F. Godel, P. Hirschauer, A. Vecchiola, K. Bouzehouane, S. Collin, B. Servet, A. Cantarero, F. Petroff, et al., ACS Applied Electronic Materials 2, 3508 (2020).