On the Integration of Spectrum-Based Fault Localization Tools into IDEs

Attila Szatmári

Department of Software Engineering, University of Szeged

Qusay Idrees Sarhan

Department of Computer Science, University of Duhok

Gergő Balogh

Department of Software Engineering, University of Szeged

Péter Attila Soha

Department of Software Engineering, University of Szeged

Árpád Beszédes

Department of Software Engineering, University of Szeged

Spectrum-Based Fault Localization (SBFL) is a technique to be used during debugging, the premise of which is that, based on the test case outcomes and code coverage, faulty code elements can be automatically detected.
SBFL is popular among researchers because it is lightweight and easy to implement, and there is a lot of potential in it when it comes to research that aims to improve its effectiveness.
Despite this, the technique cannot be found in contemporary development and debugging tools, only a handful of research prototypes are available.
Reasons for this can be multiple, including the algortihms' sub-optimal effectiveness and other technical weaknesses.
But, also the lack of clear functional and non-functional requirements for such a tool, either standalone or integrated into IDEs.
In this paper, we attempt to provide such a list in form of recommendations, based on surveying the most popular SBFL tools and on our own researchers' and tool builders' experience.

<concept_desc>Software and its engineering Integrated and visual development environments</concept_desc>
<concept_desc>Software and its engineering Software evolution</concept_desc>
<concept_desc>Software and its engineering Software testing and debugging</concept_desc>
<concept_desc>Software and its engineering Empirical software validation</concept_desc>

[500]Software and its engineering Integrated and visual development environments

[500]Software and its engineering Software testing and debugging
[500]Software and its engineering Empirical software validation

§ INTRODUCTION

Spectrum-Based Fault Localization (SBFL) is a lightweight debugging technique that profiles the program's execution through its test cases, collects code coverage and test results (collectively called the spectrum), and then, based on statistics of failing and passing test cases and their relation to code elements, assigns suspiciousness scores to each such element, a statement or function in particular <cit.>.
We provide a brief overview of the technique in <Ref>.

Although it is a well-researched topic, SBFL is not widely adopted in the industry, and the research community is mostly aware of reasons why SBFL can be challenging.
Sometimes meeting technical requirements can be difficult, and due to its statistical nature, SBFL can occasionally mislead developers during the debugging process leading to the rejection of the technique by practitioners <cit.>.
Sarhan and Beszédes identified additional challenges in SBFL <cit.>.

In this paper, we concentrate on the aspects of implementing SBFL techniques into practical tools, in particular their integration into Integrated Development Environments (IDEs).
Hence, we do not deal with any other technical or theoretical aspects of the technique.
With this, we distinguish our study from a more conceptual comparison of related tools such as the one performed by Archana and Agarwal <cit.>.

We base our investigation on three sources.
First, we perform a lightweight survey of existing SBFL tools to identify their main properties, and more importantly, the existing strengths and weaknesses (<Ref>).
Second, we summarize our findings from a recent empirical study that we performed with actual users who have been given a debugging task to be performed in an IDE with some of our own SBFL tools (<Ref>).
Third, we collect our own experience as researchers working in the SBFL domain for several years and as tool builders who have experience in integrating debugging tools into various IDEs including Eclipse and JetBrains.

We list our findings in <Ref> from three perspectives: users', developers, and researchers', with the hope that future tool builders in this area could benefit from it when designing new tools, preferably integrated into IDEs.

The Research Questions (RQs) we address in this study are the following.

1What are the general expectations of developers and users regarding fault localization tools?
2To what is the current level of integration among the inspected tools, their identified features, and the integrated development environments?
3What are the open questions that need to be answered and what recommendations should be observed to improve integration?

§ SPECTRUM-BASED FAULT LOCALIZATION

SBFL is a lightweight statistical fault localization approach in which every element (such as a statement or a function) will be assigned a suspiciousness score (usually between 0 and 1), indicating the possibility that the fault is caused by that element <cit.>.
This score is then used to provide a ranked list of potentially faulty code elements to the user who can rely on this information during debugging.

To calculate these scores, SBFL operates on the so-called program spectrum. It consists of a coverage matrix and a test result vector.
In the most common case, the rows of the coverage matrix denote test cases of the program and the columns represent the elements of the source code. A cell value, $c_{i,j}$ is 1 if during the execution of the $i$th test case the $j$th element was executed, and 0 otherwise.
The test result vector ($e$) represents the results of the executions of the test cases, where $e_i$ is equal to 1 if the $i$th test case failed and 0 otherwise (<Ref>).

The next step is to calculate suspiciousness scores, which is usually done based on four basic metrics, where $\operatorname{metric~}_{\text{exec},\text{res}}(j)$ is the number of runs when the $j$th element was executed ($\text{exec} = 1$) or not ($\text{exec} = 0$) and whether the inspected test case failed ($\text{res} = 1$) or passed ($\text{res} = 0$).
These four basic metrics are used to compose various suspiciousness formulas, such as Tarantula <cit.>, Ochiai <cit.>, or Barinel <cit.>.

Researchers advised many different types of extensions to this basic approach, including program slicing <cit.>, adding contextual information <cit.>, user feedback <cit.>, and machine learning <cit.>, to enhance the effectiveness.

\[
\begin{array}{cccc}
& n\text{ source code items} & & m\text{ tests} \\
C = &
\begin{bNiceMatrix}
c_{1,1} & c_{1,2} & \cdots & c_{1,n} \\
c_{2,1} & c_{2,2} & \cdots & c_{2,n} \\
\vdots & \vdots & \ddots & \vdots \\
c_{m,1} & c_{m,2} & \cdots & c_{m,n} \\
\end{bNiceMatrix} &
e = &
\begin{bNiceMatrix}
e_{1} \\
e_{2} \\
\vdots \\
\end{bNiceMatrix}
\vspace{3mm}
\\\\
& 4\text{ basic metrics} \\
\operatornamewithlimits{metric}\limits_{\text{exec},\text{res}}(j) = &
\left|\left\{i\;|\;M_{i,j}=\text{exec} \land e_i = \text{res}\right\}\right| &
\multicolumn{2}{c}{\text{exec},\text{res}\in \{0,1\}}
\vspace{3mm}
\\\\
& n\text{ score values} \\
s = &
\begin{bNiceMatrix}
s_{1} & s_{2} & \cdots & s_{n}
\end{bNiceMatrix}
\end{array}
\]

Overview of SBFL

§ SBFL TOOLS

In this section, we provide an overview of the most frequently cited SBFL tools, highlighting their main features. It is worth noting that our research does not take into account non-functional requirements like speed or memory usage. Nevertheless, we acknowledge that these factors are crucial for boosting the acceptance of SBFL tools in the industrial sector, and we plan to address them in follow-up research.

Due to the nature of SBFL, it calls for its implementation into an IDE directly rather than as a standalone tool, but there are examples for both.

Wang  <cit.> proposed a fault localization tool named FLAVS for developers utilizing the Microsoft Visual Studio platform. The tool collects program spectrum information during program execution to identify suspicious program elements. It monitors all environmental parameters of the running program, such as thread counts, CPU use, and memory usage. Chen and Wang <cit.> have expanded the features of FLAVS to another tool named UnitFL. To shorten the program execution time, the tool makes use of program slicing.

A tool called SFLaaS was proposed by Sarhan <cit.> to locate faults in Python programs. It is offered as a cloud-based service instead of a plugin or command-line tool.
The program offers various tie-breaking techniques, approximately 80 SBFL formulas, the ability for the users to define their own formulas, and the display of code elements in various colors according to their suspiciousness scores, from most suspicious (red) to not suspicious (green).

For Java developers, Ribeiro <cit.> proposed the SBFL tool Jaguar. The tool supports control and data flow, the two advanced spectra types. Moreover, it presents suspicious program elements graphically so that the user can quickly examine suspicious variables, statements, or methods.

Whyline is a debugging tool for Java developers that was proposed by Ko and Myers <cit.>. The tool utilizes slicing to aid developers in understanding the program behavior under test through a set of questions that are presented in a graphical and interactive way. The tool also logs program execution traces and the status of each program element, indicating its execution status. The tool allows users to view a program's execution trace and select an element at a specific execution point for examination.

The Eclipse plug-in tool VIDA was proposed by Hao <cit.> for Java programs. The tool provides the top ten most suspicious elements as possible breakpoints, along with a history of previous breakpoints and their current level of suspicion. Static dependency graphs are also produced to assist developers in comprehending the relationships between program elements.

A tool called GZoltar was proposed by Campos <cit.> to locate faults in Java programs, and it is provided as a plugin for the Eclipse IDE. It generates visually appealing and interactive diagnostic report visualizations like Sunburst and Treemap.

A tool called CharmFL was proposed by Sarhan <cit.> to locate faults in Python programs using SBFL. The tool can be used as a standalone or as a plugin for the PyCharm IDE. It supports different code coverage types (i.e., statements, methods, and classes) with the possibility to investigate these types in a hierarchical approach.

The CharmFL tool has been extended in <cit.> to support interactivity in fault localization. With the help of this feature, users can provide their feedback on the suspicious elements and help reorder them, which may improve the fault localization process. This is achieved by utilizing contextual information (i.e., function call graphs) during a failed test. As a result, users are able to examine the data flow traces of any failed test and pinpoint the fault's location more precisely. This interactivity feature is also provided by iFL4Eclipse an Eclipse plug-in SBFL tool <cit.>.

§ EXPERIENCES FROM A USER STUDY

In a recent study, empirical experiments were conducted to assess the effectiveness of the SBFL technique with user feedback integrated into an IDE <cit.>.
The research was performed on different levels; with simulation, using students, and with professional developers.
Among other things, conclusions could be drawn from this study regarding the user's perception of the tool used, so this information is very useful for our purposes in the present paper.

We reuse this data from the user study, in particular, the participants' oral responses in form of transcripts of the experiment sessions.
For constructing the transcripts, a think-aloud technique was utilized which was performed with six professional developers. It involved 24 debugging sessions, with each of the developers participating in four of them.
Their task was to find and fix a bug in existing software using an SBFL tool plug-in in the Eclipse IDE.
During the process, their ways of thinking were recorded, which included navigating and understanding the code, and in particular using the tool's functions.

In the original paper by Horváth  <cit.>
the main goal was to evaluate the effectiveness of interactive FL in a variety of scenarios.
The tasks for the experiments were selected from various projects by choosing bugs that did not require specific domain knowledge.

This approach was intended to simulate situations where developers debug an unfamiliar program, which is common in real-world software development.
The participant pool included undergraduate and graduate students as well as professional developers, aiming to cover a diverse range of experience levels.

The experimental setup was balanced in terms of participant distribution across different groups.
The complexity of tasks and potential prior knowledge of the participants about projects or bugs was considered during the design phase.

We processed the transcript of these sessions with a focus on the participants' opinions about the tools.
To enhance objectivity, we instructed the ChatGPT 4.0 LLM engine <cit.> to extract all the expectations (both implicit and explicit) of the software engineers from the transcripts. Implicit expectations refer to improvements in the IDE and plug-ins that make their tasks easier, which can be inferred from their actions and behavior. On the other hand, explicit expectations are specific requests for features or explicitly expressed wishes by the developers.

Recommendation extraction process

The recommendation extraction process is shown in <Ref>.
The transcripts of the think-aloud sessions, prompt instructions and metadata from the previous experiment are entered into ChatGPT to help process and summarize these diverse data sources.
All prompts are available in the online appendix of this paper <cit.>.
Users' proposals for integration to the IDE and their opinions on the current level of integration summarized by ChatGPT were then carefully investigated by the authors of this paper.
We treat this step as an expert evaluation as we could contribute valuable insights based on our experience with the development of SBFL tools.
We then constructed a list of proposals and opinions.
Depending on their actionability, recommendations for integration with the IDE are formulated or questions are raised that address open challenges and issues.

ChatGPT extracted more than 150 expectations from over 250 thousand tokens' transcriptions. We utilized a tool to filter semantic duplicates, which resulted in 17 distinct raw expectations.
To validate the raw expectations, we used the Elo rating system <cit.>, typically used for calculating the relative skill levels of players in zero-sum games like chess. In this case, each expectation was considered a player competing for the votes of software engineering experts who had to decide which expectation was more important during debugging or fault localization. To determine the winner, we counted the votes for each expectation and updated their Elo rating accordingly.

We used two free scaling parameters, K and c, with their typical values of K=32 and c=400. Each expectation had an initial rating of 1500. Our matching strategy combined elements of randomness, exploration, and exploitation to ensure a balanced and fair evaluation of all items. The source code of our rating strategies is available in the online appendix <cit.>.

In the final phase, we compared the expectations that were ranked with the features provided by the fault localization tools. This helped us create the final recommendations and assemble the list of open questions, to be discussed in <Ref>.

§ RECOMMENDATIONS

In this section, we summarize and blend our findings from the tool survey in <Ref>, the user study from <Ref>, and our own experiences.
First, we give an overall list of expectations we identified and assess the investigated tools from the perspective of how they implement them in <Ref>.
In the last part of this section, we summarize what we believe are the most important recommendations from the users', developers', and researchers' perspectives, respectively.

Summary of expectations and their relationship to existing SBFL tools.

C = CharmFL, F = FLAVS, G = GZoltar, J = Jaguar, S = SFLaaS, U = UnitFL, V = VIDA, W = Whyline, i = iFL4Eclipse;
red = no tool implements or plans it, blue = less then 3 tools (1st quartile) implement or plan it;
= responsibility is unassigned;  = IDE is responsible;  = plug-in is responsible;
Responsibilities were determined based on our experiences, taking into account expectations, their manifestations in tools, and tools' visions.

2cImplementation     4cValidation     2cMaturity     4cEcosystem

Short Summary     2*Rating     2*Implemented     2*Planned     2*None     by     with     with     Alpha     Beta     Stand-     2*Eclipse     Visual     2*PyCharm

Authors     Students     Prof.     Version     Version     alone         Studio

code navigation and search     1.00     6 (C;F;G;J;U;i)          3 (F;G;U)          2 (J;i)     1 (i)     1 (C)     5 (F;G;J;U;i)          3 (G;J;i)     2 (F;U)     1 (C)

clearer error messages     0.90     1 (G)          1 (G)                         1 (G)         1 (G)

tests' running optimization     0.88          2 (G;J)     2 (G;J)                         2 (G;J)         2 (G;J)

code execution path visualization     0.88     1 (J)           1 (J)                         1 (J)         1 (J)

clearer debugging process     0.86     2 (V;W)          1 (V)          1 (W)     1 (W)     1 (V)     1 (W)      1 (W)     1 (V)

intuitive UI     0.86     7 (C;F;G;J;S;U;W)          5 (F;G;J;S;U)     1 (C)     2 (W;i)     2 (W;i)     2 (C;S)     5 (F;G;J;U;W)     1 (W)     1 (G;J)     1 (F;U)     1 (C)

advanced debugging tools     0.83     1 (W)                    1 (W)     1 (W)          1 (W)     1 (W)

responsive IDE     0.81     3 (C;J;F;G)          3 (C;G;J)                    1 (C)     2 (F;G)         1 (G)     1 (F)     1 (C)

customizable interface     0.79

intuitive code coverage visualization     0.78     2 (C;G)     1 (J)     3 (C;G;J)                    1 (C)     2 (G;J)         2 (G;J)          1 (C)

streamlined test processes     0.77     8 (C;F;G;J;S;U;V;i)          7 (C;F;G;J;S;U;V)              1 (i)     3 (C;S;V)     5(F;J;G;U;i)     1 (S)     4 (G;J;V;i)     2 (F;U)     1 (C)

IDEs' compatibility with plugins     0.70      (C;G;U)           (C;G;U)                    1 (C)     2 (G;U)          2 (G;U)          1 (C)

code changes' error message clarity     0.69

plugin integration and interaction     0.61     3 (C;G;U)          3 (C;G;U)                    1 (C)     2 (G;U)          1 (G)     1 (F)     1 (C)

integrated domain knowledge     0.60

integrated documentation     0.00

interactivity between SBFL and developers     -     3 (C;V;i)   1(S)     3 (C;S;V)            1 (i)    3 (C;S;V)     1 (i)     1 (S)    2 (V;i)         1 (C)

hierarchical view based on code structure     -     3 (C;G;J)         2 (C;G)       1 (J)         1 (C)   2 (G;J)       2 (G;J)        1 (C)

accessibility-focused UIs     -    1 (G)         1 (G)                1 (G)            1 (G)

enabling teamwork and sharing     -

inspect suspicious items from different aspects     -     1 (J)                1 (J)             1 (J)        1 (J)

optimize SBFL with test selection & prioritization     -     1 (V)         1 (V)                1 (V)            1 (V)

incorporate AI into SBFL     -

handling code element context switching     -

on-demand reanalysis upon code change     -

suspiciousness score visualization     -     5 (F;G;J;U;V)    1(S)    5 (F;G;S;U;V)         1 (J)        2 (S;V)    4 (F;G;J;U)     1 (S)     3 (G;J;V)     2 (F;U)

understanding the tool's reasoning     -

(smart) customizable feature set     -

customizable SBFL algorithm     -    2 (F;S)        2 (F;S)                    2 (F;S)     1 (S)        1 (F)

<Ref> is composed of two parts: expectations from the user study in the upper half and other generic expectations based on the tool survey and the authors' own experiences in the lower half.
The first column is a short summary of the expectation with the associated Elo rating in the second column (for user study only).

Columns 3 and 4 indicate if the expectation is implemented or planned in the respective tools, columns 5–8 show how the feature has been validated, columns 9 and 10 estimate the tool's maturity, and the last 4 columns show how the tool is implemented, either a standalone or an IDE plugin.

Note that since we identified a relatively large number of expectations (column one of <Ref>), due to space limits we cannot explain all in detail;
their description can be found in the online appendix <cit.>.

§.§ Users perspective

Based on the data presented in <Ref>, we identified two interwoven trends in user expectations. First, users expect SBFL tools to be seamlessly integrated in their workflow and efficient. Second, users prefer these tools to be easy to understand and use.

[Seamless integration into IDEs and developers workflow.]
For developers, IDEs are considered complete tools that
help them in their daily workflow rather than just collections of plug-ins. They expect the UI to be intuitive, along with various visualizations such as coverage and suspiciousness score.
The plug-ins should work cohesively with each other and with the IDE to meet the users' expectations.

[Transparent reasoning behind the tool.]
As problem solvers, developers love to automate complex processes. However, they may not fully trust the SBFL algorithms due to the lack of familiarity. To earn their trust, SBFL tools should provide clear error messages, easily accessible documentation, explainable operation, and drill-down views that help developers understand the reasoning behind the tool's suggestions.

§.§ Developers perspective

In this section, we provide advice on how to incorporate SBFL tools into IDEs, based on our experience as developers.

[Developers should focus on tool development guidelines.]

It is necessary for developers to follow these recommendations when integrating a tool into any IDE.

* Developers investigate the compatibility of the IDE through its documentation and website. They may experience compatibility issues due to the tools they make having specific versions or dependencies that may not be compatible with the components or versions of the IDE.

* Tool developers should prefer official and actionable tutorials. Start by looking for a step-by-step guide from the IDE.
Look for configuration templates or samples shared by the community or developers who have successfully incorporated the tool into the IDE; these can significantly reduce the need to configure from the beginning.

* Developers need to understand the IDE developers' concepts for effective work.
We suggest searching for documentation before seeking examples of solutions to the problem or feature the developer is attempting to implement. This will ensure they have the right frame of mind while evaluating and maybe adapting others' solutions.[Developers should always respect authors' rights and check the license before making any derived work.]

* Tools must support the user's preferred IDE version. It is highly recommended to create a separate testing environment to prepare for any issues that may arise from updates before they are applied to the main development system. Doing so will help identify any integration issues without disrupting any current projects.

[Find efficient ways to produce, store and process runtime data.]
The SBFL spectrum, including test case execution information, should be kept in a data structure that allows for quick access to its individual elements.
This is essential if we want to ensure efficient operation with a responsive user interface of the tool.

[Programmers should strive to fully utilize IDEs' data and API features.]
The IDE should take charge of certain components of the SBFL process, and the developer should work together with the IDE to make sure that the process is handled properly and minimize solutions outside of the IDE.
For instance, it is recommended that test execution is done directly within the IDE.

[Ensure that code elements are easily identifiable.]
IDEs store program execution data in their own format, which may differ from the static source code structure. SBFL tools require both dynamic analysis and static source code representation, especially when working with loosely typed scripting languages like Python or JavaScript.
Information from static and dynamic analysis is often a challenge to match.

[Reporting about validation efforts.]
During the inspection of the selected set of tools against the expectations collected from users and developers, we noticed a concerning trend regarding the authors' validation efforts.
Although most of the papers did a good job of reporting the features and methods underlying their research, in many cases we were unable to find concrete evidence of how the authors validated their contributions, and we believe this should be improved.

[Decide on the responsibility of tool and IDE developers.]
The developers of tools and IDEs should put into practice the expectations outlined in <Ref>. However, it is not always obvious who should be responsible for what.
Also, it is not always reasonable to expect IDE developers to respond to a feature request made by a plug-in developer.
For instance, implementing IDE specific features such as enabling code navigation and search within the codebase should be the responsibility of the IDE developers.
But implementing a new, hierarchical code visualization, for instance, is probably the tool-builder's job.
To allow easier assignment of responsibility, we may consider the following questions. Can the plugin implement the expectation without the help of the IDE? Does the plugin fulfill its goal without the given expectation? Are the IDE and plugin necessary to tightly cooperate to implement the expectation?

§.§ Researchers perspective

Although SBFL has extensive literature, active work continues with new formula exploration, adding context to the spectrum, and developing different score calculation algorithms including AI-enabled approaches, to name a few. Researchers can take steps to prepare for different types of follow-up research.

[Make data computed by SBFL tools easily available for researchers.]
One way to do this is to provide dedicated logging and dumping mechanisms to retrieve data from the tools. This can be useful for analyzing users' behavior as well.

[Make SBFL tools' underlying logic customizable.]
Another way is to offer customization options within the tool itself. This can be achieved through settings, a modular architecture, or simply by making the tool open-source. While expecting researchers to include these customization systems out-of-the-box may be unrealistic, researchers should not prevent others from building upon their work either.

[Easy implementation and experimentation with new algorithms.]
Devising new human-computer interactions for emerging scientific methods, like different flavors of SBFL, is presumably more suited for researchers than professional programmers.
Hence, it is important for researchers to make it as easy as possible to implement new features and perform experimentation with prototype ideas.

[Contribute to open science.]
Finally, we highly encourage tool developers to contribute to open science wherever they can.
Besides the recommendations we already mentioned above, this would mean making  the implementation, test data and other artifacts openly available.

A possible framework that could be followed in particular is the FAIR guideline for software <cit.>, which includes aspects like Findability, Accessibility, Interoperability and Reusability, among others.

§ THREATS TO VALIDITY

Our study focused on integrating SBFL tools into IDEs. However, we understand that there are several critical factors that could impact the robustness and applicability of our findings. We acknowledge that the selection of specific tools and environments for this study was necessary, but it limits the breadth of our conclusions. Therefore, the insights gathered from this study may not be applicable to all varieties of these tools or different development environments. Future research could benefit from including a wider range of tools to broaden the scope of our findings.

It is important to recognize that the interpretation of feedback from users and developers is subjective and based on individual experiences and perceptions. Therefore, to minimize the impact of this subjectivity, future experiments should consider increasing the number of participants and implementing measures to ensure anonymity.

The methodology used to assess the efficacy and usability of tools integrated within IDEs may not encompass every facet of the user and developer experience, which could result in a partial evaluation. Therefore, a more comprehensive investigation that solicits feedback from a diverse group of users is necessary to offer a more holistic understanding of the subject matter.

Finally, the rapidly evolving nature of SBFL tools and IDEs poses a formidable challenge to the long-term relevance of research findings. It is crucial to periodically re-evaluate the efficacy of these tools, taking into account the latest advancements, to ensure that our research remains relevant and cutting-edge. Such periodic assessments are crucial for maintaining the credibility and applicability of our research outcomes.

§ CONCLUSIONS

This paper is a work towards practically usable SBFL in IDEs.
Out of the total of 29 expectations, only 18 were implemented (62%), which implies that 11 expectations were left unfulfilled. It is noteworthy that only one of the unimplemented expectations was planned. Hence, it is safe to assume that the acceptance of SBFL tools by industrial Integrated Development Environment (IDE) users is still far from being achieved.
The technique itself is promising since it could significantly help in semi-automated debugging, but currently the implementations are not mature enough to be considered by professional programmers.

Based on surveying existing tools, asking users' opinions, and our own experiences, we compiled a list of concrete recommendations for future tool builders for this task.
It is without doubt that the underlying technology should also be further researched to reach the efficiency and precision that are required in a practical, everyday context as well, not only in a lab setting.
However, our concerns regarding the implementation into IDEs should be equally considered, and parallel development of the two can hopefully give birth to usable SBFL plug-ins in some of the popular IDEs in the future.

§ ACKNOWLEDGEMENTS

This research was carried out in project TKP2021-NVA-09 supported
by the Ministry of Innovation and Technology of Hungary from the
National Research, Development and Innovation Fund, financed
under the TKP2021-NVA funding scheme.

#1     #1#1#1     #1     #1     #1     #1#1          #1#1

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# Magnetic Proximity induced efficient charge-to-spin conversion in large area
PtSe2/Ni80Fe20 heterostructures

Richa Mudgal  [  Alka Jakhar  [  Pankhuri Gupta  [  Ram Singh Yadav  [  B.
Biswal  [  P. Sahu  [  Himanshu Bangar  [  Akash Kumar  [  Niru Chowdhury  [
Biswarup Satpati  [  B. R. K. Nanda  [  S. Satpathy  [  Samaresh Das  [  P. K.
Muduli<EMAIL_ADDRESS>[

###### Abstract

As a topological Dirac semimetal with controllable spin-orbit coupling and
conductivity, PtSe2, a transition-metal dichalcogenide, is a promising
material for several applications from optoelectric to sensors. However, its
potential for spintronics applications is yet to be explored. In this work, we
demonstrate that PtSe2/Ni80Fe20 heterostructure can generate a large damping-
like current-induced spin-orbit torques (SOT), despite the absence of spin-
splitting in bulk PtSe2. The efficiency of charge-to-spin conversion is found
to be $(-0.1\pm 0.02)$ nm-1 in PtSe2/Ni80Fe20, which is three times that of
the control sample, Ni80Fe20/Pt. Our band structure calculations show that the
SOT due to the PtSe2 arises from an unexpectedly large spin splitting in the
interfacial region of PtSe2 introduced by the proximity magnetic field of the
Ni80Fe20 layer. Our results open up the possibilities of using large-area
PtSe2 for energy-efficient nanoscale devices by utilizing the proximity-
induced SOT.

Indian Institute of Technology Delhi] Department of Physics, Indian Institute
of Technology Delhi, Hauz Khas, New Delhi-110016, India Indian Institute of
Technology Delhi] Center for Applied Research in Electronics, Indian Institute
of Technology Delhi, Hauz Khas, New Delhi-110016, India Indian Institute of
Technology Delhi] Department of Physics, Indian Institute of Technology Delhi,
Hauz Khas, New Delhi-110016, India Indian Institute of Technology Delhi]
Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New
Delhi-110016, India Indian Institute of Technology Madras] Condensed Matter
Theory and Computational Lab, Department of Physics, Indian Institute of
Technology Madras, Chennai 600036, India [Indian Institute of Technology
Madras] Center for Atomistic Modelling and Materials Design, Indian Institute
of Technology Madras, Chennai 600036, India Indian Institute of Technology
Madras] Condensed Matter Theory and Computational Lab, Department of Physics,
Indian Institute of Technology Madras, Chennai 600036, India Department of
Physics & Astronomy, University of Missouri, Columbia, MO 65211, USA Indian
Institute of Technology Delhi] Department of Physics, Indian Institute of
Technology Delhi, Hauz Khas, New Delhi-110016, India Indian Institute of
Technology Delhi] Department of Physics, Indian Institute of Technology Delhi,
Hauz Khas, New Delhi-110016, India [University of Gothenburg] Department of
Physics, University of Gothenburg, Gothenburg-412 96, Sweden Indian Institute
of Technology Delhi] Department of Physics, Indian Institute of Technology
Delhi, Hauz Khas, New Delhi-110016, India Saha Institute of Nuclear
Physics]Surface Physics & Material Science Division, Saha Institute of Nuclear
Physics, A CI of Homi Bhabha National Institute, 1/AF Bidhannagar, Kolkata
700064, India Indian Institute of Technology Madras] Condensed Matter Theory
and Computational Lab, Department of Physics, Indian Institute of Technology
Madras, Chennai 600036, India [Indian Institute of Technology Madras] Center
for Atomistic Modelling and Materials Design, Indian Institute of Technology
Madras, Chennai 600036, India Indian Institute of Technology Madras] Condensed
Matter Theory and Computational Lab, Department of Physics, Indian Institute
of Technology Madras, Chennai 600036, India Department of Physics & Astronomy,
University of Missouri, Columbia, MO 65211, USA [Indian Institute of
Technology Madras] Center for Atomistic Modelling and Materials Design, Indian
Institute of Technology Madras, Chennai 600036, India Indian Institute of
Technology Delhi] Center for Applied Research in Electronics, Indian Institute
of Technology Delhi, Hauz Khas, New Delhi-110016, India Indian Institute of
Technology Delhi] Department of Physics, Indian Institute of Technology Delhi,
Hauz Khas, New Delhi-110016, India

The next generation of spintronic memories can be realized using spin-orbit
torques (SOT), an energy-efficient and faster way to manipulate magnetization.
1 In ferromagnet (FM)/heavy metal (HM) bilayers, SOT describes the current-
induced torque exerted on the FM layer. The flow of a charge current in an
FM/HM system can generate a spin current, transverse to the direction of
charge current flow, by mechanisms such as the spin Hall effect, 2 or Rashba-
Edelstein. 3 Typically heavy metals, such as Pt, 4, 5 W, 6, 7, 5 and Ta 8, 9
are used to generate spin currents. Significant efforts have been reported to
improve the energy efficiency of HM-based SOT devices. 10, 11, 12 One method
to achieve a higher SOT efficiency is by replacing the HM layer with
alternative materials that have large charge-to-spin conversion efficiency and
high conductivity. Transition metal dichalcogenides (TMDs) are potential
replacements of HM due to various properties such as tunable conductivity, 13,
14 high spin–orbit coupling, 15, 16, 17 the presence of Dzyaloshinskii Moriya-
interaction, 18 tunable band structure, 19, 20 spin-layer locking 21 and long
spin-life time. 22 The use of TMDs in SOT devices has shown a number of
advantages, e.g., the ability to control SOT using the crystal symmetry 23,
24, 25 and electric field. 26

The Pt-based TMDs offer advantages such as high air stability,27, and large
spin-orbit coupling. 28 However, SOT studies on Pt-based TMDs have been
limited to PtTe2 for which a recent work showed a large damping-like torque
and SOT switching. 29 PtSe2 is another Pt-based TMD offering high and tunable
spin-orbit coupling. 28 It is also a type-II Dirac semi-metal, offering
several topologically protected phenomena potentially useful for spintronic
applications. 30 In addition, the band structure of PtSe2 exhibits topological
surface states, 31 which can be exploited for topological spintronic devices.
It has been demonstrated that the monolayer PtSe2 film possesses spin-layer
locking 21 with many interesting electronic properties. 32 These intriguing
properties suggest that PtSe2 might be a promising candidate for investigating
the SOT phenomenon. However, unlike other TMDs 17, the band structure of PtSe2
does not show spin splitting. In addition, the type II Dirac cone appears much
below the Fermi energy in the bulk PtSe2. 30

In this work, we investigate SOT in PtSe2/Ni80Fe20(or NiFe)/Pt
heterostructures using the spin torque ferromagnetic resonance (STFMR)
technique. We found a large increase in the effective damping constant (164%)
in PtSe2/NiFe/Pt compared to the NiFe/Pt control sample. Using angle-resolved
STFMR measurements, we demonstrated that only conventional SOTs are generated
in PtSe2/NiFe/Pt, with spin polarization along the y-axis for a charge current
flowing along the x-direction, which is in accordance with theoretical
predictions. 33 From the line shape analysis, we determine an enhanced
effective damping-like torque due to PtSe2. We found a maximum interfacial
charge-to-spin conversion efficiency of $-0.1\pm 0.02$ nm-1 due to PtSe2. Our
band structure calculation of PtSe2 that includes the proximity of the FM
layer shows that NiFe introduces: (a) charge transfer from NiFe to PtSe2, (b)
a Rashba SOC due to the surface symmetry breaking, and (c) a proximity
magnetic field induced spin-splitting that could lead to enhanced spin Hall
conductivity (SHC) in the interface region. The enhanced SOT due to PtSe2 is
qualitatively explained using the substantial spin splitting introduced by the
proximity magnetic field.

Figure 1: (a) cross-sectional HRTEM image of PtSe2/NiFe/Pt stack. The
interface is indicated by the red dashed lines. The magnified view of the
square region is shown in the bottom part of the figure, showing the formation
of high-quality PtSe2 lattices (with 1T structure). (b) Raman spectra of PtSe2
thin film (red curve) and that of the device after deposition of NiFe/Pt
(black curve). The spectra show two strong peaks labeled as Eg and A1g and one
shoulder peak labeled as longitudinal optical (LO) mode. (c) X-ray
photoelectron spectra of Pt-4f core level. Spectra were fitted with four peaks
corresponding to PtSe2 and PtSex. Splitting between doublets of Pt-4f peaks is
found to be 3.3 eV.

We used a thermally assisted conversion process to grow large-area PtSe2 thin
films. 34 HRTEM and XRD (section S1 in supplementary) measurements on PtSe2
show the growth of crystalline films. Figure 1 (a) shows the cross-sectional
HRTEM image of PtSe2/NiFe/Pt stack. The image shows that the whole Pt layer
gets selenized, and a high-quality PtSe2 lattice with a 1T structure is
formed. The thickness of PtSe2 is found $\approx$ 9 nm, and the separation
between two consecutive layers is $\approx$ 0.5 nm. Each layer corresponds to
a monolayer of PtSe2, which contains one Pt layer sandwiched between two Se
layers. A magnified view of the square region is shown at the bottom of the
figure. Based on HRTEM and AFM measurements (Section S1 in supplementary), we
determine the thickness of PtSe2 after selenization of 3 nm thick Pt to be (10
$\pm$ 1.0) nm. This increase in the thickness of Pt due to its selenization is
well-known in the literature, 35 and it further confirms the complete
selenization of the Pt layer. Figure 1 (b) shows the Raman spectra of PtSe2,
measured with a laser of wavelength 532 nm. The spectrum contains two distinct
peaks that corresponds to PtSe2: Eg at 176 cm-1 and A1g at 206 cm-1. Here, the
Eg corresponds to the in-plane vibrations of Se atoms moving away from each
other while the A1g corresponds to out-of-plane vibrations of Se atoms moving
in the opposite directions. 36 A small peak labeled as longitudinal optical
(LO) mode is also observed at 233 cm-1, which is a combination of in-plane and
out-of-plane vibrations of Pt and Se atoms. 36, 37 The position and intensity
ratio of A1g and Eg peaks confirm the presence of PtSe2 in bulk form. 36
Similar spectra were obtained at multiple locations on the sample with a ratio
of the intensity of A1g and Eg peaks nearly identical (0.75 $\pm$ 0.02),
confirming the formation of a large-area homogeneous thin film of PtSe2. The
chemical composition of PtSe2 was verified further by X-ray photoelectron
spectroscopy (XPS). Figure 1 (c) shows the Pt-4f core-level spectra. The
binding energies of the different core levels have been calibrated using the
C-1s peak and the core-level spectra have been best fitted with Gaussian
profiles. Peaks corresponding to IV valency of Pt are observed at 76.3 and 73
eV, while peaks centered at 75.1 and 71.8 eV show the presence of PtSex phase
in a small amount. The splitting between doublet for each phase is found to be
3.3 eV, consistent with literature 38.

Subsequently, we fabricated microstrip ($100\times 40~{}\mu$m2) devices for
STFMR measurements using maskless lithography and lift-off method in two
levels. To confirm the presence of PtSe2 after deposition of NiFe/Pt and
device fabrication, we perform Raman measurements [Fig. 1 (b)] by focusing the
laser on the microstrip. The intensity ratio of A1g and Eg was found to be
similar compared to pure PtSe2, indicating that the quality of PtSe2 was not
affected by the deposition of NiFe/Pt and our fabrication steps. The overall
reduction in the intensity of the peaks is due to the finite thickness of the
top metal layers.

Figure 2 (a) depicts a schematic representation of the sample stack used for
STFMR experiments, while Fig. 2 (b) shows the schematic of the STFMR circuit.
11 An amplitude-modulated radio frequency (RF) current, $I_{\mathrm{RF}}$ is
applied to the device through the RF port of a bias-tee. The DC port of the
bias-tee is used for both measuring the rectified mixing voltage using a lock-
in amplifier and applying DC current. We vary the in-plane field angle,
$\theta$ with respect to RF current, as defined in the zoomed-in image of Fig.
2 (b).

Figure 2: (a) Schematic of sample stack showing the direction of RF current
and the precession of magnetization. (b) Schematic of STFMR set-up consisting
of an optical image of the device. The directions of the RF current and
applied field are also shown in the enlarged image. (c) Anisotropic
magnetoresistance of PtSe2 (10 nm)/NiFe (5 nm)/Pt (3 nm) to gather with
control sample NiFe (5 nm)/Pt (3 nm). (d) Example of STFMR spectra measured at
5 GHz and $\theta=50^{\circ}$ for PtSe2(t)/NiFe/Pt for varying thickness of
PtSe2 layer. The plots are shifted for clarity. Angular dependence of
$V_{\mathrm{S}}$ and $V_{\mathrm{A}}$ for (e) NiFe/Pt (f) PtSe2 (10
nm)/NiFe/Pt, measured at 5 GHz. In all the plots, symbols represent the
measured data, while solid lines represent fits as described in the main text.

Figure 2 (c) shows the measured anisotropic magnetoresistance (AMR) of PtSe2
(10 nm)/NiFe (5 nm)/Pt (3 nm) to gather with control sample NiFe (5 nm)/Pt (3
nm). The solid lines are calculated AMR curve with
$R=R_{\perp}+(R_{\parallel}-R_{\perp})\cos^{2}\theta$, where $R_{\perp}$
denotes the resistance for $\theta=90^{\circ}$ and $R_{\parallel}$ denotes the
resistance for $\theta=0^{\circ}$. The percentage of AMR, i.e.,
$(R_{\parallel}-R_{\perp})/R_{\perp}$ is found to be 0.19% for PtSe2/NiFe/Pt
and 0.24% for NiFe/Pt. Using a parallel resistor model, we estimate that the
resistance of PtSe2 to be $\approx 2~{}k\Omega$ and the resistivity to be
$\approx 1955~{}\mu\Omega$ cm. Figure 2 (d) shows the STFMR spectra for
PtSe2/NiFe/Pt to gather with the control sample NiFe/Pt measured at 5 GHz with
a magnetic field applied at an angle of $\theta=~{}50^{\circ}$ for various
thickness of PtSe2. The data for other frequencies can be found in
supplementary Sec. S2. The lineshape of STFMR spectra for PtSe2/NiFe/Pt is
found to be more symmetric compared to the control sample. The measured STFMR
spectra can be fitted using the following equation: 4, 11

$V_{\rm{mix}}=V_{\rm S}\frac{\Delta H^{2}}{\Delta
H^{2}+(H-H_{\mathrm{r}})^{2}}+V_{\rm A}\frac{\Delta
H({H-H_{\mathrm{r}}})}{\Delta H^{2}+(H-H_{\mathrm{r}})^{2}}$ (1)

where, $H$ is the applied magnetic field, $\Delta H$ is the linewidth,
$H_{\mathrm{r}}$ is the resonance field, and $V_{\rm S}$ and $V_{\rm A}$ are
the amplitudes of the symmetric and antisymmetric voltage components,
respectively. By fitting the measured $V_{\rm mix}$ with above equation, we
determine ${\Delta H}$, $H_{\mathrm{r}}$, $V_{\rm S}$ and $V_{\rm A}$. First,
we performed angular-dependent STFMR measurements to determine the spin
polarization of the interface-generated spin current. The angular dependence
of $V_{\rm S}$ and $V_{\rm A}$ is depicted in Fig. 2 (e) and (f) for NiFe/Pt
and PtSe2( 10 nm)/NiFe/Pt respectively, which follows the conventional $\sin
2\theta\cos\theta$ dependence (solid lines), showing that the spin-
polarization is along $y-$axis, for a charge current along the $x-$axis, which
is similar to Pt and other heavy metals. 4, 23. Next, we determine the Gilbert
damping constant, $\alpha$ by fitting the ${\Delta H}$ versus frequency data
[Fig. 3 (a)] using:4, 11

$\Delta H=\frac{2\pi\alpha}{\gamma}f+\Delta H_{0}$ (2)

Here, $\gamma$ is the gyromagnetic ratio, and $\Delta H_{0}$ is inhomogeneous
linewidth which depends on magnetic inhomogeneity. The extracted value of
$\alpha$ was plotted with the thickness of PtSe2 ($d_{\mathrm{PtSe_{2}}}$) in
the inset of Fig. 3 (a). The value of $\alpha$ increases and becomes nearly
constant for $d_{\mathrm{PtSe_{2}}}\geq 6.5$ nm. The average value of $\alpha$
for $d_{\mathrm{PtSe_{2}}}\geq 6.5$ nm is (0.045 $\pm$ 0.007), which is 165%
higher than the control sample. From this, we determine spin mixing
conductance to be $\approx 7.6\times 10^{19}\textrm{m}^{-2}$, which is higher
than other TMD/NiFe systems. 17, 16 The inhomogeneous linewidth, $\Delta
H_{0}$ is found to be similar for all the devices $\approx$ (5 $\pm$ 3) Oe,
indicating no significant degradation in the quality of magnetic layer (NiFe)
grown on PtSe2. Furthermore, the linear behavior of linewidth with frequency
indicates the absence of two-magnon scattering. 39 We calculate
$M_{\mathrm{eff}}$ for different stacks by fitting the behavior of the
frequency versus resonance field [Fig. 3 (b)] with the Kittel formula:

$f=\frac{\gamma}{2\pi}\sqrt{(H_{\mathrm{r}}+H_{\mathrm{k}})(H_{\mathrm{r}}+H_{\mathrm{k}}+4\pi
M_{\mathrm{eff}})}$ (3)

Here, $H_{\mathrm{k}}$ and $M_{\mathrm{eff}}$ are the anisotropy field and
effective magnetization of the FM layer, respectively. By fitting the
experimental data with the above equation, we found $4\pi M_{\mathrm{eff}}$
decreases with the thickness of PtSe2 as shown in the inset of Fig. 3(b). The
effective magnetization $4\pi$$M_{\mathrm{eff}}$ is given by $4\pi
M_{\mathrm{eff}}=4\pi M_{s}-2K_{s}/M_{s}t_{\rm{NiFe}}$, where $K_{s}$ is the
surface anisotropy constant, $t_{\mathrm{NiFe}}$ is the thickness of the FM
layer, and $M_{\mathrm{s}}$ is the saturation magnetization. Since
$K_{\mathrm{s}}$ is proportional to interfacial spin-orbit coupling, we
believe the decrease of $M_{\rm{eff}}$ for PtSe2/NiFe/Pt is caused by the
increase in interfacial spin-orbit coupling due to d-d hybridization, similar
to previous reports for other TMD/FM systems. 40, 41

As stated previously, PtSe2 has a resistance greater than $2~{}k\Omega$;
therefore, the current flowing through the PtSe2 layer is only 6% of the total
current. Consequently, we anticipate SOT arising from (i) the interface
between PtSe2 and NiFe and (ii) the spin Hall effect of the Pt capping. Here,
we neglect self-induced torque in NiFe, which is normally one order of
magnitude lower. 42 In order to quantify charge-to-spin conversion due to
PtSe2, we have used line shape analysis. In this method, the SOT efficiency,
$\xi_{\mathrm{SOT}}$ is expressed as: 4

${\xi_{\mathrm{SOT}}=\frac{V_{\mathrm{S}}}{V_{\mathrm{A}}}\frac{e\mu_{0}M_{\mathrm{s}}t_{\mathrm{NiFe}}d}{\hbar}\sqrt{1+\frac{4\pi
M_{\mathrm{eff}}}{H_{\mathrm{r}}}}}$ (4)

Here, $e$ is the electronic charge, and $\hbar$ is the reduced Planck’s
constant. Here, $d$ is the thickness of the non-magnetic layer. The above
expression is valid when the field-like torque is negligible. In our case, we
determined field-like torque from the anti-symmetric component of
$V_{\mathrm{mix}}$ as discussed in the supplementary Sec. S4. We found field-
like torque to be negligible for both NiFe/Pt and PtSe2/NiFe/Pt. However, the
above equation is normally used for the case of FM/NM bilayer samples. For the
trilayer system of PtSe2/NiFe/Pt, the lineshape method represents an effective
spin-orbit torque efficiency, $\xi_{\mathrm{SOT}}^{\mathrm{eff}}$. 43 Since
the conductivity of PtSe2, is much lower than that of Pt, we assume that the
Oersted field is only due to the Pt layer. With these assumptions, we
determine $\xi_{\mathrm{SOT}}^{\mathrm{eff}}$, which includes the contribution
of the top Pt layer and the interfacial contribution of PtSe2.

Figure 3:  (a) The linewidth versus frequency for NiFe/Pt and PtSe2(10
nm)/NiFe/Pt. The inset shows a variation of the Gilbert damping parameter
($\alpha$) with the thickness of PtSe2 ($d_{\mathrm{PtSe_{2}}}$) in the
PtSe2/NiFe/Pt stack. The dashed line in the inset shows the average value of
$\alpha$ for $d_{\mathrm{PtSe_{2}}}\geq 6.5$ nm (b) Resonance field versus
frequency for NiFe/Pt and PtSe2(10 nm)/NiFe/Pt. The inset shows the variation
of effective magnetization (Meff) with $d_{\mathrm{PtSe_{2}}}$. (c) Variation
of effective SOT efficiency with frequency for PtSe2(10)/NiFe/Pt and NiFe/Pt.
The dotted lines represent the average values. (d) Variation of effective SOT
efficiency, $\xi_{\mathrm{SOT}}^{\mathrm{eff}}$ with $d_{\mathrm{PtSe_{2}}}$.
Each data point represents the average of three devices.

For this case, we use the thickness of Pt for $d$ in Eq. 4. 43. In Fig 3 (c),
the value of $\xi_{\mathrm{SOT}}^{\mathrm{eff}}$ has been plotted with
frequency. The average value of $\xi_{\mathrm{SOT}}^{\mathrm{eff}}$ was
further calculated and plotted in Fig. 3 (d) for different thicknesses of
PtSe2. The value of $\xi_{\mathrm{SOT}}^{\mathrm{eff}}$ for
$d_{\mathrm{PtSe_{2}}}$ $\approx$5 nm, was found to be very close to the
control sample, but it increases upto $(50\pm 13)\%$ for higher thickness. The
value of $\xi_{\mathrm{SOT}}^{\mathrm{eff}}$ is constant with
$d_{\mathrm{PtSe_{2}}}$ $>5$ nm. We also performed dc Planar Hall effect
measurements by fabricating Hall bars. These measurements also show a similar
increase of damping-like torque as discussed in supplementary material Sec.
S5. The increase of $\xi_{\mathrm{SOT}}^{\mathrm{eff}}$ due to the presence of
PtSe2 indicates that the sign of spin current due to PtSe2 is opposite to that
of the Pt layer. In order to extract the contribution of PtSe2, we use the
symmetric and asymmetric part of the $V_{\mathrm{mix}}$ of the control sample
(see supplementary Sec. S3), which also eliminates SOT from the Pt cap layer
[mechanisms (ii) mentioned above]. Considering the interfacial effect as the
origin of SOT, we extract the interfacial charge-to-spin conversion
($q_{\mathrm{ICS}}$) following Kondou et al. 44 Here, $q_{\mathrm{ICS}}$ is
defined as 3D spin current ($J_{\mathrm{s}}$) per unit 2D charge current
($j_{\mathrm{c}}$). The maximum interfacial charge-to-spin conversion due to
PtSe2 ($q_{\mathrm{ICS}}^{PtSe_{2}}$) is determined to be $-0.1$ nm-1. For the
control samples, the interfacial charge-to-spin conversion is $0.03$ nm-1.
Thus the magnitude of interfacial charge-to-spin conversion is nearly three
times larger compared to Pt. $q_{\mathrm{ICS}}$ of PtSe2 is also higher
compared to that of PtTe2. 29. In this reference, the authors reported spin
Hall angle/damping-like torque. Since we report an interfacial damping-like
SOT, the efficiency of PtTe2-work needs to be divided by the thickness of
PtTe2 for comparison with our work. Accordingly, the $q_{\mathrm{ICS}}$ of
PtTe2-work is $0.003-0.033$ nm-1, which is lower than our study.
$q_{\mathrm{ICS}}$ value for PtSe2 is also found to be higher compared to W,
($q_{\mathrm{ICS}}=0.06$ nm-1) 45 Bi2Te3,($q_{\mathrm{ICS}}=0.05$ nm-1) 45 and
PtTe2($q_{\mathrm{ICS}}=0.003-0.033$ nm-1) 29 but it is lower than sputtered
BixSe1-x thin films 46 and comparable to Ta ($q_{\mathrm{ICS}}=0.1$ nm-1). 45

The spin degeneracy in bulk PtSe2 band structure is protected due to the
presence of both inversion and time-reversal symmetries. 21 Hence, the Rashba-
Edelstein effect can be ruled out as the cause of SOT. In such cases, the
origin of SOT by the interface is not very clear. Another possibility is that
NiFe at the interface with PtSe2 is playing a crucial role in generating SOT.
In order to understand the mechanism in detail, we have performed a series of
ab-initio calculations using density-functional theory (DFT). The results show
that NiFe introduces three things: (a) Charge transfer from NiFe to PtSe2, (b)
A Rashba SOC due to the surface symmetry breaking, and (c) A proximity
magnetic field that could lead to enhanced SHC in the interface region.

Figure 4: Density functional theory results for the PtSe2/NiFe interface. (a)
Band structure of bulk PtSe2 indicating the electron pocket at K and the hole
pocket at $\Gamma$ at the Fermi energy $E_{F}=0$, and the type-II Dirac cone
at D, along the $\Gamma-A$ line. Inset shows the Brillouin zone, where the
electron (green circle) and hole pockets (red circles and crosses) have been
indicated. (b) Band structure of (PtSe${}_{2})_{6}$/NiFe showing the bulk-like
bands of PtSe2 (red for Pt and green for Se) with electron and hole pockets at
$\Gamma$ and K, interspersed with the NiFe bands (thin lines). The BZ in
PtSe${}_{2}/$NiFe is different from that of PtSe2, but the $\Gamma$ is the
same, and the projection of the K point has been indicated by the square
bracket. (c) Electron charge density difference contours indicating charge
transfer from NiFe to the PtSe2 interface layer, due to the interface
formation. The orange and purple colors indicate, respectively, the charge
accumulation and depletion regions.

Monolayer PtSe2 is semi-conducting, and the gap closes for (PtSe${}_{2})_{n}$,
when the number of monolayers $n\geq 4$, with the band structure tending
towards that of the bulk, with electron and hole pockets as indicated in Fig.
4 (a). In the (PtSe${}_{2})_{6}/$NiFe in Fig. 4 (b), we can clearly identify
the bulk-like PtSe2 bands intermixed with the NiFe bands running around the
gap region. We find a significant electron transfer to the interface PtSe2
layers from NiFe ($\sim 0.15\ |e|$), consistent with the charge density
difference contours shown in Fig. 4 (c), suggesting an enhanced conductivity
as well as spin splitting of the PtSe2 band structure near the interface.

A potential mechanism for spin accumulation is the Rashba-Edelstein effect
(REE) due to the symmetry breaking at the interface. It is difficult to
compute the Rashba SOC parameter $\alpha_{R}$ from the PtSe${}_{2}/$NiFe
calculations due to the intermixing of the NiFe bands. We have instead
estimated it for the simpler case (PtSe${}_{2})_{4}/$Ni, where the four
monolayers are enough to reproduce the bulk band structure, and a single Ni
overlayer, representing NiFe, provides the symmetry breaking. For the top-most
valence band at $\Gamma$, which represents the hole pocket in bulk PtSe2, we
find $\alpha_{R}\sim 0.01\ $eV.Å (see Fig. S6 of supplementary materials),
which is rather small. However, it has been estimated that PtSe2 has a rather
large momentum relaxation time $\tau\approx 80\ $fs 47. This leads to the
Rashba-Edelstein length for the spin-charge conversion efficiency to be
$\lambda_{RE}=j/j_{s}=\tau\alpha_{R}/\hbar\approx 1.2\ $ Å. This relatively
low efficiency would be further reduced due to the proximity magnetic field,
which tends to align the spin moments out of the plane, thereby reducing the
REE. This suggests that the REE might play some role but is not a dominant
mechanism for the spin accumulation at the interface. The type II Dirac cone
in bulk PtSe2 is also not expected to affect spin accumulation since it occurs
well below the Fermi energy.

Due to the NiFe slab, the interface PtSe2 layers will experience a proximity
magnetic field, which could affect spin transport. Even though the PtSe2
layers acquire very little magnetization ($0.03\mu_{B}$ for the first and
$0.01\mu_{B}$ for the second layer PtSe2, compared to $0.59\mu_{B}$ for Ni),
there is a substantial spin-splitting of the PtSe2 band structure due to the
presence of NiFe. We have estimated this value to be $\Delta E\approx
0.10-0.15$ eV for the PtSe2 states near $E_{F}$ (see Fig. S7 of supplementary
materials). This is significant and could lead to a large enhancement of the
spin Hall conductivity (SHC). In fact, for the Pt$/$NiFe interface, earlier
calculations by Kelly and coworkers48 have revealed that the SHC for the Pt
interface layers adjacent to the NiFe is enhanced by a factor of approximately
twenty-five as compared to the Pt bulk layers. This suggests that the
proximity magnetic field in the interfacial PtSe2 plays an important role in
the strong spin-charge conversion observed in the samples.

In conclusion, we demonstrated efficient charge-to-spin conversion in
PtSe2/NiFe/Pt using scalable large-area thin films of PtSe2 . Our findings
indicate that the interface between PtSe2 and NiFe can generate a significant
current-induced damping-like torque. The corresponding interfacial charge-to-
spin conversion efficiency is $-0.1\pm 0.02$ nm-1, which is three times that
of the control sample NiFe/Pt as well as PtTe2 29. Our band structure
calculations suggest that the proximity magnetic field in the interfacial
PtSe2 plays an essential role in the strong charge-to-spin conversion observed
in our samples. Our work demonstrates a novel form of SOT to obtain high
charge-to-spin conversion efficiencies for device applications. Additionally,
our work demonstrates that ”SOT through a proximity magnetic field” needs to
be considered for explaining SOT observed in other TMD-based material systems.

##  1 Methods

Large-area PtSe2 thin films were grown using thermally assisted conversion
process. 34 First, a 3-nm-thick Pt layer was deposited on a Si/SiO2 substrate
using magnetron sputtering. The base pressure of the sputter deposition system
was better than $5\times 10^{-8}$ Torr. The sample was then transferred to a
two-zone furnace for the selenization process. The substrate with the pre-
deposited Pt layer was maintained at 500 ∘C, while the Se precursors were
maintained at 280 ∘C. N2 gas was used as a carrier gas to direct Se species
toward the substrate. By optimizing the substrate temperature, we found that
the thermally assisted conversion of Pt into PtSe2 takes place at a substrate
temperature of 500 ∘C. 34

Structural characterization of PtSe2 was done using cross-sectional HRTEM,
XRD, Raman spectroscopy, XPS and AFM. The HRTEM measurements were performed on
an FEI, TECNAI G2 F30, and ST microscope with an accelerating voltage 300 kV.
XRD of PtSe2 film was measured in $\theta-2\theta$ mode, where X-rays of Cu-Kα
line having a wavelength of $1.54~{}\mathrm{\AA}$ were used. Raman spectra of
PtSe2 were measured with a laser of wavelength 532 nm. XPS was recorded using
AXIS Supra with the monochromatic Al-Kα X-ray source (1486.6 eV). The
thickness of thin films was measured using AFM.

Subsequently, we fabricated microstrip ($100\times 40~{}\mu$m2) devices for
STFMR measurements using a lift-off method in two levels. In the first level,
a 3-nm-thick Pt layer was deposited on the patterned area and was later
selenized following the method discussed above. Using magnetron sputtering, a
NiFe (5 nm)/Pt (3 nm), bilayer was subsequently deposited. In the second
level, co-planar waveguides were fabricated using optical lithography and
lift-off from Au(80 nm)/Cr(10 nm).

## Acknowledgement

The partial support from the Science & Engineering research board (SERB File
no. CRG/2018/001012), the Ministry of Human Resource Development under the
IMPRINT program (Grant no: 7519 and 7058), the Department of Electronics and
Information Technology (DeitY), Joint Advanced Technology Centre at IIT Delhi,
and the Grand Challenge project supported by IIT Delhi are gratefully
acknowledged. Richa gratefully acknowledges the financial support from the
Council of Scientific and Industrial Research (CSIR), Government of India.
Theory work including the DFT calculations is funded by the Department of
Science and Technology, India, through Grant No. CRG/2020/004330. SS thanks
the United States-India Educational Foundation (USIEF) for their support
through a Fulbright-Nehru Fellowship, jointly funded by the Governments of the
United States and India. BRKN acknowledges the support of HPCE, IIT Madras for
providing computational facilities.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### DATA AVAILABILITY

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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