# Sensing the Environment with 5G Scattered Signals (5G-CommSense): A
Feasibility Analysis

Sandip Jana  Dept. of Electrical Engineering
Indian Institute of Technology
Hyderabad, India
<EMAIL_ADDRESS>Amit Kumar Mishra  Dept. of Electrical Engineering
University of Cape Town
Cape Town, South Africa
<EMAIL_ADDRESS>Mohammed Zafar Ali Khan  Dept. of Electrical Engineering
Indian Institute of Technology
Hyderabad, India
<EMAIL_ADDRESS>
###### Abstract

By making use of the sensors and AI (SensAI) algorithms for a specialized
task, Application Specific INstrumentation (ASIN) framework uses less
computational overhead and gives a good performance. This work evaluates the
feasibility of the ASIN framework dependent Communication based Sensing
(CommSense) system using 5th Generation New Radio (5G NR) infrastructure.
Since our proposed system is backed up by 5G NR infra, this system is termed
as 5G-CommSense. In this paper, we have used NR channel models specified by
the 3rd Generation Partnership Project (3GPP) and added white Gaussian noise
(AWGN) to vary the signal to noise ratio at the receiver. Finally, from our
simulation result, we conclude that the proposed system is practically
feasible.

###### Index Terms:

ASIN, CommSense, 5G New Radio, Tapped Delay Line, Cluster Delay Line

##  I Introduction

Inspired by thousands of years of inter-species co-evolution in nature, the
CommSense system takes advantage of existing communication infrastructure111In
recent literature [1, 2] the similar concept is being referred to as Channel
Impulse Response (CIR) or Impulse Radio (IR) based sensing. to sense the
environment. CommSense system is based on ASIN framework [3], which is
dedicated to a specific task and might use crude resolution sensors that
require less computational power. A CommSense system exploits the reference
symbols used in communication and senses the immediate environment, which may
not require high resolution, unlike conventional radar, where we compute the
precise range and Doppler of a target. In our paper, we are using the upcoming
5G NR telecommunication standard to explore the possibility of sensing using a
5G NR system. To do this, we simulate the sensing results using the ASIN
framework for the 5G NR channel models [4].

For 4th generation Long Term Evolution (4G LTE), there were six channel models
defined by International Telecommunication Union (ITU) [5], which were similar
to TDL models. Whereas for 5G NR, 3GPP defines [4] three different cluster
delay line (CDL) channel models (i.e. CDL-A, CDL-B, and CDL-C) for non-line of
sight (NLOS) scenarios and two models (CDL-D and CDL-E) for line of sight
(LOS) scenarios, these CDL models are useful for Multiple Input Multiple
Output (MIMO) channel modeling, which is an integral part of the NR. Till now
CDL channels have not been used for sensing applications. For simplified
evaluations e.g. non MIMO evaluations [4], 3GPP defines three tapped delay
line (TDL) models (i.e. TDL-A, TDL-B, and TDL-C) for NLOS and two models (i.e.
TDL-D and TDL-E) for LOS, but these five TDL channels have more number of
“Taps” as compared to ITU specified LTE channels. In this paper, first, we
have generated multiple data points for each of the specified channel models.
Then by using channel equalization blocks our proposed system can distinguish
each of the five channel models from both the CDL and TDL models. Moreover, we
are varying the signal to noise ratio (SNR) to verify the performance of the
system. The result we got from the simulation is as expected: each of the
clusters generated using different channel models is well distinguishable by
visual inspection. As the SNR increases, we get more compact clusters and an
increase in inter-cluster separations.

The rest of the paper is arranged as follows: Section II will give the
necessary concepts of a CommSense system, TDL model, and CDL model; then
Section III gives the simulation results and discusses the feasibility of the
proposed system. Finally, conclusion and future scope is given in Section IV.

CSI from UEs ASIN framework to estimate the event Phenomenological data for an
event Detection of event  Figure 1:  CommSense flow-diagram to detect an event
of interest

##  II Theory

###  II-A CommSense System

Figure 2: An example Tapped Delay Line (TDL). $a_{i}$ and $\tau_{i}$ denotes
scaling factor and delay of the signal corresponding to $i^{th}$ path. In (a),
we are considering three scattered paths from gNodeB to the user equipment
(UE) multipath power profile is given. TDL representation of the given
wireless channel is given in (b)

In most communication standards, to filter out the channel modulation, we
estimate the fading and non-ergodic wireless channel by sending pilot symbols.
As illustrated in Fig.1, we extract the channel state information (CSI) from
channel equalization blocks at the receiver or user equipment (UE). In the
ASIN framework, first, we gather information about the event of interest, then
this stored data and extracted CSI is used for training and pattern
classification; then it gives the prediction (i.e. if the event of interest
has occurred or not).

###  II-B Tapped Delay Line (TDL)

A “Tap” refers to a point in the delay line that introduces a certain amount
of delay and optionally scales the signal [6]. To model the multi-path nature
of the wireless channel shown in Fig.2(a), the signals from each tap are
summed. The difference equation of the TDL from Fig.2(b) can be given by,

$y(t)=a_{0}s(t-\tau_{0})+a_{1}s(t-\tau_{1})+a_{2}s(t-\tau_{2})$ (1)

The corresponding transfer function from eq.1 is given as,

$H(z)=a_{0}z^{-\tau_{0}}+a_{1}z^{-\tau_{1}}+a_{2}z^{-\tau_{2}}$ (2)

###  II-C Cluster Delay Line (CDL)

Figure 3: An example of CDL with three clusters; $\theta_{i}$s represent
Angles of Departure (AoD) with respect to the Line of Sight Direction of
Departure

Sub-paths in wireless channels might get clustered around a particular delay
[7]. A simple illustration of CDL is shown in Fig.3, where three clusters are
present and each cluster consists of several scatterers. The power profile for
each sub-path and each cluster is shown in terms of the impulse response.

For our simulation we are using the 3GPP standard [4]; for the TDL channel
models normalized delay and scaling factor for each tap, while for the CDL
channels normalized delay, power, angle of departure (AoD), angle of arrival
(AoA), and other angle measurements for each sub-paths are mentioned in
details.

##  III Simulated Results and Feasibility

(a) SNR = 0dB

(b) SNR = 10dB

(c) SNR = 20dB

Figure 4: Projection of data (generated using TDL channel models specified by
3GPP) onto the first two Principal Components’ direction using PCA and SNR is
varied to check the robustness of the proposed system. In (a) For each of the
TDL channel model, SNR of each symbol is 0dB, in (b) and (c) SNR is 10dB and
20dB respectively. By using SVM classifier, we get accuracy of $96\%$ for (a),
$97.3\%$ for (b) and $100\%$ for (c)

(a) SNR = 0dB

(b) SNR = 10dB

(c) SNR = 20dB

Figure 5: Projection of CDL data onto first two Principal Components’
direction using PCA, In (a) For each of the CDL channel models, SNR of each
symbol is increased from (a) to (c). By using SVM classifier, we get sensing
accuracy of $93.33\%$ for (a), $100\%$ for (b) and $100\%$ for (c)

At the carrier frequency of $4GHz$, for both the TDL and CDL model we
generated 50 samples using MATLAB for each of the five channel models
according to the 3GPP specifications; then we added AWGN noise to vary the SNR
at the receiver; we are considering SNR of 0dB, 10dB and 20dB. After the pilot
symbol is received at the UE, we use MMSE based equalizer to estimate the
channel. This high-dimensional CSI is projected to two dimensions using PCA
[8], then we are using the SVM classifier to evaluate the accuracy.

Fig.4 shows the results by varying the SNR for five TDL models and accuracy
using SVM based classifier; it achieves the accuracy of 96%, 97.3% and 100% at
the SNR of 0dB, 10dB and 20dB respectively. Fig.5 shows the results for CDL
models; here we achieve an accuracy of 93.33%, 100% and 100% for the SNR of
0dB, 10dB and 20dB respectively. In lower SNR, data points in CDL clusters are
more dispersed compared to TDL due to the presence of correlated multipaths,
but as the SNR increases the classification accuracy goes up as expected.

##  IV Conclusion and Future Work

Our work analyzed the feasibility of environment sensing using 5G NR
infrastructure, especially for the CDL channels which was not done before. The
performance from our simulation shows that our proposed system is feasible
using 5G NR. Since this system can co-exist with the communication system, it
will be a cost-effective solution for sensing applications. Here, we have
considered one UE in the simulations. In the future study, we will consider
multiple UEs and develop an optimal decision fusion algorithm.

## Acknowledgment

This work was mainly supported by University Grants Commission (UGC) and
partly by project VAJRA, Department of Science and Technology (DST), Govt. of
India.

## References

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  * [6] J. O. Smith, _Physical Audio Signal Processing_. http:http://ccrma.stanford.edu/ jos/pasp///ccrma.stanford.edu/~jos/pasp/, accessed 28 August, 2022, online book, 2010 edition.
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# D-CAST: Distributed Consensus Switch in Wireless Trustworthy Autonomous
System

Dachao Yu  School of
Information and Control Engineering,
Qingdao University of Technology
<EMAIL_ADDRESS>Jiayuan Ma  College of
Electronic and Information Engineering
Tongji University
<EMAIL_ADDRESS>Hao Xu  College of
Electronic and Information Engineering
Tongji University
<EMAIL_ADDRESS>
###### Abstract

The protocols of distributed consensus normally aim to tolerate different
types of faults including crash faults and byzantine faults that occur in the
distributed systems. However, the dynamic network topology and stochastic
wireless channels may cause the same trustworthy system to suffer both crash
fault and byzantine fault. This article proposes the concept of a distributed
consensus autonomous switch mechanism in trustworthy autonomous systems
(D-CAST) to reach the different fault tolerance requirements of the dynamic
nodes and discusses the challenges of D-CAST while it is implemented in the
wireless trustworthy system.

###### Index Terms:

Distributed consensus, Crash fault tolerance, Byzantine fault tolerance, Raft,
Hotstuff, Wireless trustworthy system

##  I Introduction

The concept of Trustworthy Autonomous Systems (TAS) has gained significant
prominence since it is applied to wireless networks. These systems,
characterized by their ability to operate independently and make critical
decisions without human intervention, are becoming increasingly integral in
various fields such as autonomous driving, industrial internet of things, and
metaverse. However, the dynamic and unpredictable nature of wireless
environments poses unique challenges to TAS, especially from the perspective
of maintaining consistency and reliability in critical decision-making.

Distributed consensus, which has been widely used in distributed ledger
technology (DLT), can solve the challenges caused by wireless communication in
TAS [1]. The distributed consensus aims to ensure all normal nodes in a
network can achieve agreements on unified states even if the network
encounters faulty progress or malicious attack [2]. In TAS, distributed
consensus can work as an internal algorithm that regulates critical decision-
making and processing based on the information collected by nodes, which
allows participant nodes to transmit and receive commands to change their
states by following specific fault-tolerant protocols. Crash fault tolerance
(CFT) and Byzantine fault tolerance (BFT) protocols are two types of
distributed consensus protocols. CFT protocols like Raft [3] and Paxos [4] are
implemented to manage reliable state duplication and prevent system breakdown
from node crash failure, whereas BFT protocols like Practical Byzantine Fault
Tolerance (PBFT) [5] and Hotstuff BFT [6] intends to help with the network
against potential malicious attacks and arbitrary behaviors.

Based on their characteristics in fault tolerance, the BFT and CFT consensus
protocols have been separately deployed in traditional distributed systems
with constant network conditions but different scenarios of fault tolerance
requirement [7] [8]. In wireless TAS, however, the dynamic node entry/exit,
stochastic fluctuations of wireless channels, and the emergence of novel
attack mode can cause both crash fault and byzantine fault to occur in the
same network, which means the network with the configuration of only CFT or
BFT protocol cannot support the reliable critical decision making or
processing within it.

In response, people are exploring adaptive schemes capable of dynamically
adjusting the fault tolerance strategies to suit the prevailing conditions.
The essential approach lies in the idea of autonomous switchable consensus,
which allows TAS to adapt its consensus algorithms in response to changing
network conditions and operational demands. This adaptability is crucial in
wireless environments where factors such as signal interference, variable
latency, and bandwidth constraints can significantly impact system
performance. By employing a switchable consensus mechanism, TAS can seamlessly
transition between different consensus algorithms, such as from a less
resource-intensive algorithm during times of stable connectivity to a more
robust algorithm in the face of network volatility.

This article delves into the characteristics of distributed consensus
autonomous switch mechanism, exploring why it can be integrated into wireless
TAS frameworks while ensuring security and scalability. Furthermore, we
address the challenges and relevant solutions of distributed consensus
autonomous switch mechanism in trustworthy autonomous systems (D-CAST), which
includes the timing of switching to appropriate consensus algorithms based on
specific conditions of the network and outline the process of leader change
and state synchronization across the system during a consensus switch to
maintain coherence and reliability.

##  II Review of current applications with switchable consensus

Switchable consensus mechanisms are normally implemented in DLT-based
applications to provide adaptability, security, and scalability by allowing
distributed systems to choose different distributed consensus protocols based
on varying network conditions or performance requirements while maintaining
security through robust cryptographic techniques and fault tolerance. The
switchable consensus mechanisms rely on specific governance mechanisms by
distributing decision-making power among validators or stakeholders to prevent
centralization. Common switchable consensus mechanisms, which can be sorted as
module switch and inter-chain switch, have been applied in different DLT-based
systems. This section introduces these two types of switchable consensus
schemes with the example of existing developed DLT-based applications.

###  II-A Hyperledger Fabric

Unlike public blockchains like Bitcoin or Ethereum, Hyperledger Fabric is an
open-source permissioned blockchain framework, which means the parties that
join the network are known and verified entities[9]. It is part of the
Hyperledger suite hosted by the Linux system, designed for use in enterprise
contexts. Fabric is known for its high degrees of confidentiality, resiliency,
flexibility, and scalability. The framework of Hyperledger Fabric is highly
modular, which enables users to plug in their preferred components like
consensus and membership services [10]. Fabric proposes the concept of
channels to enable a group of participants to create a separate ledger of
transactions, which ensures that only relevant parties can view certain
transactions.

In Hyperledger Fabric, the consensus can be switched or configured by the
network’s requirement, which is supported by the modular architecture of
Fabric. Users change the type of consensus protocols by updating the network
configuration, which involves modifying the channel configuration and getting
the requisite number of signatures from the network members according to the
channel’s policy. The new consensus mechanism then becomes part of the
channel’s configuration and dictates how transactions are ordered and
validated in Hyperledger Fabric.

###  II-B Cosmos

Cosmos is a decentralized network within independent parallel blockchains,
which can be powered by different consensus algorithms [11]. The framework of
Cosmos aims to enable different blockchains to communicate with each other and
switch the consensus through inter-blockchain communication (IBC) protocol
[12]. It allows multiple blockchain systems to transfer tokens and data among
nodes while maintaining their consistency of state.

Cosmos mainly uses Tendermint, which is a proof-of-stake (PoS) algorithm known
for its high efficiency, speed, and robustness [13]. Tendermint separates the
blockchain’s application layer, which can process transactions and update the
state, from the consensus layer, making it simpler for developers to design
blockchain systems in Cosmos. Cosmos also offers the Cosmos Software
Development Kit (SDK), a framework for building blockchain applications with
Tendermint. This modular framework allows developers to create customizable,
interoperable blockchains with different consensus to improve the scalability
of the overall system. If the Cosmos network intends to switch its consensus
mechanism, it can cause a complicated problem because the new consensus
algorithm may not be compatible with the existing chain’s data and state.

While Cosmos uses Tendermint Core as its standard consensus protocol, the
architecture allows different blockchains within the network to operate with
their consensus mechanisms. This means that within the Cosmos ecosystem,
various blockchains can use different consensus algorithms, but they can still
communicate with each other through IBC, provided they adhere to the IBC
standards.

##  III Consensus protocols for autonomous switch

The frequent critical decision-making in wireless trustworthy autonomous
systems requires an instantaneous consensus switch mechanism instead of manual
consensus switch schemes in Hyperledger Fabric or Cosmos. This new consensus
switch mechanism needs to have the following features or capabilities:

  * •

Besides the fault caused by crash nodes or malicious attacks, wireless
autonomous systems may suffer from failed or delayed connection caused by
dynamic channel conditions and limited communication resources. These failures
are more stochastic than ordinary crash or byzantine faults in wired
distributed networks. Switchable consensus mechanisms should allow the network
to adapt to these changes and maintain optimal performance.

  * •

As the network grows in size, the initial consensus mechanism might not scale
efficiently. The ability to switch to the consensus mechanism with higher
scalability can be crucial for maintaining the performance and reliability of
the network as it expands. A mechanism that is secure for a small, closely-
knit network might become vulnerable as the network grows or becomes more
open. The ability to switch to a more secure consensus mechanism is vital for
maintaining the integrity of the network.

  * •

In wireless networks, especially those involving mobile or IoT devices, energy
consumption is a critical concern. Some consensus mechanisms consume more
energy than others. The ability to switch to a more energy-efficient consensus
mechanism can prolong the battery life of devices and reduce overall energy
consumption. CFT and BFT consensus mechanisms have different thresholds of
fault tolerance to the node and link failures. The ability to switch consensus
mechanisms can enhance the network’s robustness, especially in environments
where node failures are common.

The communication complexity, which can be different in the protocols of
consensus with various communication topologies, has a tremendous influence on
the performance of wireless distributed consensus. Fig. 1 shows two types of
communication topology in the wireless distributed consensus: leader-based and
full-connected. The leader-based consensus represents all nodes in a
consensus-enabled network that only need to communicate with a temporary
leader node that is pre-voted or selected randomly from the network. The full-
connected consensus requires all nodes to communicate with each other to
achieve log replication or state synchronization. The full-connected consensus
has a much higher communication complexity O($N^{2}$) than leader-based
consensus O(N), which requires more communication resources to reach the
target performance when it is implemented in a wireless autonomous system.

Figure 1: Different communication topology of distributed consensus

Therefore, the leader-based consensus can be more practical to work in
wireless TAS than the full-connected consensus if the TAS has limited
communication resources or terrible channel conditions. Two leader-based
consensus protocols are selected in the proposed autonomous consensus switch
mechanism and their procedure and characteristics are introduced in this
section.

###  III-A Leader-based CFT consensus: Raft

Raft, as a typical CFT consensus algorithm, is generally implemented in a
private, trustworthy, distributed system to oppose the breakdown of replicas
[3]. The main procedure of Raft has two stages, leader election and log
replication. The followers need to vote for the first candidate that
successfully sends the voting request to them, which means the leader
candidate with the most reliable wireless connections and lowest latency is
most likely to be chosen as a leader.

In the log replication, the leader needs to pack the commands in log entries
and replicate the entries to all followers ceaselessly through downlink
transmission. Depending on the successful reception of log messages, the
followers need to reply confirmation packets to the leader through uplink
unicast and start to execute the confirmed commands. A successful log
replication represents that more than 50% overall followers have received the
log entries from the leader and sent the confirmation back to the leader
successfully within the time interval of two neighbor heartbeat commands. The
performance of Raft is influenced by the reliability of link transmission when
it is implemented in wireless networks [14].

###  III-B Leader-based BFT consensus: Hotstuff

Hotstuff, as a BFT state machine replication protocol, aims to ensure that
non-faulty replicas agree on the order of execution for client-initiated
service commands in the distributed system with $N\geq 3f+1$ replicas, despite
the efforts of $f$ Byzantine replicas[6]. The Libra blockchain has implemented
the Hotstuff BFT as the consensus protocol in its project because of the
responsiveness and linearity in this protocol [15]. The view, as a round of
consensus in Hotstuff BFT, contains three phases: prepare, pre-commit, and
commit. The basic Hotstuff protocol works in a succession of view numbers with
monotonically increasing view numbers. Each view number has a unique dedicated
leader for other replicas. The leader must collect votes from a quorum of
$N-f$ replicas in three phases. The collection of $N-f$ votes to one leader is
referred to as a quorum certificate (QC), which is associated with a
particular node and a view number.

In the prepare phase, the leader should collect new-view messages from
replicas and process these messages to select a branch that has the highest
preceding view. If over $N-f$ replicas have sent their messages to the leader
successfully, a valid prepare QC can be formed through a threshold signature
scheme. Then the leader broadcasts prepare QC in pre-commit messages to
replicas, and replicas respond to the leader with the pre-commit vote if they
receive and verify the prepare QC. Similarly, while receiving more than $N-f$
pre-commit votes, the leader combines them into a pre-commit QC and broadcasts
it in commit messages to replicas. Over $N-f$ replicas should send the commit
vote back to the leader for the final commit QC combination. After a
successful commit QC assembly, the leader needs to send a decision message to
all other replicas to notify them the consensus protocol in this view is
completed, and the replicas will update their state according to the decision
message.

Compared with the high communication complexity $O(N^{2})$ in the phases of
other BFT consensus protocols [5], Hotstuff has lower communication
complexity, which keeps $O(N)$ in all three phases of the consensus protocol.
In the scenario of wireless communication, low communication complexity can
cause less interference and bandwidth cost [16]. However, because the basic
Hotstuff BFT has three phases in its protocol, the communications between the
leader and replicas in Hotstuff will cause longer time latency than a BFT
protocol with fewer consensus phases.

According to the statement of basic Hotstuff BFT, the leader only needs to
collect the vote message in the form of threshold signatures through all three
phases. This feature ensures that changing the view on every prepare phase of
different proposals cannot actively influence the reliability of the
consensus. Therefore, the basic hotstuff protocol can be adapted to a pipeline
scheme and the prepare message of the next view is binding with the pre-commit
message of the former view in the same package [6]. Every new view of chained
Hotstuff BFT needs to start automatically after the prepare phase of the last
view. This approach, which is named chain Hotstuff, aims to significantly
improve the throughput of the views change in the Hotstuff BFT consensus
protocol because the average latency for every view in chain Hotstuff will be
shorter than the basic Hotstuff protocol if the success rate of the consensus
is reasonably high [17].

##  IV Timing of consensus switching

Although the switchable consensus can improve the performance of wireless TAS,
some crucial problems should be addressed before it is implemented in
practical applications. The most critical procedure of autonomous consensus
switches is determining the timing of switch between Crash Fault Tolerance
(CFT) and Byzantine Fault Tolerance (BFT) protocols. This section tries to
discuss the solution to this challenge from the perspective of latency, the
ratio of malicious nodes, and bandwidth allocation.

The success of consensus switch heavily relies on accurately identifying the
optimal boundary for transitioning between these protocols. The wireless TAS
must possess the capability to evaluate various factors to determine the
opportune moment for protocol transition. The primary considerations are
assessing the network latency, including gauging the feasibility and
effectiveness of consensus switching.

###  IV-A Latency

The ability to swiftly switch between protocols without causing disruptions or
delays is paramount for maintaining the integrity and functionality of the
distributed system. Time latency emerges as a dominant factor in the process
of autonomous consensus switch because it directly impacts the responsiveness
and liveliness of the distributed consensus mechanism. The latency of wireless
distributed consensus is influenced by various factors, including the number
of nodes in the network, the efficiency of wireless transmission among nodes,
network congestion levels, and the computational overhead associated with
protocols [18]. D-CAST mechanism should ensure the functioned consensus can
reach the latency requirement of the wireless TAS or it needs to switch to the
consensus protocol with less time-sensitivity.

Figure 2: The procedures of two leader-based consensus protocols

###  IV-B Ratio of malicious node

The dynamic switching BFT and CFT can be regarded as a hybrid approach based
on observed node conditions to balance the trade-off of performance and cost.
The switch between Crash Fault Tolerance (CFT) and Byzantine Fault Tolerance
(BFT) consensus depends on the necessity of the system’s tolerance to both
crash faults and malicious behavior. In environments with a low ratio of
malicious nodes, where most node failures are caused by crash, employing a CFT
consensus algorithm with simplicity and efficiency might be sufficient to
tolerate the failures. Conversely, in scenarios with a high ratio of malicious
nodes, BFT consensus becomes necessary to maintain the reliability of critical
decision-making in the system with more potential Byzantine faults [19]. BFT
algorithms provide stronger security guarantees by tolerating malicious
behavior, albeit at the cost of increased communication complexity and
overhead compared to CFT algorithms.

###  IV-C Bandwidth

In wireless autonomous systems, the decision to switch between Crash Fault
Tolerance (CFT) and Byzantine Fault Tolerance (BFT) consensus is also linked
to the available bandwidth allocated to channels. Bandwidth constraints
significantly impact the performance of wireless distributed consensus, with
CFT consensus being favored in environments with limited bandwidth because it
has lower communication overhead and simplicity. Conversely, Byzantine Fault
Tolerance (BFT) consensus, while imposing higher bandwidth requirements with
additional message exchanges, becomes indispensable in scenarios where the
risk of malicious behavior or Byzantine faults is pronounced, ensuring data
integrity and system resilience against malicious nodes. The distributed
consensus in TAS can dynamically transition between CFT and BFT consensus
based on bandwidth allocation, enabling the system to optimize performance and
the type of fault tolerance in response to fluctuations in bandwidth
availability within wireless autonomous systems.

By accurately assessing the condition of network, wireless TAS can process
smooth transitions between CFT and BFT protocols while maintaining the
reliability and throughput of the wireless distributed network. This proactive
approach to protocol management is essential for adapting to dynamic network
conditions and mitigating potential risks or performance bottlenecks.

##  V Leader change and state consistency

Besides the timing determined for consensus transitions, Fig. 2 presents the
main procedures of two leader-based consensus, which indicates that Raft and
Hotstuff have different leader selection and log replication mechanisms in
their protocols. Therefore, when these two protocols are transitioned from
each other, the consensus switch mechanism must be adapted to manage leader
changes and maintain state consistency within the nodes of TAS.

###  V-A Leader change

In leader-based distributed consensus, dynamic leader nodes are imperative to
sustaining uninterrupted consensus progress. These leader nodes usually are
determined by different mechanisms in consensus protocols. For example, the
leader in Raft is elected by other followers but in Hotstuff the leader is
selected by a predefined rotation mechanism. If TAS switches its consensus
between these two consensus protocols, it should first expire the current
leader node and use the new leader selection mechanism to choose a valid
leader for further state replication.

The leader selection during the progress of transitioning from CFT to BFT
should consider factors such as node reputation, performance, and
cryptographic mechanisms for ensuring trustworthiness. It ensures that the new
leader is trustworthy and capable of maintaining the consensus process.
Conversely, when switching from BFT to CFT, the leader selection process may
become simpler, possibly involving a straightforward voting or round-robin
approach [20], as the TAS no longer requires Byzantine fault tolerance.

Additionally, the autonomous consensus switch must prioritize state
consistency, ensuring that most of nodes within the network maintain a
coherent view of the shared state despite changes of leader node or protocol
configurations. It involves implementing mechanisms to synchronize and
reconcile state information among nodes, preventing inconsistencies of states
that may arise from the dynamic switch between consensus protocols.

###  V-B State consistency

Maintaining state consistency in the TAS when switching consensus algorithms
from Crash Fault Tolerance (CFT) to Byzantine Fault Tolerance (BFT) or vice
versa requires careful coordination and synchronization mechanisms. A
checkpointing mechanism can be implemented in it, where the state of the
system is periodically saved, allowing nodes to recover to a consistent state
if necessary [21]. In BFT consensus, strong consistency is typically
guaranteed by replicated state machines, ensuring that all normal nodes agree
on the order and execution of critical decisions. When it transits to CFT
consensus, state consistency mechanisms may become less stringent, as CFT
algorithms provide eventual consistency rather than immediate consistency.
However, it’s still important to ensure that all normal nodes eventually
converge to the same state. Additionally, validation mechanisms should be in
place to ensure that the state transition is legitimate and consistent with
the rules of the new consensus algorithm [22]. It may involve cryptographic
signatures or hash-based validation techniques to verify the integrity of the
state transition.

###  V-C Fraud consensus switching

The issues of leader change and state consistency indicate that the frequent
consensus switch can compromise the performance of TAS. Therefore, TAS may
suffer a special attack called fraud switching from some malicious nodes,
which changes the network condition significantly to increase the frequency of
consensus switch and damage TAS’s performance.

Some solutions can be implemented to reduce the threat of fraud switching
attacks within TAS. Firstly, integrating advanced cryptographic protocols like
digital signatures and robust hash functions can heighten consensus integrity,
thereby raising the bar for malicious entities seeking to manipulate network
conditions [23]. Moreover, the implementation of anomaly detection algorithms
is vital for real-time identification and mitigation of suspicious activities
[24], enabling swift responses to potential fraud switching attempts. By
synergizing these proactive measures, TAS may significantly fortify its
resilience against fraud switching attacks, safeguarding the integrity and
reliability of its operations within the network.

##  VI conclusion

This article introduces the concept of distributed consensus autonomous switch
(D-CAST) in the wireless trustworthy autonomous system and discusses the
challenges of the consensus switch mechanism implemented in TAS, including
determining the timing of the consensus switch, leader change, and state
consistency issues represented by a walk-through of consensus states. Further
research is set to focus on the design of a specific consensus switch
mechanism from the perspective of protocol to solve potential challenges in
mission-critical wireless systems.

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# Magnetic property control of Cr2Ge2Te6 through oxidation and thickness
effects

Joachim Dahl Thomsen  Division of Physical Sciences, College of Letters and
Science, University of California, Los Angeles, California 90095, USA
Department of Materials Science and Engineering, Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139, USA  Myung-Geun Han<EMAIL_ADDRESS>Condensed Matter Physics and Materials Science Division, Brookhaven National
Laboratory, Upton, NY 11973, USA  Aubrey Penn  MIT.nano, Massachusetts
Institute of Technology, Cambridge, Massachusetts 02139, United States
Alexandre C. Foucher  Department of Materials Science and Engineering,
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Michael Geiwitz  Department of Physics, Boston College, Chestnut Hill,
Massachusetts 02467, USA  Kenneth S. Burch  Department of Physics, Boston
College, Chestnut Hill, Massachusetts 02467, USA  Lukas Dekanovsky  Department
of Inorganic Chemistry, University of Chemistry and Technology Prague,
Technická 5, Prague 6, 166 28, Czech Republic  Zdenek Sofer  Department of
Inorganic Chemistry, University of Chemistry and Technology Prague, Technická
5, Prague 6, 166 28, Czech Republic  Yu Liu  Present address: Los Alamos
National Laboratory, Los Alamos, NM 87545, USA.  Condensed Matter Physics and
Materials Science Division, Brookhaven National Laboratory, Upton, NY 11973,
USA  Cedomir Petrovic  Condensed Matter Physics and Materials Science
Division, Brookhaven National Laboratory, Upton, NY 11973, USA  Frances M.
Ross  Department of Materials Science and Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, USA  Yimei Zhu  Condensed
Matter Physics and Materials Science Division, Brookhaven National Laboratory,
Upton, NY 11973, USA  Prineha Narang  Division of Physical Sciences, College
of Letters and Science, University of California, Los Angeles, California
90095, USA  Electrical and Computer Engineering Department, University of
California, Los Angeles, California, 90095, USA

###### Abstract

Van der Waals (vdW) magnetic materials such as Cr2Ge2Te6 (CGT) show promise
for novel memory and logic applications. This is due to their broadly tunable
magnetic properties and the presence of topological magnetic features such as
skyrmionic bubbles. A systematic study of thickness and oxidation effects on
magnetic domain structures is important for designing devices and vdW
heterostructures for practical applications. Here, we investigate thickness
effects on magnetic properties, magnetic domains, and bubbles in oxidation-
controlled CGT crystals. We find that CGT exposed to ambient conditions for 30
days forms an oxide layer approximately 5 nm thick. This oxidation leads to a
significant increase in the oxidation state of the Cr ions, indicating a
change in local magnetic properties. This is supported by real space magnetic
texture imaging through Lorenz transmission electron microscopy. By comparing
the thickness dependent saturation field of oxidized and pristine crystals, we
find that oxidation leads to a non-magnetic surface layer with a thickness of
about 10 nm, thicker than the oxide layer alone. We also find that the stripe
domain width and skyrmionic bubble size are strongly affected by the crystal
thickness in pristine crystals. These findings underscore the impact of
thickness and surface oxidation on the properties of CGT such as saturation
field and domain/skyrmionic bubble size and suggest a pathway for manipulating
magnetic properties through a controlled oxidation process.

##  I Introduction

The discovery of long-range ferromagnetic ordering in van der Waals (vdW)
materials has opened new avenues for investigating fundamental magnetism and
applications within novel memory, computing, and quantum computing [1, 2, 3,
4, 5]. The tunability of vdW magnetic materials by thickness, i.e. number of
atomic layers, as well as by electric fields, doping, and strain, and the
presence of topological spin textures such as domain walls and skyrmions, make
these materials promising for such applications [1, 2, 3]. However, an
understanding of the evolution of spin textures as a function of flake
thickness is highly desired for the development of future spintronic
applications.

Figure 1:  (a) Atomic structure of CGT. (b, c) HAADF-STEM images of the CGT
crystal in top view (b) and cross-sectional view (c). An atomic model of CGT
is overlaid on both images. The grey-scale intensity of the image averaged
horizontally is plotted on top of (c).

Cr2Ge2Te6 (CGT) is one such material, a vdW Heisenberg semiconducting
ferromagnet with a bulk Curie temperature of about 61 K and strong
perpendicular magnetic anisotropy [6, 7, 8, 9, 10]. The properties of CGT can
be modified via doping [11], electric field [12, 10, 13], strain [9], and
pressure [14, 15]. The latter two result from its strong magneto-elastic
coupling [16]. Because CGT is centrosymmetric it lacks a Dzyaloshinskii-Moriya
interaction (DMI) to stabilize Bloch or Neel-type skyrmions observed in
noncentrosymmetric chiral magnets, such as B20 metals [5, 17]. Instead, it
hosts topological skyrmionic Bloch-type bubbles that are stabilized through a
competition between the dipolar energy and magnetocrystalline anisotropy [18,
19], making it a potential candidate for novel quantum computing methods [20].

The tunability of CGT and other vdW magnets stems from their large surface to
volume ratio making the interfaces property-determining [3]. Proximitized
spin-orbit coupling [21] and twisted homo- or hetero-bilayers [22, 23] are two
interface effects that can tune magnetic properties of vdW magnets. A
different approach may be to consider chemical effects, such as oxidation,
where controlled oxidation can be used to create a chemically well-defined and
non-reactive interface. CGT flakes are known to degrade in ambient air on the
time scale of one hour [6, 16]. Consequently, to leverage this promising
material in future applications, it is crucial to understand the effects of
oxidation on its crystal and magnetic structure, and assess possibilities for
magnetic property control.

Here, we prepare both pristine CGT and oxidized CGT (O-CGT) samples, and
determine how crystal thickness and oxidation affect magnetic properties and
magnetic domain structures. Exposure to ambient conditions leads to the
formation of a $\sim$5 nm thick oxide layer. By direct imaging of magnetic
domains through Lorentz transmission electron microscopy (LTEM), we find a
consistently lower saturation field for O-CGT compared to CGT. These
measurements suggest that up to 10 nm of the surface of the crystal, thicker
than the oxide layer alone, becomes non-magnetic when it is oxidized.
Compostitional analysis using electron energy loss spectroscopy (EELS) and
energy dispersive x-ray (EDX) analysis shows that the oxide has a lower Te
content compared to bulk CGT, and that the oxidation state of Cr increases
from 3+ in the bulk to a value between 3+– 5+ in the oxide. Finally, having
shown that oxidation leads to a decrease in the effective magnetic thickness,
we consider how magnetic textures, which are useful for future applications,
are affected by crystal thickness. We show that skyrmionic bubble sizes and
stripe domain width are tuned by crystal thickness. Our results thus show that
deliberate chemical modifications of the crystal surface may be another avenue
towards tuning magnetic properties of vdW magnets.

##  II Results and Discussion

###  II.1 Thickness dependent saturation field of CGT and O-CGT

Figure 2:  Magnetic structure and saturation field. (a) Schematics of contrast
formation in Fresnel LTEM. Contrast is only formed by in-plane magnetization
which leads to a phase shift in the electron beam, and either a dark-bright or
bright-dark domain wall in the image plane, depending on the direction of the
magnetization. (b-e) LTEM images after RFC at different magnetic fields for
110 nm thick CGT (measured by AFM). The saturation field is reached at 164 mT
when there is no more magnetic contrast in the image. The stationary, and,
therefore, non-magnetic, arch-shaped contrast in the images are bend contours.
Overlays in (a) indicate the dark-bright or bright-dark contrast of the domain
wall and the magnetization direction of the Bloch-type wall. (f) Plot of the
saturation field as a function of thickness and comparison with literature for
oxidized and un-oxidized CGT. Red crosses are data extracted from Ref. [18]
(oxidized), and black (oxidized) and green (un-oxidized sample) crosses are
extracted from Ref. [24]. The green, black, and red lines are guides to the
eye.

Crystal growth and sample fabrication is described in Methods. CGT
crystallizes in the trigonal R$\overline{3}$ space group (Fig. 1(a)) and the
nominal oxidation states in bulk CGT are Cr3+, Ge3+, and Te2-. The resulting
samples are single crystalline and free from observable defects and interlayer
dislocations, as determined from high-angle annular dark-field scanning
transmission electron microscopy (HAADF-STEM) images along the c- and a-axes
(Fig. 1(b, c)), as well as TEM diffraction patterns (Fig. S1). Figure 1(c)
shows the vdW layered structure with ABC stacking, consistent with previous
studies [8, 18, 19]. Overlaid is an atomic model of CGT and the grey-scale
intensity profile of the image averaged horizontally, from which we measure a
layer thickness of 0.68 nm. Since the intensity in HAADF-STEM images is
proportional to $Z^{1.7}$ [25], $Z$ being the atomic mass, Te atoms appear the
brightest.

In order to control the chemical state of the surface we use one of three
approaches: (1) For O-CGT we prepare samples in ambient conditions. (2) For
CGT we either (a) prepare samples in an argon-filled glovebox to avoid oxygen
and moisture exposure [16, 26], or (b) exfoliate CGT in ambient conditions but
swiftly – within minutes – encapsulate between few-layer graphene. Details are
provided in Methods and Fig. S2 shows an illustration of sample details and
optical contrast measurements. Briefly, bulk CGT is exfoliated and suitable
flakes are identified based on their optical contrast by first calibrating
with measurements from atomic force microscopy (AFM) (Fig. S2). Optical
contrast efficiently determines crystal thickness in the range 8-30 nm, but
the range 5-8 nm requires AFM measurements. Pristine CGT samples prepared in
the glovebox are stored within an air-sealed plastic bag, and therefore only
exposed to air for some minutes before being loaded into the TEM. To form an
oxide we exfoliate and transfer flakes to TEM grids, and expose to ambient
conditions for periods up to 30 days before the measurements.

We first determine the saturation magnetic field in CGT and O-CGT for varying
crystal thicknesses by imaging the magnetic domain structure at varying
applied magnetic fields. Imaging is done using LTEM with a liquid helium
cooled holder with a base temperature of 15 K [18, 27]. In the LTEM mode the
magnetic field at the sample can be controlled by exciting the objective lens.
The magnetic field is oriented along the z-direction, into the image plane,
and the minimum achievable field in our TEM is 12 mT. Therefore, we refer to a
cooling process from above the Curie temperature down to the base temperature
of the sample holder at this magnetic field as “residual field cooling (RFC)”
to distinguish it from a true zero-field cooling process.

Contrast formation in Fresnel LTEM images is outlined in Fig. 2(a). The in-
plane magnetization of a Bloch-type domain wall leads to dark-bright or
bright-dark lines, depending on the direction of the in-plane magnetization.
Hence, by considering the contrast of the magnetic features we can determine
the direction of the domain walls.

Our experimental procedure to determine the saturation field is shown in Fig.
2(b-e). After RFC, stripe domains have formed, with bright-dark pairs of lines
indicating the domain walls (Fig. 2(b)). The domains are magnetized along the
c-directions, or in and out of the image plane, respectively, as indicated in
the image. Also indicated are the direction of magnetization of the domain
walls as determined by the domain wall contrast. At the residual field, the
domains have approximately equal widths. Note that these images also show more
slowly varying contrast such as the arch-shaped contrast. This arises from
bending of the sample and is common in magnetic imaging of vdW magnets [18,
19]. This contrast is stationary when we increase the magnetic field, and
therefore, of non-magnetic nature.

As the magnetic field is increased (Fig. 2(c, d)), the magnetic domains
aligned with the applied magnetic field grow in width while the magnetic
domains aligned in the direction opposite to the magnetic field decrease in
width. Finally, we reach the saturation field when we no longer can discern
any magnetic contrast in the image (Fig. 2(e)).

Figure 3:  EELS and EDX analysis. (a) Cross sectional HAADF-STEM image of the
surface of a CGT crystal that has been exposed to air for $\sim$1 month. EDX
and EELS data were summed up pixel-by-pixel perpendicular to the white
vertical line. (b) EDX signal of Cr, Ge, Te, and O as a function of distance
along the white line in (c). (c) EELS heatmap along the white line indicated
in (c). Dotted black lines indicate the positions of the O K, Cr L2/L3 and Te
M peaks. (d, e) The position of the Cr-L3 peak and the L3/L2 peak intensity
ratio, respectively, through the oxide layer. The dotted horizontal lines in
(c-f) are at the same location in the z-direction, at the interfaces between
the oxide and mixed oxide/CGT region, and between the mixed oxide/CGT region
and the bulk CGT. (f) Plan-view STEM-EELS survey image of a CGT crystal with
three different thicknesses shown in (g). These sample thicknesses were
determined using the low-loss EELS spectra with a mean free path for inelastic
scattering of 76.4 nm - calibrated by AFM measurements. (g) EELS spectra from
the sample shown in (f) and a spectrum from a sample prepared in the glovebox
showing the absence of the O K peak. The expected position of the O K peak is
indicated by an arrow. The un-oxidized spectrum has been offset vertically for
clarity. The black, red, and blue data are obtained form the areas denoted by
crosses of the same colors in (f). (h) Summary of overall results. The left
panel shows that the oxide and mixed oxide/CGT region is non-magnetic. The
middle panel shows that the oxide layer is amorphous (no crystallinity) and
that the sample becomes gradually more crystalline across the mixed CGT/oxide
region. The right panel combines these findings into a view of the surface
layer.

Figure 2(f) shows the saturation field plotted against crystal thickness for
CGT and O-CGT. We find that the saturation field decreases with decreasing
crystal thickness, and that CGT displays larger saturation fields compared to
O-CGT at the same crystal thickness. This is consistent with prior studies of
saturation field in CGT from which we were able to infer whether the CGT was
oxidized or not [18, 24], also plotted in Fig. 2(f). We do not observe any
qualitative difference in the morphology or appearance of the stripe domains
between CGT and O-CGT other than the difference in the saturation field. By
translating the data along the horizontal axis to make the CGT and O-CGT data
coincide, we infer that the O-CGT crystals have approximately 20 nm of non-
magnetic material at the top and bottom surfaces combined. This is consistent
with the thinnest oxidized crystal for which we observed magnetic contrast,
which had a thickness of 18 nm.

###  II.2 Oxide structure and composition

To further understand the effect of oxidation on the surface structure and
composition of CGT crystals we combine information from several measurements
(Fig. 3(a-g)). We first quantify the crystallinity using HAADF-STEM cross-
sectional imaging. Figure 3(a) shows the surface of CGT viewed along the
b-direction. This flake was exfoliated onto a SiO2/Si substrate and exposed to
ambient conditions for $\sim$30 days before preparing the cross-sectional
sample. At the top surface, we identify an amorphous oxide layer with a
thickness of about 5 nm. The interface between the oxide and bulk CGT is not
atomically sharp. On top of the image in Fig. 3(a) we plot the pixel intensity
averaged horizontally. From the intensity profile, we estimate a transition
region that is 2-3 nm thick in which some crystallinity coexists with the
amorphous oxide. The lower part of the image shows bulk CGT.

Images of the bottom surface of the same sample (Fig. S3) show an oxide
thickness of 2-2.5 nm. This oxide is thinner because it experiences less
oxygen exposure: it is exposed to atmosphere only for the few seconds it takes
to cleave the crystal using scotch tape and place it on the SiO2/Si substrate,
although it is also exposed to oxygen that is trapped at the interface between
CGT and SiO2 after exfoliation. The two oxide thickness measurements indicate
that oxidation of CGT initially proceeds quickly but then more slowly on
further air exposure as it serves as a self-passivation layer.

Figure 4:  Control of skyrmionic bubble size. (a-d) LTEM images of skyrmionic
bubbles in 150 nm thick CGT with varying magnetic field field from 52 mT to
196 mT. The image shown in (d) is the last one obtained before the saturation
field of 204 mT. (a, e, f) LTEM images at a constant magnetic field of 52 mT
with increasing CGT thickness as indicated on the images. (g) Bubble diameter
plotted against magnetic field for three samples. The dashed black line is a
fit to $A/(\mu_{0}H+B)$ where $A$ and $B$ are constants. (h) Bubble diameter
plotted against CGT thickness. In (g) and (h), the error bars are the standard
deviations of the measurements of skyrmion diameter. All scale bars are 200
nm. The thickness of all CGT crystals has been measured by AFM.

Figure 5:  Domain width analysis. (a, b) LTEM images of magnetic domain
structure in (a) 15 nm thick and (b) 150 nm thick un-oxidized CGT (thickness
measured by AFM). The SiN membrane is visible in the corners of (a). The
indicated domain widths represent the average domain width measured in the
image. (c) Domain width as a function of CGT thickness. Red crosses are
extracted from Ref. [28] for Fe3GeTe2. Data was obtained at the smallest
possible magnetic field of 11 mT.

We next investigate the elemental composition of the oxide and interface
structure with energy dispersive x-ray (EDX) analysis. Figure 3(b) shows the
EDX signal across the interface, acquired from a region similar to that shown
in Fig. 3(a). We find a large oxygen concentration at the oxide along with
decreased Te composition compared to the bulk CGT value. There is also a
decrease in the Cr and Ge signal in the mixed oxide/CGT region compared to the
bulk CGT. Real space intensity maps of the Cr, Ge, Te, and O content obtained
by EELS and EDX are given in Figs. S4 and S5, respectively.

We finally use electron energy loss spectroscopy (EELS) to investigate the Cr
oxidation states across the interface. Figure 3(c) shows an EEL spectral map
of the CGT surface shown in Fig. 3(a). We indicate the O K edge, the Cr L2 and
L3 edge, and the Te M edge with dotted lines. The red horizontal dotted lines
are in the same position as in Fig. 3(b) and indicate the transition between
the oxide, mixed oxide/CGT, and bulk CGT. Consistent with our EDX data, we
only detect an O signal at the surface of the CGT, spanning a region about 5
nm thick. We observe a 1.6-1.7 eV decrease of the Cr L2 and L3 peak positions.
The L3 peak position is plotted against $z$ in Fig. 3(d) while the L3/L2 peak
intensity ratio, also known as the white line intensity ratio, is plotted in
Fig. 3(e). The background subtraction method is outlined in Fig. S6.

We note that the shift in peak position and L3/L2 intensity ratio takes place
in the region identified in Fig. 3(a) as a mixed oxide/CGT layer. Such a shift
in peak position, decrease in L3/L2 peak intensity ratio, and the presence of
oxygen indicates an increase in oxidation state of the Cr [29]. The maximum
possible oxidation state of Cr is 6+. However, based on the changes of these
two parameters and comparing with literature values, we determine an upper
bound of 5+ for the Cr oxidation state [29]. A more precise determination by
comparing with published data is challenging, however [30].

Figure 3(f) shows an annular dark-field STEM image in plan-view, i.e. along
the surface normal of the crystal, from an O-CGT sample with varying
thickness. EEL spectra acquired from the regions indicated by the black (16 nm
thick CGT), red (22 nm), and blue (33 nm) crosses are shown in Fig. 3(g).
These spectra have been normalized by the oxygen K edge intensity. Since the
EELS signal is proportional to the thickness of the sample, these spectra
suggest a constant oxide thickness independent of CGT thickness. Also shown in
Figure 3(g) is an EEL spectrum from a CGT sample prepared in a glovebox. This
spectrum does not display an oxygen edge. Hence, our sample preparation
protocol is able to achieve CGT samples with close to pristine surfaces due to
the minimized air exposure. Samples prepared by exfoliating in ambient
conditions but then rapidly encapsulating in graphene likewise do not display
an oxygen peak (Fig. S7).

Figure 3(h) summarizes our structural and compositional findings. The left
panel shows our conclusion from Fig. 2(f) that the surface is non-magnetic;
the non-magnetic layer is thicker than the amorphous oxide layer as indicated
in the middle panel. This suggests that both the oxide and the mixed oxide/CGT
region are non-magnetic. This may be due to the change in oxidation state of
the Cr which also changes the atomic spin moment and possibly the local
magnetic interaction in the mixed oxide/CGT region and the oxide. Cr in bulk
CGT has an oxidation state of 3+ and an [Ar]3d3 electronic structure with spin
S=3/2, while a 4+ or 5+ oxidation state would correspond to an electronic
structure of [Ar]3d2 with S=1 or [Ar]3d1 electronic structure with S=1/2,
respectively.

Finally, the right panel in Fig. 3(h) summarizes our compositional findings.
The loss of Te in the oxide layer may contribute to the loss of magnetism
observed in the oxide. This is because the superexchange interaction
responsible for ferromagnetism in CGT is mediated between nearest neighbor Cr
ions through the Te cations. The loss of Te in the oxide, furthermore, is
similar to other vdW transition metal chalcogenide (TMD) compounds where the
chalcogen is seen to be removed in the oxidation process, such as WSe2 which
forms WO3 [31] and MoS2 which forms MoO3 [32]. In such materials, oxide layer
thickness and composition can be controlled using a thermal process or an
oxygen plasma [33], suggesting that for CGT it may also be possible to control
the oxidation process.

###  II.3 Thickness-dependent topological magnetic textures

Having shown how oxidation changes the effective magnetic thickness of CGT
crystals we next consider how magnetic textures change with thickness. Domain
walls [4] and skyrmions [5] hold potential for application in emerging
spintronic memory and logic devices.

In Fig. 4 we explore the control of skyrmionic bubble size through CGT crystal
thickness and magnetic field. LTEM images of CGT obtained after field cooling
at a magnetic field of 52 mT results in skyrmionic bubble lattices, as
previously reported for CGT [18, 19]. Increasing the magnetic field decreases
the bubble size until the saturation field is reached. Figure 4(a-d) show
images from a sample with a thickness of 150 nm. At 52 mT (Fig. 4(a)) the
average bubble diameter is 104 nm: it decreases to 62 nm at a magnetic field
of 196 mT (Fig. 4(d)), which is the last image obtained before the saturation
field is reached. Figure 4(g) plots the bubble diameter against the applied
magnetic field for three different samples. The size is inversely proportional
to the applied magnetic field, as shown by the dashed black line in Fig. 4(g).
This is as expected for skyrmions [34, 35, 36].

Materials where magnetic bubbles are stabilized by a competition between
magnetic dipolar interactions and magnetocrystalline anisotropy display
thickness-dependent bubble sizes [18, 37, 38]. Conversely, Bloch-type
skyrmions that are stabilized by a DMI have been reported to have a size that
is independent of the sample thickness [39, 40]. Figure 4(a, e, f) shows
bubble lattices in several CGT crystals with different thicknesses, while Fig.
4(h) shows the bubble diameter plotted against CGT thickness, measured at a
magnetic field of 52 mT. We find that the bubble diameter increases with CGT
thickness (for example, diameter 90 nm at CGT thickness 82 nm; diameter 183 nm
at CGT thickness 395 nm). This confirms that magnetic bubbles in CGT are
stabilized by a competition between magnetic dipolar interactions and
magnetocrystalline anisotropy, as expected in such a centro-symmetric material
that lacks a DMI.

Next, considering domain energetics, Fig. 5(a, b) show LTEM images obtained at
15 K after RFC for CGT crystals that are 15 nm and 150 nm thick, respectively.
The 15 nm thick crystal gives less magnetic signal and we therefore use a
larger defocus value to obtain measurable magnetic contrast. Figure 5(c) shows
measurements of the domain width plotted against CGT thickness. We also plot
data for Fe3GeTe2 (FGT) extracted from Ref. [28]. As seen in this plot, FGT
shows a similar behavior to CGT but displays larger domain width compared to
CGT for the same crystal thickness. The two materials are compositionally
analogous and both have been shown to oxidize in ambient conditions leading to
a non-magnetic surface layer [41, 42]. This suggests that the findings here
may be more widely applicable to other vdW magnets.

Kittel developed a model for the energetics of stripe domains in thick films
of ferromagnetic material with out-of-plane magnetic anisotropy [43]. Kooy and
Enz later extended this model to include thin membranes [44]. The domain width
depends on a competition between the domain wall energy, anisotropy energy,
and the demagnetizing energy (stray field energy). For very thin membranes,
the domain width increases exponentially with decreasing membrane thickness.
As the thickness is increased, a minimum domain width, $L_{\mathrm{min}}$, is
reached at a thickness of $4\sigma_{\mathrm{w}}/\mu_{0}M_{\mathrm{s}}^{2}$,
where $\mu_{0}$ is the vacuum permeability, $\sigma_{\mathrm{w}}$ is the
specific domain wall energy, and $M_{\mathrm{s}}$ is the saturation
magnetization (Sec. 3.7.3 in Ref. [45]). For CGT and FGT, $L_{\mathrm{min}}$
is reached at thickness of $t_{\mathrm{D}}$ = 60-120 nm and
$t_{\mathrm{D}}$=80-160 nm, respectively. By using
$M_{\mathrm{s,CGT}}=1.37\cdot 10^{5}$ A/m and $M_{\mathrm{s,FGT}}=3.76\cdot
10^{5}$ A/m from Ref. [46], we can estimate the domain wall energy in CGT and
FGT to be in the range (4-7)$\cdot 10^{-4}$ J/m2 and (36-71)$\cdot 10^{-4}$
J/m2, respectively. This implies that the domain wall energy is around one
order of magnitude smaller in CGT compared to FGT. The latter value fits well
with another estimate of 47$\cdot 10^{-4}$ J/m2 for the domain wall energy of
FGT [47]. We note that Refs. [16, 19] found sizable magnetostrictive effects
in CGT, and therefore a magnetostrictive term should possibly be included in
the Kooy-Enz model for completeness.

Based on the Kooy-Enz model, we would expect CGT to display behavior similar
to FGT for thin layers with thickness $<t_{\mathrm{D}}$, where the domain
width increases until a critical thickness is reached and finally the sample
becomes magnetized in a single domain. Measurements of ultra-thin (6 layers
thick) crystals with lateral dimensions $\sim$10 $\mu$m have previously been
shown to have a single magnetic domain [6]. Additionally, theoretical studies
have predicted that CGT hosts a thickness-dependent magnetic anisotropy which
decreases for thin crystals [48, 49]. Thus, one would expect the domain wall
width, $W_{d}$, to increase for thin crystals, since $W_{d}\sim\sqrt{A/K}$,
where $A$ is the exchange constant and $K$ is the anisotropy constant [45]. We
measure the domain wall width for three relatively thick crystals, with
thickness from 110 to 390 nm, to be in the range 6-14 nm (Fig. S8), without
any clear thickness dependence. This indicates that the uniaxial anisotropy
remains robust for this range of thicknesses. For thin oxidized crystals
(thickness = 24 nm) we do not observe a stripe domain structure that is as
well-defined as those shown in Fig. 5 (Fig. S9), which suggests a weaker
magnetic anisotropy. Hence, it is important to take oxidation into account
when predicting the properties of a CGT crystal. Finally, future studies
should determine whether a minimum thickness exists for the presence of domain
walls and skyrmionic bubbles in CGT.

##  III Conclusions

Our results show how oxidation yields a non-reactive and chemically well-
defined surface, serving as an additional control knob for magnetic properties
in CGT. This may be applicable to vdW magnets more generally, where control of
the oxide growth may be achievable through thermal or plasma oxidation – as
shown for TMDs [33] and with layer-by-layer control [50].

We found that exposure to ambient conditions for 30 days results in a non-
magnetic surface oxide layer that is about 10 nm thick. This is consistent
with the thinnest oxidized crystal in which we observed magnetic textures,
with a thickness of 18 nm and shows that oxidation reduces the effective
magnetic width. From EELS analysis we determined an upper bound of 5+ for the
Cr oxidation state in the oxide which increased from 3+ in the bulk,
indicating a change to the local magnetic properties.

We further observed a strong thickness dependence on the size of skyrmions
which suggests that chemical surface control can in principle tune skyrmion
sizes. Additionally, oxidation could be used for patterning, as recently
demonstrated for TMDs [51]. With increasing knowledge of the electrical and
magnetic properties of the surface oxide layer, and further evaluation of the
degree to which its growth can be controlled in a manner analogous to the
growth of oxides such as MoO3 and WO3, we speculate that surface chemical
control may become a useful tool for developing electrical or magnetic
applications of 2D magnets.

##  IV Methods

###  IV.1 CGT crystal growth

Bulk CGT used for the black data points in Fig. 2(f) and Fig. 4(c) was grown
by the self-flux technique starting from a mixture of pure elements: Cr
(99.95%, Alfa Aesar) powder, Ge (99.999%, AlfaAesar) pieces, and Te (99.9999%,
Alfa Aesar) pieces. A molar ratio of 1:2:6 for Cr:Ge:Te was used. The starting
materials were sealed in an evacuated quartz tube, which was heated to 1100
$\degree$C over 20 hours, held at 1100 $\degree$C for 3 hours, and then slowly
cooled to 700 $\degree$C at a rate of 1 $\degree$C/hour.

Bulk CGT used for the remaining data was prepared by direct reaction from
elements with an excess of Te. The high purity Te (99.9999%), Ge (99.9999%)
and Cr (99.99%) were mixed in a quartz ampoule with a stochiometric ratio of
2:2:10. The 50 g of reaction mixture was sealed under high vacuum in a quartz
ampoule (25x150 mm, 3 mm wall thickness) and heated in a muffle furnace for 6
hours at 1000 $\degree$C with heating rate of 2 $\degree$C/min. The reaction
mixture was horizontally placed in furnace and mechanically shaken several
times at 1000 $\degree$C. The ampoule was cooled to 450 $\degree$C at a rate
of 6 $\degree$C/hour and then left to cool freely to room temperature. The
ampoule was opened inside an argon glovebox and CGT crystals with size
exceeding 5x5 mm were mechanically separated from the middle of the molten
ingot.

###  IV.2 Sample fabrication

CGT crystals were obtained by exfoliating bulk CGT using scotch tape onto
substrates of 90 nm thick SiO2 on Si using 3M Magic Scotch tape. Oxidized
crystals were exfoliated in ambient conditions while un-oxidized crystals were
exfoliated in a glovebox. Some un-oxidized samples were prepared by exfolating
the CGT in ambient conditions and immediately (within $\sim$10 minutes)
assembling the CGT into a van der Waals (vdW) heterostructure with graphene
encapsulation. EEL spectra of the vdW heterostructures do not display an O
peak indicating the absence of any measurable oxidation (Fig. S7). This is in
line with previous reports of oxidation taking place on the timescale of an
hour [6].

Crystals and vdW heterostructures were then transferred to location-tagged TEM
grids purchased from Norcada, Inc., Canada. The transfer was performed using
wedging transfer in which a film of cellulose acetate butyrate is used as
polymer handle [52, 53]. After the transfer we bake the TEM sample carriers to
80 $\degree$C to improve adhesion. Finally, we dissolve the in acetone and
rinse the TEM sample carriers in isopropanol.

Cross-sectional samples were prepared using a Helios Nanolab 600 DualBeam
instrument (FEI). A protective layer of Pt was first deposited with the
electron beam (at least 2 $\mu$m thick) before the cut and the lift-out. The
lamella was then attached to a half-grid and thinned down to obtain a
thickness of 100 nm. The last step of the thinning process was performed with
the ion beam operating at 5 V with a current of 0.15 pA to avoid damage.

###  IV.3 Electron microscopy

A JEOL ARM 200CF instrument equipped with cold field emission gun and double-
spherical aberration-correctors at Brookhaven National Laboratory was used for
LTEM and the EELS data shown in Fig. 3(g). A double-tilt liquid helium cooling
holder (HCTDT 3010, Gatan, Inc.) was used for low-temperature experiments.

HAADF-STEM imaging and EELS data (for Fig. 3(a, c-e) was acquired on a probe-
corrected Thermo Fisher Scientific Themis Z G3 60-200 kV S/TEM operated at 200
kV. EELS data was acquired with a Continuum EEL spectrometer and a dispersion
of 0.3 eV/channel, a dwell time of 0.02 s, beam current of 50 pA, and a zero
loss peak full-width half maximum of 1.9 eV. The data was denoised using
principal component analysis through the implementation in Hyperspy [54].

EDX data was aqcuired with a Hitachi HF5000 environmental TEM operated at 200
kV.

###  IV.4 Data analysis

From each LTEM image, a 40 pixel Gaussian blurred version of the image was
subtracted to remove long-range intensity variations, followed by the
application of a median filter. Domain width was measured by selecting several
neighboring domain walls and measuring their average distance. Magnetic bubble
diameters are measuring by tracing out their perimeter, and calculating the
corresponding diameter assuming a perfect circle. For both bubbles and domain
walls, the position of the domain wall is determined as the transition between
bright and dark contrast on the LTEM images.

###  IV.5 Atomic force microscopy

AFM was performed on an Asylym Research Zypher VRS AFM in tapping mode.

##  V Acknowledgements

This work is primarily supported through the Department of Energy BES QIS
program on "Van der Waals Reprogrammable Quantum Simulator" under award number
DE-SC0022277 for the work on long-range correlations, as well as partially
supported by the Quantum Science Center (QSC), a National Quantum Information
Research Center of the U.S. Department of Energy (DOE) on probing quantum
matter. M.G. acknowledges support by the Air Force Office of Scientific
Research under award number FA9550-20-1-0246. The work at the Brookhaven
National Laboratory was supported by the U.S. Department of Energy (DOE),
Basic Energy Sciences, Materials Science and Engineering Division under
Contract No. DESC0012704. K.S.B. acknowledges the primary support of the DOE,
Office of Science, Office of Basic Energy Sciences under award number DE-
SC0018675. The authors acknowledge the use of the MIT.nano Characterization
Facilities. The authors thank Caroline A. Ross for fruitful discussions.
Figure 2(a) was created using Vesta [55]. P.N. gratefully acknowledges support
from the John Simon Guggenheim Memorial Foundation (Guggenheim Fellowship) as
well as support from a NSF CAREER Award under Grant No. NSF-ECCS-1944085.

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