# Factorization of Fact-Checks for Low Resource Indian Languages

Shivangi Singhal, Rajiv Ratn Shah, Ponnurangam Kumaraguru  (shivangis,
rajivratn<EMAIL_ADDRESS>IIIT-Delhi

###### Abstract.

The advancement in technology and accessibility of internet to each individual
is revolutionizing the real time information. The liberty to express your
thoughts without passing through any credibility check is leading to
dissemination of fake content in the ecosystem. It can have disastrous effects
on both individuals and society as a whole. The amplification of fake news is
becoming rampant in India too. Debunked information often gets republished
with a replacement description, claiming it to depict some different
incidence. To curb such fabricated stories, it is necessary to investigate
such deduplicates and false claims made in public. The majority of studies on
automatic fact-checking and fake news detection is restricted to English only.
But for a country like India where only _10%_ of the literate population speak
English, role of regional languages in spreading falsity cannot be undermined.
In this paper, we introduce FactDRIL: the first large scale multilingual Fact-
checking Dataset for Regional Indian Languages. We collect an exhaustive
dataset across _7_ months covering _11_ low-resource languages. Our propose
dataset consists of _9,058_ samples belonging to English, _5,155_ samples to
Hindi and remaining _8,222_ samples are distributed across various regional
languages, _i.e._ Bangla, Marathi, Malayalam, Telugu, Tamil, Oriya, Assamese,
Punjabi, Urdu, Sinhala and Burmese. We also present the detailed
characterization of three M’s (multi-lingual, multi-media, multi-domain) in
the FactDRIL accompanied with the complete list of other varied attributes
making it a unique dataset to study. Lastly, we present some potential use
cases of the dataset. We expect this dataset will be a valuable resource and
serve as a starting point to fight proliferation of fake news in low resource
languages.

Fake News Dataset, Low-Resource languages, Indian Fact-checking, Multilingual,
Multi-Domain, Multimedia, Multimodal

††ccs: Information systems Multimedia and multimodal retrieval††ccs:
Information systems Multilingual and cross-lingual retrieval Figure 1. An
excerpt from our proposed FactDRIL and LIAR (Wang, 2017) is shown. The pink
highlighted text shows the investigation steps adopted by fact-checkers.
Though the justification (veracity_reasoning) in both the dataset is present
but the _investigation_reasoning_ in FactDRIL gives minute details of the
fact-checking process. This attribute is exclusive of FactDRIL and is not
present in any of the existing fact-checking datasets.

##  1\. Introduction

Fake news is spreading like wildfire. All the major happenings around the
globe like 2016 U.S. elections (Bovet and Makse, 2019), global pandemic
(COVID-19) (Apuke and Omar, 2020; Akbar et al., 2020) and 2019 Indian General
elections (Reis et al., 2020) have been heavily affected by the proliferation
of infodemic on social and mainstream media. To limit the escalation of fake
news, fact-checkers are constantly making an effort to find out the
authenticity behind the unverified claims. Fact-checking is generally defined
as a process to find out the veracity behind such viral claims. The conclusion
drawn is always backed up by evidence and logical reasonings (Vlachos and
Riedel, 2014). Fake news is a global concern but majority of the automatic
fact-checking (Vlachos and Riedel, 2014; Ferreira and Vlachos, 2016; Wang,
2017; Alhindi et al., 2018; Tchechmedjiev et al., 2019; Augenstein et al.,
2019) and fake news detection (Shu et al., 2018; Wang et al., 2018; Khattar et
al., 2019; Zhou et al., 2020; Singhal et al., 2019, 2020) solutions have been
designed for English, a language predominantly used in web-based social
networking. Though that is good on a global scale, but when it comes to India,
it fails due to following reasons, _(i)_ people speak diversified range of
languages, _(ii)_ due to housing a number of languages, the communication in
English is bit problematic because out of the 74% literates in the country,
only 10% can read
English111https://en.wikipedia.org/wiki/2011_Census_of_India. Recently, Rasmus
Kleis Nielsen, director at Reuters Institute for the Study of Journalism, also
addresses this issue in his
interview222https://www.thequint.com/news/india/media-coverage-disinformation-
in-india-interview-rasmus-nielsen stating that, the problems of disinformation
in a society like India might be more sophisticated and tougher than they are
within the West. We wish to understand the menace of misinformation in Indian
territory where false information, manipulative photos and deduplicate news
reappear on the online ecosystem time and again. To the best of our knowledge,
there is no existing fact-checking data for Indian languages. This has caused
hindrance in devising solutions for automatic fact-checking, which can
negatively affect the large group of population.

In this paper, we aim to bridge the gap by proposing FactDRIL: the first large
scale multilingual Fact-checking Dataset for Regional Indian Languages. Our
contribution can be summarized as follows:

  * •

We curated _22,435_ samples from the eleven Indian fact-checking website
certified with IFCN ratings. The samples are in the various low-resource
languages: Bangla, Marathi, Malayalam, Telugu, Tamil, Oriya, Assamese,
Punjabi, Urdu, Sinhala and, Burmese. We release the dataset that can act as a
prime resource for building automatic fact-checking solutions for Indian
ecosystem.333https://bit.ly/3btmcgN

  * •

We introduced an attribute in the feature list termed as
_investigation_reasoning_. This attribute provides an explanation of the
intermediate steps performed by fact-checkers to conclude the veracity of the
unverified claim. This is important to study because it will help us to dig
into the fact-checking mechanism and propose solutions to automate the
process. We discuss in detail the use-case of this curated feature and the
methodology designed to excavate it from the crawled unstructured data dump.

##  2\. Related Work

There have been several datasets released in past that focused on fact-
checking. An overview of the core fact-checking datasets is given in Table 1.

The very first effort towards this direction was made by (Vlachos and Riedel,
2014) in 2014. The paper released a publicly available dataset that consist of
sentences fact-checked by journalist available online. The statements were
picked from the fact-checking blog of Channel 4 and the Truth-O-Meter from
PolitiFact. The statements mainly captured issues prevalent in U.S. and U.K.
public life. Apart from statements, the meta-data features like, _(i)_ publish
date, _(ii)_ speaker, _(iii)_ fine-grained label associated with the verdict
and, _(iv)_ URL were also collected.

Another study was done in 2016 by (Ferreira and Vlachos, 2016). In this paper,
the data was collected from numerous sources including rumor sites and Twitter
handles. The news pertaining to the world, U.S. national and technology were
captured. For each claim, journalist would search for the articles that are
either in _support_ , _against_ or _observing_ towards the claim. The final
dataset consist of claims with corresponding summarized headings by the
journalist and associated veracity label with the final verdict on the claimed
statement.

Both the previously mentioned datasets were quite small in numbers. To
overcome this drawback, the LIAR dataset was introduced by (Wang, 2017) in
2017. It consists of around 12.8K short statements curated from Politifact
website. It mainly contain samples collected from a variety of sources
including, TV interviews, speeches, tweets and debates. The samples cover wide
range of issues ranging from the economy, health care, taxes to elections. The
samples were annotated for truthfulness, subject, context, speaker, state,
party, and prior history. For truthfulness, the dataset was equally
distributed into six labels: pants-fire, false, mostly false, half-true,
mostly-true, and true. In 2018, Alhindi _et al._ (Alhindi et al., 2018)
proposed LIAR-PLUS, an extended version of the LIAR dataset. For each sample,
human justification for the claim was automatically extracted from the fact-
checking article. It was believed that justification combined with extracted
features and meta-data would boost the performance of classification models.
Another dataset that came into existence in 2018 was FEVER (Thorne et al.,
2018). It consists of 185,445 claims that were not naturally occurring but
were generated by altering sentences extracted from Wikipedia.

Later in 2019, two new functionalities _i.e._ evidence pages and knowledge
graph triples were introduced to fact-checking data that resulted in overall
improvement of the accuracy. Augenstein _et al._ (Augenstein et al., 2019)
presented the largest dataset on fact-checking that had _34,918_ claims
collected from _26_ fact-checking websites in English listed by Duke Reporters
Lab and on fact-checking Wikipedia page. The prime benefit introduced was the
_10_ relevant evidence pages per claim. Other features included claim, label,
URL, reason for label, categories, speaker, fact-checker, tags, article title,
publication, date, claim date, and the full text associated with claim.
Authors in (Tchechmedjiev et al., 2019) argue the need of labelled ground
truth and other features to perform supervised machine learning methods. and
emphasis on the requirement of a huge storage space. To solve the problem,
they proposed ClaimsKG, a knowledge graph of fact-checked claims. It enables
structured queries for features associate with the claim. It is a semi-
automated method that gather data from fact-checking websites and annotate
claims and their corresponding entities from DBpedia.

Next, we discuss how our proposed dataset- _FactDRIL_ is different from the
existing fact-checking datasets.

Table 1. Comaprison of dfferent fact-checking dataset. The table clearly shows that the proposed dataset is rich in terms of linguistic diversity and features. It also captures the information in the form of multiple modalities and from differnent domains. Values in ( ) denote the number of meta-features extracted in the each dataset. _‘NA’_ means that the information is not explicitly mentioned. | Region |  | Moda-
---
lity
Domain |  | Multi-
---
Ling-
ual
| Investi-
---
gation
steps
# Claims |  | Claim
---
Sources
ACL 2014 (Vlachos and Riedel, 2014) |  | U.S.A,
---
U.K.
text | public life | No | No | 106 (4) |  | Politifact,
---
Channel
4 News
Emergent (Ferreira and Vlachos, 2016) | U.S.A | text |  | world,
---
U.S.-
national,
technology
No | No | 300 (4) |  | snopes.com,
---
Twitter
handle:
@Hoaxalizer
LIAR (Wang, 2017) | U.S.A | text |  | economy,
---
health care,
taxes,
elections
No | No | 12800 (5) |  | Politifact,
---
Channel
4 News
LIAR-plus (Alhindi et al., 2018) | U.S.A | text |  | economy,
---
health care,
taxes,
elections
No | No | 12836 (5) |  | Politifact,
---
Channel
4 News
Multi-FC (Augenstein et al., 2019) | NA | text | NA | No | No | 36534 (12) |  | Duke
---
Reporters
Lab,
Fact
Checking
Wikipedia
page
ClaimsKG (Tchechmedjiev et al., 2019) | NA | text | NA | No | No | 28383 (9) |  | AfricaCheck
---
FactScan,
PoilitiFact,
Snopes,
Check your
fact,
Truth or
fiction
| FactDRIL
---
(Proposed
Dataset)
India |  | text,
---
image,
video,
social
media
post
| health,
---
society,
religion,
politics,
world,
elections
Yes | Yes | 22435 (22) |  | All IFCN
---
rated Indian
fact-checking
websites

##  3\. What is new in the proposed dataset?

The dataset presented in the paper is unique due to following reasons:

  * •

Misinformation in India: Till date, various datasets proposed in the fake news
research, consist of news samples pertaining to USA and its neighbouring
countries (Pathak and Srihari, 2019; Golbeck et al., 2018; Torabi Asr and
Taboada, 2018; Shu et al., 2018; Wang et al., 2018; Khattar et al., 2019; Zhou
et al., 2020; Singhal et al., 2019, 2020). We believe that studying
disinformation in India will be more challenging than West due to, _(i)_ low
literacy rates that not only make it hard to induce decision-making ability in
an individual, but add to an explosion of fake news and divisive propaganda,
_(ii)_ Most Indians tend to trust messages from family and
friends444https://qz.com/india/1459818/bbc-study-shows-how-indians-spread-
fake-news-on-whatsapp/. This means that content gets forwarded without any
checks, further driving misinformation in the social sphere, _(iii)_ majority
of population access news primarily through
WhatsApp555https://www.latimes.com/world/la-fg-india-whatsapp-2019-story.html
where information rarely gets checked for validity and authenticity.

  * •

Multilingual information: The 2011 Census of
India666https://en.wikipedia.org/wiki/Multilingualism_in_India shows that the
languages by highest number of speakers (in the decreasing order) are as
follows: Hindi, Bengali, Marathi, Telugu, Tamil, Gujarati, Urdu, Odia,
Malayalam and Punjabi. Whereas, only 10.67% of the total population of India
converse in English. Though current datasets are in English but the above
statistics explicitly indicates a need to shift the study of fake news from
English to other languages too.

  * •

Investigation reasoning: With this dataset, we present a detailed explanation
of how the investigation was carried out by manual labourers in concluding the
truthfulness of the viral news. The proposed attribute is totally different
from the _veracity reasoning_ label present in the fact-checking datasets
(Wang, 2017; Alhindi et al., 2018). The primary difference is that the former
attribute explains the intermediate steps performed during manual intervention
whereas the latter attribute concludes the veracity of unverified claim with a
reasoning without emphasising on how they searched for that reasoning. Figure
1 explains the difference between the two. We believe such an information will
be helpful in preparing solutions to automate the manual fact-checking
efforts.

  * •

Multimedia and multi-platform information: Fake news can be published in any
form and on any social and mainstream platform. The curated dataset
incorporates the information about media (images, text, video, audio or social
media post) used in fake news generation and the medium (Twitter, Facebook,
WhatsApp and Youtube) used to populate it in the surroundings.

  * •

Multi-domain information: Previous fact-checking dataset as shown in Table 1
covers information in certain domain only. For example, Emergent (Ferreira and
Vlachos, 2016) only captures the national, technological and world related
happening in U.S.A whereas (Wang, 2017; Alhindi et al., 2018) includes health,
economy and election related issues. This is due to the fact that different
fact-checking websites focuses on capturing news of specific genre. Since in
our proposed dataset, we crawled information from all the fact-checking
websites that exist in the country. This gives us a leverage to encapsulate
all the happenings around the territory making it a rich dataset to study.

To sum up, in our perception, this is the first dataset introduced in the fake
news domain that collects information from Indian territory. The detailed
characterization of three M’s (multi-lingual, multi-media, multi-domain) in
the dataset accompanied with veracity reasoning and other varied attributes
makes it a unique dataset to study.

##  4\. Data Collection

In our opinion, we have curated, the first large scale multilingual Indian
fact-checking data. Figure 2 shows the complete data curation process. In this
section, we focus on the first step of the curation process _i.e._ the data
collection.

Though fact-checking services play a pivotal role in combating misinformation,
little is known about whether users can rely on them or not. To corroborate
trust among audience, fact-checking services should endeavour transparency in
their processes, as well as in their organizations, and funding sources. With
an objective to look out for trusted Indian fact-checking websites, we came
across International Fact Checking Network (IFCN). Next we discuss in detail
about IFCN, its measuring criteria and sources chosen for preparing the final
dataset.

Figure 2. Our proposed dataset curation pipeline. _Step 1_ describes the data
collection process followed by _Step 2_ describing the Data Extraction and
_Step 3_ of Data Annotations.

###  4.1. International Fact-Checking Network

The International Fact-Checking Network is owned by Poynter Institute of
Medical Studies located in St. Petersburg, Florida. It was set in motion on
September 2015. The prime objective to establish IFCN was to bring together
the fact-checkers present across the globe, under one roof. It also intent to
provide a set of guidelines through the fact-checkers code of principles that
are mandatory for the fact-checking organizations to follow. The code of
principles is designed for agencies that actively work towards broadcasting
the the correct investigation against the false claim made either on
mainstream or social media platforms.

The organizations that are legally registered with an objective to routinely
scrutinize the statements made by public figures and prominent institutions
are generally granted the IFCN signatory. The statements can be in the form of
text, visual, audio and other formats particularly related to public interest
issues. On the other hand, organizations whose opinion look influenced by the
state or any other influential identity or a party are generally not admitted
the grant.

To be eligible to get an IFCN signatory, the organization is critiqued by
independent assessors on _31_ criteria. The assessment is then finally
reviewed by the IFCN advisory board to ensure fairness and consistency across
the network. There are about _82_ Verified signatories of the IFCN code of
principles among which _11_ are based on India. To ensure the authenticity and
verifiability of the curated data, we have considered those Indian fact-
checking sources that are IFCN rated verified.

Next, we discuss the _11_ Indian fact-checking websites considered for our
data collection process.

###  4.2. Indian Verified Fact-Checking Websites

The prime benefit of gathering data from fact-checking websites is that we can
read the reasoning behind the veracity of a news sample. The detailed
description of the investigation gives an useful insight to the reader about
how and why the viral claim was false. With this objective in mind, we decided
to collect data from the _11_ fact-checking websites that are on a mission to
debunk fake information from the Indian ecosystem. An overview of the fact-
checking websites considered for data curation is provided in Table 2. The
table highlights the key features of a particular website in the form of,
_(i)_ who formed the website, _(ii)_ organization establishment year, _(iii)_
languages debunked by the website and, _(iv)_ domain covered.

Table 2. An overview of fact-checking sources considered during the data collection. _‘NA’_ means that the information is not available. Website | Formed by |  | Establish
---
year
| Languages
---
supported
Domain
Alt News | Pratik Sinha | Feb 2017 | English, Hindi |  | Politics,
---
Science,
Religion,
Society
Boom Live |  | Part of Outcue Media
---
Pvt Ltd
Nov 2016 |  | English, Hindi,
---
Bangla, Burmese
General
DigitEye India |  | Part of SoftmediaHub
---
LLP
Nov 2018 | English | General
FactChecker |  | Initiative of The
---
Spending
Policy Research
Foundation
Feb 2014 | English |  | General,
---
Modi-Fied
Fact Crescendo |  | Part of Crescendo
---
Transcription
Private Limited (CTPL)
July 2018 |  | English, Hindi,
---
Tamil, Telugu,
Kannada,
Malayalam,
Oriya, Assamese,
Punjabi, Bengali,
Marathi, Gujarati,
Urdu
| General,
---
Coronavirus
Factly | Rakesh Dubbudu | Dec 2014 | English, Telugu |  | General,
---
Coronavirus
India Today |  | Part of TV Today
---
Network Limited
| English | General
News Mobile |  | Part of World Mobile
---
NewsNetwork Pvt Ltd
2014 | English | General
NewsChecker |  | Initiative of NC Media
---
Networks Pvt Ltd
|  | English, Hindi,
---
Marathi, Punjabi,
Gujrati, Tamil,
Urdu, Bengal
General
Vishvas News |  |  |  | English, Hindi,
---
Punjabi, Odia,
Assamese,
Gujrati, Urdu,
Tamil, Telugu,
Malayalam,
Marathi
| Coronavirus,
---
Politics,
Society,
World,
Viral,
Health
The Quint-Webqoof |  | Owened by Gaurav
---
Mercantiles Limited
| English, Hindi |  | General,
---
Health

##  5\. Data Extraction

In this section, we discuss the schema of our proposed dataset. This is the
second step of the data curation pipeline as shown in Figure 2.

Data Collection We list down all the authentic fact-checking sources that
unfolds claims written not only in multilingual languages but lingua franca
too. We set-up a data extraction system that make use of a Python library,
Beautiful Soup777https://pypi.org/project/beautifulsoup4/ to extract data from
web pages. Our system checks the sources for new data once in _24_ hours.

In this paper, we present a study on samples curated from a time period of
_Decemner 2019_ \- _June 2020_. By the end of the data curation process, we
had _22,435_ news samples from _11_ fact-checking websites. Among them,
_9,058_ samples belong to English, _5,155_ samples to Hindi and remaining
_8,222_ samples were distributed in various regional languages _i.e._ Bangla,
Marathi, Malayalam, Telugu,Tamil, Oriya, Assamese, Punjabi, Urdu, Sinhala and
Burmese.

###  5.1. Dataset Attributes

We curated numerous features from the unstructured data. We have then
categorized the extracted feature set into various classes like meta features,
textual features, author features, media features, social features and event
features. A sample showcasing all the attributes is present in Figure 3.

Meta Features We consider those attributes as meta_features that tells us
about the sample, like _website_ name, article_link, unique_id, publish_date_.

  * •

_website_name_ : Denotes the name of the source from where the following
sample is collected. It also gives an additional information about the
language in which the fact-checked article is originally written.

  * •

_article_link_ : The attribute gives you the original link of the curated
sample.

  * •

_unique_id_ : This attribute acts as the primary key for data storage.

  * •

_publish_date_ : The attribute signifies the date on which the article was
published by the fact-checking websites.

Textual Features A fact-checked article is generally segregated into three
divisions, _title of the article_ , _claim_ and _investigation_. All these
together form the textual features in our proposed dataset. The crawled data
from the website is highly unstructured. The information in the form of claim
and investigation is generally present in the content part of the data. This
information is extracted from the _content_ attribute using human
intervention. This is discussed in detail in Section 6.2.

  * •

_title_ : The title of the article.

  * •

_content_ : This attribute act as the body of the article that consist of
information in the form of claim and investigation.

  * •

_faaltu_content_ : Many a times, the crawled information from the website also
contains the text present in the social media post (say, text present in the
tweets or Facebook posts) attached as a reference within the article. Though,
such text pieces will be a hindrance while reading the content but they might
give useful information if the corresponding social media post is deleted from
web. To take into account all such possibilities, we coined an attribute,
_faaltu_content_ 888The word ‘faaltu’ is a Hindi word that means ‘useless’ in
English. in our proposed _FactDRIL_ that takes into account the text parts of
the social media post attached with the article. The example of the same is
shown in Figure 3.

  * •

_claim_ : This attribute gives reader a background information about _what was
said in the corresponding post_.

  * •

_investigation_ : This attribute help readers in understanding _why the fact-
checkers concluded a particular post to be fake_. The whole inspection process
is discussed in detail with tools and technology used for its exploration.

  * •

Other features like _claim_title, investigation_title, post_summary_ are
present in some samples. These attributes give one line summary of the _claim,
investigation and complete article_. Such attributes are useful when the
reader intends to take a quick look at the article to find out questions like,
_What was claimed, who was claimant and how it was investigated to be false_.

Author Information This set of attributes showcase information about the
people who are involved in fact-checking.

  * •

_author_name_ : The person who wrote the fact-checking article.

  * •

_author_website_ : This attribute is a link to the fact-checker’s profile on
the corresponding news website. The website generally list down articles fact-
checked by that individual.

  * •

_author_twitter_handle_ : The Twitter username of the fact-checker is
mentioned in this attribute.

  * •

_author_desc or author_info_ : This attribute gives you a description about
the fact-checker.

Media Features The claim viral on any social media platform or mainstream
media have many modality. Similarly, the investigation carried out to conclude
the status of any viral news is also backed by a numerous number of supporting
claims that can again be in any multimedia form. The set of attributes that
are categorized into multimodal features are as follows:

  * •

_top_image_ : The first image that is present at the very beginning of the
fact-checking article. It generally show the picture present in the viral
claim.

  * •

_image_links_ : The links of all other images that will either belong to the
original claimed images group or are presented in support to the viral claim
are put under this feature as a list object.

  * •

_video_links_ : For those samples where prime media used for fabrication is
video, the link to the original video is provided by fact-checkers to backed
their investigation. This attribute stores all such links.

  * •

_audio_links_ : All the supporting audio links related to the viral claim are
presented in this attribute.

  * •

_links_in_text_ : To provide complete justification to what was said in the
investigation section of the report, authors provide different media links in
support of their investigation. All such links are piled in this attribute.
But to identify, where a specific link is mentioned in the fact-checked
article, an attribute named as, _bold_text_ is used for easy identification
and matching of the corresponding text from the article.

Social Features The attribute stores the tweet ids present in the sample. The
tweet ids can be the post that, _(i)_ needs to be investigated or, _(ii)_ is
present in the support of the fake claim. With this attribute, we can extract
the complete information from the tweet thread.

Event Features The set of features in this group gives information about the
event to which a news sample belong to. These include _domain_ and _tags_
attributes. _For example_ , the Boom article titled: ‘False: Chinese
Intelligence Officer Reveals Coronavirus Is A Bioweapon’ had the following
tags (_Coronavirus China, COVID-19, Coronavirus outbreak, Bioweapon,
Biological warfare, China, Intelligence Officer_) associated with it. This
kind of information is helpful in identifying the genre of the article.

Figure 3. A excerpt from the dataset displaying different attributes present
in the proposed dataset. The feature list is paced under four headers namely,
_meta features_ , _text features_ , _social features_ , _media features_ ,
_author information_ and _event information_. These attributes are discussed
in detail in Section 5.1.

##  6\. Data Annotation

In this section, we address the three key questions that facilitated the data
annotation process.

###  6.1. Need to perform Annotation

The need to do annotations were two fold. First, we want to highlight the key
pieces of extracted text to underline its usability. Since the extracted text
neither showed a particular pattern for automatic extraction nor had any
distinction between the different textual features discussed in Section 5.1,
we performed manual annotations to excavate the key pieces from the data dump.
Second, there was a need to scrutinize each sample to make sure that the
proposed dataset do not contain samples, _(i)_ that were investigated to be
true, _(ii)_ articles containing general fact information that news websites
usually publish999https://www.boomlive.in/technologies-will-tackle-irrigation-
inefficiencies-agricultures-drier-future/ and, _(iii)_ weekly-wrap up articles
that increase the chance of deduplication in the dataset.

###  6.2. Annotation Process

We chose against crowd-sourcing the annotation process due to non-trivial
nature of the sub-tasks. We hired individuals who were well versed with the
any of the low-resource languages mentioned earlier. They were in the age
group of _19-45_. Due to unavailability of language professionals, we
performed the annotation process for regional languages with a single entity,
whereas two professionals were hired each for lingua franca (_i.e._ Hindi and
English). The annotators were first provided with the annotation guidelines
which included instructions about each sub-task, definition of the attributes
that need to derived from the text and few examples. They studied this
document and worked on a few examples to familiarize themselves with the task.
They were given feedback on the sample annotations, which helped them to
refine their performance on the remaining subset. The annotation process was
broken down into two sub-tasks. In the first sub-task, annotators have to
segregate the text into two attributes namely, _claim_ and _investigation_. In
the second sub-task, annotators have to make sure to chose samples that were
sentenced to be false by fact-checkers.

Table 3. Inter-annotator agreement for the two sub-tasks. The values in bold indicates that Gwet‘s AC(1) and AC(2) scores were calculated for the samples.  Website | Language | Inter Annotator Agreement Score | # Samples
---|---|---|---
|  |  | Sub Task 1
---
(Percent Agreement)
| Sub Task 2
---
(Cohen‘s Kappa /Gwet‘s
AC(1) AC(2)
Alt News | English | 0.78 | 0.48 | 2058
| Hindi | 0.76 | 0.53 | 1758
Boom | English | 0.42 | 0.66 | 909
| Hindi | 0.90 | 0.53 | 880
DigitEye | English | 0.86 | 0.56 | 147
FactChecker | English | 0.31 | 0.15 | 156
Fact Crescendo | English | 1.00 | 1.00 | 256
| Hindi | 0.99 | 1.00 | 264
Factly | English | 0.92 | 0.76 | 971
India Today | English | 0.95 | 0.44 | 788
News Mobile | English | 0.71 | 0.29 | 1543
Vishvas News | English | 0.94 | 0.91 | 254
| Hindi | 0.98 | 0.90 | 1369
Webqoof | English | 0.86 | 0.47 | 1771
| Hindi | 0.95 | 0.97 | 328

###  6.3. Annotation Evaluation Metric

There were two sub-task given to the annotators. To evaluate the performance
on the first task, a customized metric was prepared. For second task, inter-
annotator agreement score using Cohen’s Kappa and Gwet’s AC(1) and AC(2)
statistic (Gwet, 2008) was considered. Next, we will discuss in detail these
evaluation metric.

For the first sub-task, annotators were required to do a close reading of the
text to extract meaningful information and place it under correct header
(_i.e._ claim or investigation). To evaluate the performance, we checked for
matched ordinal positions in each annotated piece. A counter value is kept to
calculate the number of mismatches. Having tested multiple possible values, we
chose a threshold value, d=6 and if d goes beyond the chosen value, then that
sample is sent in the conflict resolution bin. The final inter agreement score
is computed using the percent agreement for two raters (Topf, 1986). It is
calculated by dividing total count of matched sample with the total number of
samples in the data.

For the second sub-task, we evaluated inter-annotator agreements using Cohen’s
Kappa (McHugh, 2012). We observe a mix of moderate and substantial agreement
for most of the task. Table 3 summarizes the Cohen’s kappa measures for the
sub-task. Though Cohen’s Kappa performs exceptionally well when dichotomous
decision is involved and takes care of chance agreement too but it fails badly
when annotators show near to 100% agreement. This phenomenon is termed as ‘the
paradoxes of Kappa’. During our evaluation, we observe high agreement between
annotators for _1000_ samples. To solve the ‘the paradoxes of Kappa’ issue, we
used Gwet’s AC(1) and AC(2) statistic (Gwet, 2008). It overcomes the paradox
of high agreement and low reliability coefficients. Table 3 summarizes the
Gwet’s score for these samples.

Conflict Resolution We chose a straightforward approach for adjudication in
case of disagreements in all the sub-tasks. If the two annotators present a
contradictory views for a sample, the annotations for all the disagreed tasks
are then adjudicated by verbal discussions among them.

##  7\. Basic Dataset Characterization

We begin by providing a statistical overview of our proposed dataset.

###  7.1. Summary Statistics

Figure 4 _(a)_ shows the distribution of samples across languages in our
proposed _FactDRIL_. Surprisingly, _Regional_ languages surpasses _Hindi_ by
_37%_. The diffusion of samples in the regional interface is majorly dominant
by _Bangla_ , _Malayalam_ , _Urdu_ and _Marathi_ langauge. Figure 4 _(b)_
represents the number of samples belonging to the _eleven_ fact-checking
websites. Among them _Fact Crescendo_ website rules in debunking fake news
dissemination in different languages.

Figure 4. _(a)_ shows the distribution of different languages in our proposed
dataset, _(b)_ shows the spread of data across different websites. It also
depicts the languages supported by each website.

###  7.2. Popular Fake Events in India

We analyze the topic distribution of fact-checking articles in different
languages, _i.e._ English, Hindi and Regional languages. From Figure 5 (a),
(b), (c), we can conclude that political activity is an important ground for
fake news creation. With the onset of _2020_ , the world has witnessed a
global pandemic _i.e._ Coronavirus. This has not only affected lives of people
but has also given rise to infodemic of misinformation. To no surprise, the
second popular domain for fake news creation in India was Coronavirus followed
by health and religion.

Figure 5. Topic Distribution in English, Hindi and Regional languages (left to
right). All the figures clearly shows that the majority of the fake news
dissemination across the country is centered towards political domain.

###  7.3. Circulation of Fake News in India

Figure 6 _(a)_ shows that the fact-checking trend came to India in 2012,
majorly debunking news in English Language. As and when fake news
dissemination in English got little popular _i.e._ 2017, we saw it intruding
in the other languages too. This steady shift to other languages was observed
quite lately _i.e._ in 2017 and 2018. We observe sharp peaks and drops in the
graph that will be an interseting study to do in future. Figure 6 _(b)_ shows
the year-wise distribution of samples in the dataset. The graph shows a steady
increase in fake news creation over the years with a major peak observed in
2019. For both these observations, the data considered for the year _2020_ is
till June.

Figure 6. Circulation of fake news over the years in India. For the year
_2020_ , the data is collected till _June 2020_.

##  8\. Use Cases

There are varied threads of misinformation research that can be initiated with
the help of FactDRIL. We would like to formally propose some ideas for the
same.

  * •

Improve Misinformation Detection System: Till date, various efforts have been
made to eliminate misinformation from the ecosystem. The major drawback
observed in such methods is two fold. First, the system performs well on
trained samples and fails drastically for the real-world data. Secondly, the
performance of classifiers varies considerably based on the evaluation
archetype and performance metric (Bozarth and Budak, 2020). We present a
dataset that provides a detailed investigation of the fake sample that
includes, _(i)_ the modality faked in the news, _(ii)_ ‘how’ the sample was
concluded to be false and, _(iii)_ tools used to draw that conclusion. We
believe that a detailed study in understanding the formation of fake news
pattern can improve the performance of classifiers to tackle misinformation in
the real world.

  * •

Suppressing Fake News Dissemination at an Early Stage: We all know that fake
news is not new, probably it is as old as humanity. Despite constant efforts
made to eliminate it from the ecosystem, it finds a way to dissolve in our
lives. The impact of fake information is devastating. We believe eradicating
fake news is bit challenging but creating systems that can suppress its effect
is a feasible task. With _FactDRIL_ , we can develop technologies that can be
stationed at different social media platforms. Such system can use information
from the debunked pieces and stop proliferation of its variants on the
platform.

  * •

Bias among fact-checkers: Fact-checking is tedious. Different websites aim to
debunk news of different genre. There can be websites that aims at exposing a
particular kind of information. It will be interesting to look out for biases
in the fact-checking pattern and its related effects.

##  9\. Conclusion

In this paper, we presented FactDRIL: a Fact-checking Dataset for Regional
Indian Languages. To our knowledge, this is first large scale multi-lingual
Indian fact-checking data that provide fact-checked claims for low resource
languages. The dataset can be accessed on the request via
link.101010https://bit.ly/3btmcgN We believe such datasets will allow
researchers to explore the fake news spread in regional languages.
Additionally, researchers could also look out for dissemination of fake
content across the different language silos. The dataset comprises of _22,435_
samples crawled from the _11_ Indian fact-checking websites with IFCN
certification. A vast range of low-resource languages has been covered
including, Bangla, Marathi, Malayalam, Telugu, Tamil, Oriya, Assamese,
Punjabi, Urdu, Sinhala and Burmese. The features curated from the data dump is
further grouped under _meta_ , _textual_ , _media_ , _social_ , _event_ and
_author_ features. We also present a new attribute to the feature list _i.e.
investigation reasoning_ and explain its relevance and need in the current
fact-checking mechanism. Currently, this feature is extracted via manual
intervention. In future, we plan to automate the attribute extraction from the
text. We would also like to organize challenges around this data to instigate
researchers in asking interesting questions, find limitations and propose any
improvements or novel computational techniques in detecting fake news in low-
resource languages.

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# Colossal Band Renormalization and Stoner Ferromagnetism induced by Electron-
Antiferromagnetic-Magnon Coupling

T. L. Yu  Laboratory of Advanced Materials, State Key Laboratory of Surface
Physics and Department of Physics, Fudan University, Shanghai 200438, People’s
Republic of China  R. Peng  Laboratory of Advanced Materials, State Key
Laboratory of Surface Physics and Department of Physics, Fudan University,
Shanghai 200438, People’s Republic of China  Shanghai Research Center for
Quantum Sciences, Shanghai 201315, People’s Republic of China  M. Xu  W. T.
Yang Y. H. Song C. H. P. Wen  Q. Yao  X. Lou  T. Zhang  W. Li  X. Y. Wei
Laboratory of Advanced Materials, State Key Laboratory of Surface Physics and
Department of Physics, Fudan University, Shanghai 200438, People’s Republic of
China  J. K. Bao  G. H. Cao  Department of Physics, Zhejiang University,
Hangzhou 310027, People’s Republic of China  P. Dudin  Diamond Light Source,
Harwell Science and Innovation Campus, Didcot OX11 0DE, United Kingdom  J. D.
Denlinger  Advanced Light Source, 1 Cyclotron Road Lawrence Berkeley National
Laboratory Berkeley, CA 94720-8229, USA  V. N. Strocov  Swiss Light Source,
Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland  H. C. Xu
<EMAIL_ADDRESS>Laboratory of Advanced Materials, State Key Laboratory
of Surface Physics and Department of Physics, Fudan University, Shanghai
200438, People’s Republic of China  D. L. Feng<EMAIL_ADDRESS>Laboratory
of Advanced Materials, State Key Laboratory of Surface Physics and Department
of Physics, Fudan University, Shanghai 200438, People’s Republic of China
Shanghai Research Center for Quantum Sciences, Shanghai 201315, People’s
Republic of China  Collaborative Innovation Center of Advanced
Microstructures, Nanjing 210093, China  Hefei National Laboratory for Physical
Science at Microscale, CAS Center for Excellence in Quantum Information and
Quantum Physics, and Department of Physics, University of Science and
Technology of China, Hefei 230026

###### Abstract

The interactions between electrons and antiferromagnetic magnons (AFMMs) are
important for a large class of correlated materials. For example, they are the
most plausible pairing glues in high-temperature superconductors, such as
cuprates and iron pnictides. However, unlike electron-phonon interactions
(EPIs), clear-cut observations regarding how electron-AFMM interactions (EAIs)
affect the band structure are still lacking. Consequently, critical
information on the EAIs, such as its strength and doping dependence, remains
elusive. Here we directly observe that EAIs induces a kink structure in the
band dispersion in Ba1-xKxMn2As2, and subsequently unveil several key
characteristics of EAIs. We found that  the coupling constant of EAIs can be
as large as 6, and it shows huge doping dependence and temperature dependence,
all in stark contrast to the behaviors of EPI and beyond our current
understanding of EAIs. Such a colossal renormalization of electronic bands by
EAIs drives the system to the Stoner criteria, giving the intriguing
ferromagnetic state in Ba1-xKxMn2As2. Our results expand the current knowledge
of EAIs, which may facilitate the further understanding of many correlated
materials where EAIs play a critical role, such as high-temperature
superconductors.

Electron-boson interactions belong to the most fundamental microscopic
processes in solids, which are responsible for various facinating properties.
For example, electron-phonon interactions (EPIs) could result in conventional
superconductivity or charge density waves PhysRev.108.1175 ;
PhysRevLett.92.086401 , whereas the high temperature superconductivity in
cuprate and iron-based superconductors is proposed to be related to the
interactions between electrons and antiferromagnetic (AFM) spin fluctuations,
i.e., magnons Science.284:1282 ; J.Phys.Condens.Matt.16:R755 ;
Sci.Bull.(2016)61(7):561 . The electron-boson interactions “dress” the
electrons up, and convert the electrons into quasiparticles. Consequently, the
band structure is renormalized, and sometimes an abrupt distortion in the
otherwise smooth band dispersion can be detected by angle resolved
photoemission spectroscopy (ARPES) 10.1088/0953-8984/14/24/306 ;
10.1088/1367-2630/11/12/125005 . More specifically, a kink structure has been
widely observed in the dispersion along the nodal direction of many cuprate
superconductors Nature(London)423:398(2003) ; PRL.87.177007(2001) ;
Nature412:510(2001) ; PRL.91.157003(2003) ; PRL.96.117004(2006) , which is now
attributed to the EPI as it is present in the heavily overdoped regime without
many AFM fluctuations PRL.93.117004(2004) ; PRB79.054528(2009) ;
PhysRevB.69.220502(2004) ; PhysRevB.73.144507(2006) . Theoretically, the
effects of electron-boson interaction can be described by a complex self-
energy of the electronic structure 10.1088/0953-8984/14/24/306 ;
10.1088/1367-2630/11/12/125005 . Based on the ARPES data, one can extract the
self-energy and the Eliashberg function determined by both the electron-boson
matrix element $g$ (i.e. interaction potential) and the material-specific
bosonic structure Mahan-book . Meanwhile, the electron-boson coupling constant
$\lambda$, which characterizes the total renormalization strength and directly
gives $T_{c}$ in BCS theory, is found to be less than 1 for electron-phonon
interaction in most metals PRL.93.117004(2004) ; PRB79.054528(2009) ; BKBO .

The magnon effects on the electronic degrees of freedom have been hard to
detect in general, either ferromagnetic or antiferromagnetic. In ferromagnets,
slight deviations from parabolic dispersion are suspected to be from
ferromagnetic magnons but embedded in the electron-electron correlation effect
10.1103/PhysRevLett.92.097205 ; Ni110 ; Fe110 , while a kink well above magnon
energy is dominated by the Stoner excitations rather than magnons
https://doi.org/10.1038/s41467-019-08445-1 . For AFMM, its contribution to the
electronic self-energy has not been experimentally identified, although
electron-AFMM interactions (EAIs) holds the key to the general understanding
of many correlated phenomena like unconventional superconductivity. The energy
scale of AFM spin fluctuations is comparable to the bandwidth in cuprates or
iron pnictides, which would lead to a renormalization of the entire band
rather than a kink near the Fermi energy ($E_{\mathrm{F}}$). Therefore, one
cannot isolate or identify the EAIs in the retrieved total self-energy.

To reveal the characteristics of the EAIs, one requires a compound that has
weak electron correlations and robust AFMM excitations. This dilemma condition
is usually difficult to fulfil, but could be realized in Ba1-xKxMn2As2.
BaMn2As2 is an isostructure material for 122-type Fe-based superconductors
PhysRevLett.101.107006(2003) . It is an AFM insulator (AFI) with a Néel
temperature _T_ N = 625 K. The magnetic moments of Mn2+ ions in BaMn2As2 point
along the $c$ axis, forming a G-type AFM order (Fig. 1b). K doping turns
Ba1-xKxMn2As2 into a metal. Despite of the carrier doping, the _T_ N is
slightly suppressed and large magnetic moments persist (Fig. 1a) (ref.
PhysRevLett.108.087005(2012), ; PhysRevB.85.144523(2012), ). Inelastic neutron
scattering studies find strong AFMM excitations across the phase diagram
PhysRevB.95.224401(2017) . The electron-electron correlations are weak
according to previous studies on BaMn2As2 (ref. PhysRevB.94.155155(2016), ).
At $x>0.19$, it shows a novel ferromagnetic ground state (FM) with the FM
moments in the $ab$-plane contributed by As-$4p$ orbital rather than the
canting of Mn AFM moments PhysRevB.85.144523(2012) ;
PhysRevLett.114.217001(2015) , while the underlying mechanism of the emergent
itinerant FM is unknown. If the weak electron-electron correlations remains in
Ba1-xKxMn2As2 following the parent compound BaMn2As2 PhysRevB.94.155155(2016)
, it would be an ideal playground for studying EAIs, as its AFMM excitations
should be strong.

Figure 1: Phase diagram and the basic electronic structure of Ba1-xKxMn2As2
($\mathbf{x}$ = 0.3). (a) Phase diagram of Ba1-xKxMn2As2. The open circle
indicates the Curie temperature determined by magnetic susceptibility
measurements on our sample. The filled circles indicate data from ref.
PhysRevB.85.144523(2012), ; PhysRevB.80.100403(2009), ;
PhysRevB.87.144418(2013), ; PhysRevLett.111.047001(2013), . (b-c) Crystal
structure of Ba1-xKxMn2As2 and the corresponding three-dimensional Brillouin
zone. The blue arrows indicate the alignment of the Mn magnetic moments in the
G-type antiferromagnetic (AFM) state. (d-f) Photoemission intensity maps in
the high symmetric planes of the Brillouin zone, integrated over an energy
window of _E F_ $\pm$ 20 meV. The $k_{y}-k_{z}$ map in the $\Gamma$XZ plane is
measured with photon energies ranging from 58 eV to 100 eV, while the
$k_{x}-k_{y}$ maps in the $\Gamma$XM plane and ZRA plane are measured with 78
eV and 62 eV photons, respectively. (g-h) Photoemission intensity and its
second derivative with respect to energy along cut #1 in panel e. The bands
are outlined by the dashed curves. (i) Momentum distribution curves (MDCs)
along cut #1. The circles track the local maxima for the dispersion of bands
$\alpha$, $\beta$ and $\beta$’. The ARPES data were measured at 30 K.

## Weak electron correlations in Ba1-xKxMn2As2

Figures 1d-f show ARPES results measured using vacuum ultra-violet (VUV)
photons, which resolve the Fermi surface structure of Ba1-xKxMn2As2 ($x$ =
0.3) in its three-dimensional Brillouin zone. In the $\Gamma$-X-M plane
measured with 78 eV photons, the Fermi surfaces consist of a large pocket
$\alpha$ and two small elliptical pockets $\beta$ and $\beta$’ perpendicular
to each other, all centred at $\Gamma$. The $\alpha$ band is absent in the ZRA
plane and highly dispersive along $k_{z}$, forming a drum-shaped Fermi surface
in the $k_{y}-k_{z}$ plane. $\beta$ and $\beta$’ are two-dimensional with
negligible dispersion along $k_{z}$. Except for some variation in the spectral
weight due to the photoemission matrix element, the Fermi surfaces measured
using VUV photons are consistent with the soft X-ray ARPES results
(Supplementary Section 1), confirming the bulk nature of the measured bands.
The single set of bands and Fermi surface, and the fact that the Fermi surface
volume is consistent with its doping level demonstrate that Ba1-xKxMn2As2
samples are homogeneous (Supplementary Section 2, PhysRevB.94.155155(2016) ;
nphys1908 ; PhysRevB.87.144418(2013) ).

Along $\Gamma$-X, the bands $\alpha$, $\beta$, and $\beta$’ that cross
$E_{\mathrm{F}}$ are all resolved, showing hole-like dispersions (Figs. 1g-i).
Both the Fermi surface structure and band dispersion of Ba1-xKxMn2As2 roughly
agree with a rigid band shift of the pristine BaMn2As2
PhysRevLett.108.087005(2012) ; PhysRevB.94.155155(2016) . The overall
bandwidths near $E_{\mathrm{F}}$ show little renormalization compared with the
DFT calculations of BaMn2As2 (ref. PhysRevB.94.155155(2016), ;
PhysRevB.85.144523(2012), ), consistent with the weakly correlated As-$4p$
states. The weak band renormalization in Ba1-xKxMn2As2 is distinct from the
strongly renormalized bands in the isostructural Ba1-xKxFe2As2 (ref.
PhysRevLett.105.117003(2010), ). The weak electron-electron correlation would
contribute little electronic self-energy near $E_{\mathrm{F}}$, which provides
a clean playground for studying electron-boson interactions in Ba1-xKxMn2As2.

## Strong electron-magnon interactions in Ba1-xKxMn2As2

Figure 2: Kink and self-energy analysis showing the electron-magnon
interaction for Ba0.7K0.3Mn2As2. (a) Second derivative spectra of the
enlargement near the Fermi crossing of the $\alpha$ band (rectangular area in
Fig. 1g), overlaid with the fitting of the Fermi velocity _v F_ (solid line)
and the bare band velocity _v ${}_{F}^{0}$_ (dashed line). (b) Momentum
distribution curves (MDCs) of photoemission intensity around the Fermi
crossing of the $\alpha$ band. The circles track the MDC peaks and illustrate
the band dispersion. (c) The reported electron-boson coupling constant
obtained based on MDC analysis of kinks in ARPES data of Be(1010) Be1010 ,
Bi2212 Bi2212 , Bi2201 Bi2201 , Ba1-xKxBiO3 BKBO , La0.6Sr0.4MnO3 LSMO113 ,
La2-2xSr1+2xMn2O7 LSMO327 , Fe(110) Fe110 ; Fe110/2 , Ni(110) Ni110 , Pd(110)
Pd110 , and (Ba/Sr)1-xKxFe2As2 BKFA , together with that of Ba0.7K0.3Mn2As2.
(d) Re $\Sigma$ (red) and the KK transformation of Im $\Sigma$ below 115 meV
(blue curve). (e) The KK transformation of Re $\Sigma$ (blue curve), the
electron-electron scattering (green curve), and a constant background (grey
curve). The orange curve shows their combination, which matches well with Im
$\Sigma$ (red circles). (f) Eliashberg function (red) extracted from the Im
$\Sigma$, compared with the phonon (purple) and magnon (blue circles)
intensity from inelastic neutron scattering (INS) and simulated magnetic
intensity (blue curve) on Ba1-xKxMn2As2 ($x$=0.25) (ref.
PhysRevB.95.224401(2017), ).

Band $\alpha$ shows a kink around the binding energy $E_{B}$=50 meV, which is
better visualized in the second derivative image and MDCs (Figs. 2a-b). This
kink in electronic dispersion is a general signature of electron-boson
interactions 10.1088/1367-2630/11/12/125005 . The Fermi velocity
$\emph{v}_{F}$ is reduced from the bare band velocity $\emph{v}^{0}_{F}$ by a
factor of $\sim$7 (Fig. 2a), from which one can estimate the electron-boson
coupling constant $\lambda$=$\emph{v}_{F}^{0}$/$\emph{v}_{F}$-1 to be as large
as 6. The observed electron-boson coupling constant is colossal as compared to
those relating with electron ferromagnetic magnons interations and EPI (Fig.
2c) Be1010 ; Bi2212 ; Bi2201 ; BKBO ; LSMO113 ; LSMO327 ; Fe110 ; Fe110/2 ;
Ni110 ; Pd110 ; BKFA

Based on the quasiparticle spectra measured by ARPES, we can extract the
complex self-energy. The real part of the self-energy is obtained by Re
$\Sigma(E)$ = $[\emph{k}(E)-\emph{k}_{0}(E)]\times|\emph{v}_{F}^{0}|$, where
$\emph{k}_{0}(E)$ is the bare band momentum and $\emph{v}_{F}^{0}$ is the bare
band velocity. The imaginary part of the self-energy can be obtained by $|$Im
$\Sigma(E)|$ = $|\emph{v}_{F}^{0}|\times\mathrm{FWHM}$/2, where FWHM is the
full-width at half-maximum of the MDC peaks. By analyzing the kink of
Ba1-xKxMn2As2, the real part of the self-energy Re $\Sigma$ peaks at
approximately 50 meV (Fig. 2d), where the imaginary part of the self-energy Im
$\Sigma$ also shows a step (Fig. 2e), indicating the energy scale of the
corresponding bosonic modes. The Kramers-Kronig (KK) transform of Im $\Sigma$
matches well with Re $\Sigma$ below 100 meV (Fig. 2d), while that of Re
$\Sigma$ also matches Im $\Sigma$ well after including a constant background
and a quadratic term (Fig. 2e). The quadratic term from the electron-electron
scattering accounts for the deviation above 100 meV. The KK conjugation of Im
$\Sigma$ and Re $\Sigma$ demonstrates the self-consistency of the self-energy
extraction.

The obtained Im $\Sigma$ and Re $\Sigma$ consistently indicate a bosonic
energy scale that extends from 0 meV to 120 meV and peaks at approximately 50
meV (Figs. 2d-e).  Given the quasiparticle self-energy, we can estimate the
Eliashberg function $\alpha^{2}F(\omega)$ of the kink by
$\alpha^{2}F(\omega)=\frac{\partial\mathrm{Im}\Sigma(E)}{\pi\partial{E}}|_{E=\omega}$
[see Methods], which characterizes the corresponding bosonic density of states
weighted by their effective interactions with electrons
10.1088/1367-2630/11/12/125005 . As shown in Fig. 2f, the energy scale of
$\alpha^{2}F(\omega)$ is distinct from the phonon energies below 25 meV
according to the inelastic neutron scattering (INS) on Ba1-xKxMn2As2 ($x$ =
0.25) (ref. PhysRevB.95.224401(2017), ), and the phonon spectra calculated for
Ba1-xKxMn2As2 ($x$ = 0 and 0.5) (Supplementary Section 3, KRESSE199615 ;
PhysRevB.54.11169 ; TOGO20151 ; PhysRevLett.77.3865 ), which excludes the
phonons as the origin of the kink. Finite effect on the electronic self-energy
from EPI could exist below 25 meV, but its observation is hindered by the much
larger contribution from the electron boson interaction that peaks at
approximately 50 meV. Instead, the energy scale of $\alpha^{2}F(\omega)$
matches that of magnon spectra of Ba0.75K0.25Mn2As2 (Fig. 2f), which has been
resolved by the INS magnetic intensity and well reproduced by Heisenberg-
model-based simulations (Supplementary Section 4, PhysRevB.95.224401(2017) ;
Toth_2015 ). After considering the momentum restriction of single magnon
absorption/emission processes, the simulated $\alpha^{2}F(\omega)$ also
exhibits the same energy scale (Supplementary Section 5,
PhysRevB.95.224401(2017) ). The consistent energy scale provides compelling
evidence that the kink feature in Ba1-xKxMn2As2 is due to the strong
interactions between itinerant electrons and a large range of AFMMs allowed by
the energy and momentum restrictions of the corresponding scattering
processes.

Figure 3: Doping dependence of electron-magnon interactions. (a-c)
Photoemission intensity near the Fermi crossing of the $\alpha$ band along
$\Gamma$X, measured with 78 eV photons at 30 K for samples of $x$ = 0.1, 0.2
and 0.3, respectively. The overlaid dispersion is obtained by fitting the
MDCs. The solid lines and dashed lines illustrate the Fermi velocity and the
bare band velocity, respectively. (d-f) Corresponding second derivative of
panels (a-c). (g) Eliashberg function $\alpha^{2}F(\omega)$ for samples of
different dopings. (h) Evolution of the coupling constant as a function of the
doping calculated through the band velocity renormalization (red) and Im
$\Sigma$ (blue).

Figures 3a-f show that kinks are present for various dopings, indicating the
robust presence of electron-boson interactions in Ba1-xKxMn2As2. Following the
same procedure, $\alpha^{2}F(\omega)$ is obtained for each doping. The
intensity gradually shifts towards lower energy with increasing doping (Fig.
3g), which is consistent with the doping dependent energy shift of magnons as
revealed by both the INS magnetic intensity and the calculated magnon DOS
(Supplementary Section 4, PhysRevB.95.224401(2017) ; Toth_2015 ). The
intensity of $\alpha^{2}F(\omega)$ increases by nearly 50% from $x$ = 0.1 to
$x$ = 0.2, and is similar between $x$ = 0.2 and 0.3, indicating a nonlinear
doping dependence of the EAIs coupling constant. As the doping increases from
$x$ = 0.1 to 0.3, the bare band velocity $v_{F}^{0}$ increases from $\sim$ 3.9
eV$\cdot\rm{\AA}$ to $\sim$ 7.7 eV$\cdot\rm{\AA}$, while the renormalized
Fermi velocity $v_{F}$ remains at approximately $\sim$ 1.1 eV$\cdot\rm{\AA}$
(Figs. 3a-c). Therefore, the EAIs constant
$\lambda$=$\emph{v}_{F}^{0}$/$\emph{v}_{F}$-1 increases with higher doping
(Fig. 3h), as the system enters deep into the ferromagnetic regime.

## The mechanism of the ferromagnetic ground state

The microscopic origin of the weak ferromagnetism in Ba1-xKxMn2As2 has been
under debate. The picture of the canted Mn2+ local moment PRB89.060403  was
excluded by various studies, and meanwhile, the ferromagnetism was attributed
to the spin polarization of As-$4p$ holes, suggesting an itinerant picture
following Stoner mechanism PhysRevLett.111.047001(2013) ;
PhysRevLett.114.217001(2015) . Currently, one strong criticism for the Stoner
mechanism is that the calculated DOS at $E_{\mathrm{F}}$ ($N(E_{\mathrm{F}})$)
in Ba1-xKxMn2As2 is too small to meet the Stoner criterion even at the high
doping level of $x$ = 0.4 (ref. PRB89.060403, ). However, the EAIs were not
considered in previous calculations, and the observed colossal EAIs would
greatly enhance the DOS at $E_{\mathrm{F}}$. Particularly, it becomes even
stronger when entering the ferromagnetic state with increasing doping (Fig.
3h). Therefore, the Stoner mechanism needs to be reexamined.

Figure 4: Evolution of Electron-magnon interaction as a function of the
temperature. (a) Photoemission intensity along momentum cut #2 of
Ba1-xKxMn2As2 ($x=0.3$) at temperatures of 30 K, 65 K, 100 K and 120 K,
overlaid with the band dispersion determined by the MDC peaks (red circles).
The solid lines and dashed lines illustrate the Fermi velocity and the bare
band velocity, respectively. (b) Sketch of the Fermi surface and momenta of
photoemission cuts. (c-d) Photoemission spectra of different temperatures
integrated along cut #3 and cut #4 in panel b, respectively. The spectra are
divided by a resolution-convolved Fermi-Dirac function to remove the thermal
effect near $E_{\mathrm{F}}$. The insets show integrated spectra at a larger
energy window. (e) Coupling constant as a function of the temperature. The
results are obtained by band velocity renormalization (red) and Im $\Sigma$
(blue). (f-g) Quasiparticle peak intensity integrated over
[$E_{\mathrm{F}}$-0.08 eV, $E_{\mathrm{F}}$+0.05 eV] as a function of the
temperature for the spectra in panels c and d, respectively. The colour
background illustrates the transition between the AFM phase and FM-AFM
coexisting phase. The spectra were measured with 78 eV photons.

In addition to increasing the doping level, another route into the
ferromagnetic state is through cooling. Figure 4 examines how the electronic
structure of Ba0.7K0.3Mn2As2 evolves across the Curie temperature. Figure 4a
shows that the kink is always present from 30 K to 120 K, indicating that the
EAIs persist in both the coexisting FM-AFM phase and the pure AFM phase,
however, the Fermi velocity $\emph{v}_{F}$ increases from $\sim$ 0.55
eV$\cdot\rm{\AA}$ to $\sim$ 0.76 eV$\cdot\rm{\AA}$. As the bare band velocity
$\emph{v}_{F}^{0}$ is almost fixed around 3.8 eV$\cdot\rm{\AA}$, the EAIs
coupling constant shows a prominent increase of approximately 50% from 120 K
to 30 K (Fig. 4e), and also confirmed by the self-energy analysis
(Supplementary Section 6). Meanwhile, as the temperature decreases, a
quasiparticle peak emerges near $E_{\mathrm{F}}$ for both $\alpha$ and $\beta$
bands (Figs. 4c-d). It becomes sharper at lower temperature due to enhanced
coherence in the ferromagnetic phase PhysRevB.63.094415(2001) ;
PhysRevB.69.132411(2004) ; Zhangeaao6791(2018) . We characterize the emergence
of the quasiparticle peak by its spectral weight, which increases continuously
with decreasing temperature. The major enhancement taking place between 90 K
and 60 K (Figs. 4f-g), where the broad ferromagnetic transition occurs
(Supplementary Section 7). The temperature dependence of the spectral weight
follows that of $\lambda$, indicating the intimate relationship between the
ferromagnetic state and the EAIs.

Figure 5: Density of states and coupling constant in the temperature-doping
phase diagram. (a) Electronic density of states ($N(E_{\mathrm{F}})$, red
circles) and EAIs coupling constant ($\lambda$, blue circles) as a function of
the doping at 30 K. (b) Same as (a) but as a function of the temperature for
$x$=0.3. The colour background illustrates the transition between the AFM
phase and FM-AFM coexisting phase. The horizontal dashed line illustrates the
Stoner criteria assuming $I_{\mathrm{As}}\sim$0.8 eV, to fit the phase
boundary of the ferromagnetic phase.

The EAIs in Ba1-xKxMn2As2 could influence the ferromagnetic state through the
DOS at $E_{\mathrm{F}}$, $N(E_{\mathrm{F}})$. Considering no EAIs, the bare
band DOS $N^{0}(E_{\mathrm{F}})$ is approximately 0.2 spin-1eV-1As-1
calculated from the measured Fermi surface and bare band velocity [see
methods], which is comparable to that estimated by DFT calculations and does
not meet the Stoner criteria PRB89.060403 . After considering the EAIs,
$N(E_{\mathrm{F}})$ is greatly enhanced from $N^{0}(E_{\mathrm{F}})$,
following the doping dependence and temperature dependence of EAIs coupling
constant $\lambda$ (Fig. 5). $N(E_{\mathrm{F}})$ becomes most enhanced in the
ferromagnetic regime, reaching 1.53$\pm$0.36 spin-1eV-1As-1 at $x=0.3$, which
is 3 times of that estimated by DFT calculations at an even higher doping $x$
= 0.4 (ref. PRB89.060403, ). Clearly, when $N(E_{\mathrm{F}})$ is roughly
above $\sim$1.2 spin-1eV-1As-1, Ba1-xKxMn2As2 enters the ferromagnetic phase.
If this corresponds to the Stoner criteria,
$I_{\mathrm{As}}N(E_{\mathrm{F}})\geq 1$, the Stoner parameter of As,
$I_{\mathrm{As}}$, is estimated to be approximately 0.8 eV for Ba0.7K0.3Mn2As2
with a Curie temperature $T_{C}$ of 90 K. We note that the Stoner picture
based on mean field theory usually fails to predict the $T_{C}$ of transition-
metal ferromagnets with strong local exchange splitting above $T_{C}$ (ref.
Z.Physik.B.29.34(1979), ), however, a crude estimation of $T_{C}$ by the
Stoner criteria could still be feasible on low-$T_{C}$ weak ferromagnets
fazekas1999lecture , as Ba1-xKxMn2As2 is supposed to be. Consistently at 30 K,
with this $I_{\mathrm{As}}\sim$0.8 eV, the Stoner criteria are fulfilled just
at doping $x$ = 0.2, whose $T_{C}$ is approximately 30 K, while not fulfilled
for the doping $x$ = 0.1 with no ferromagnetic ground state. These results
show that the Stoner mechanism is at work and that the ferromagnetic ground
state is driven by the As-$4p$ holes renormalized by EAIs.

In a Stoner ferromagnet, exchange band splitting will occur. Considering the
finite resolution, the upper limit of exchange splitting is estimated by
fitting the MDC peaks of band $\alpha$ with two Lorentzian peaks, which gives
a momentum splitting of 0.065 Å-1 in Ba1-xKxMn2As2 ($x$ = 0.3) at 30 K
(Supplementary Section 8). Assuming an isotropic splitting over the Fermi
surface, this splitting corresponds to a spin polarization of 0.07 holes/f.u.
(f.u. = formula unit), which accounts for only 32% of the ferromagnetic moment
of 0.25 $\mu_{B}$/f.u. at 30 K by magnetic susceptibility measurements
(Supplementary Section 7). Despite that Stoner picture is still at work in
driving the ferromagnetism, at least 68% of the ferromagnetic moments are not
from itinerant carriers. Since the magnetic moment is found to be of As
character based on previous X-ray dichroism measurements
PhysRevLett.114.217001(2015) , our results imply that the non-magnetic element
As gives a considerable contribution of local moments. Magnetic moments on
non-magnetic atoms could be induced by local environments as exemplified by
the V moments observed in VAu4 (ref. PhysRevLett.18.851(1967), ;
doi:10.1143/JPSJ.48.62, ). In Ba1-xKxMn2As2, projection of the As-$4p$ orbital
was found both at the dispersive bands ($\alpha$, $\beta$, and
$\beta^{\prime}$), and at the flat bands at higher binding energies with
localized nature PhysRevB.94.155155(2016) . Driven by the spontaneous spin
polarization of the itinerant As-$4p$ holes, the As-$4p$ states with both
itinerant and localized nature in Ba1-xKxMn2As2 can host an emergent
ferromagnetic state with mixed itinerant and localized As moments.

## Summary and Outlook

The EAI is one of the fundamental interactions in condensed matter. Our
findings illustrate quantitatively how the EAIs can renormalize the electronic
band, invoke the Stoner mechanism, and induce ferromagnetism in Ba1-xKxMn2As2.
It offers an unprecedented opportunity to directly study the self-energy and
Eliasgberg function $\alpha^{2}F(\omega)$ of EAIs, and our quantitative
analysis reveals various important facts about the EAIs for the first time.

  1. 1.

The coupling constant $\lambda$ of EAIs in Ba1-xKxMn2As2 is as high as 6,
which is much higher than any other known electron-boson coupling in metals.
High density of states (DOS) of magnons are expected in the Mn AFM order with
spin $S$=5/2, which could be partly responsible for the large coupling
constant $\lambda$. The large coupling constant demonstrates that the effect
of the EAIs can be overwhelmingly strong and could dominate the ground states.

  2. 2.

The EAIs vary strongly with both temperature and doping, even if the AFM order
is robust. In the case of in Ba1-xKxMn2As2, the EAIs is enhanced by nearly
150% from $x$ = 0.1 to 0.3, which could be induced by the expanded Fermi
surface volume and the increased scattering phase space at higher dopings.
This observation is in contrast to the EPI, which usually exhibits an opposite
behavior.

Our data put constrains on the theories of EAIs. The extracted electronic
self-energy and Eliashberg function $\alpha^{2}F(\omega)$ will motivate future
inelastic neutron scattering studies to obtain the magnon spectra with
absolute value, so that the electron-magnon matrix element $g$ and other
microscopic characteristics of EAIs could be further revealed at a more
quantitative level. As these characteristics of the EAIs could be general in
other materials with AFM excitations, such as high temperature
superconductivity in cuprates and iron pnictides, our results would facilitate
further understanding of the related emergent phenomena.

## Methods

###  .0.1 Sample growth and characterization.

The Ba1-xKxMn2As2 single crystals used in this study were grown by the flux
method as described elsewhere PhysRevB.85.144523(2012) ; PRB79.075120 . The
chemical composition and K doping level were determined by electron probe
microanalysis (EPMA). The carrier concentrations calculated from Fermi surface
volumes based on Luttinger theorem agree well with the chemical doping
determined by EPMA measurements, indicating that the Ba1-xKxMn2As2 sample is
of single phase with homogeneous doping level. This is further supported by
STM and EPMA measurements over the cleaved surface (Supplementary Section 2,
PhysRevB.94.155155(2016) ; nphys1908 ; PhysRevB.87.144418(2013) ).  The
magnetic susceptibility was measured by Quantum Design Dynalcool system
(Supplementary Section 7).

###  .0.2 ARPES experiments.

VUV-ARPES experiments were performed at beamlines BL5-2 of the Stanford
Synchrotron Radiation Light Source (SSRL), I05 of the Diamond Light Source,
and BL4.0.3 of the Advanced Light Source (ALS). The energy and angular
resolutions were set at 15 meV and 0.3∘, respectively. SX-ARPES experiments
were performed at ADRESS of the Swiss Light Source strocov2014soft . The
energy and angular resolutions were set at 80 meV and 0.1∘, respectively. All
samples were cleaved _in situ_ under a vacuum better than 2$\times$10-10 mbar
and measured under a vacuum better than 8$\times$10-11 mbar.

###  .0.3 Extraction of self-energy and calculation of the coupling constant.

The real part of the self-energy can be obtained by Re $\Sigma(E,k)$ =
$E(k)-\epsilon(k)=(\emph{k}(E)-\emph{k}_{0}(E))\times|\emph{v}_{F}^{0}|$,
where the $\epsilon(k)$, $E(k)$, $\emph{k}_{0}(E)$, and $\emph{v}_{F}^{0}$ are
the bare band energy, renormalized energy, bare band momentum, and bare band
velocity, respectively. The bare band is estimated by cubic spline
interpolation. The imaginary part of the self-energy can be derived by
$|Im\Sigma(E,k)|$ = $|\emph{v}_{F}^{0}|\times\mathrm{(}FWHM)$ /2, where
$\mathrm{(}FWHM)$ is the full-width at half-maximum of the MDC peak and
$\emph{v}_{F}^{0}$ is the bare band velocity. The Re $\Sigma$ and Im $\Sigma$
should be the Kramers-Kronig conjugation of each other before the cut-off
energy $E_{max}$=115 meV:

$Re\Sigma(E,k)=\frac{1}{\pi}\int_{-\infty}^{+\infty}{\frac{Im\Sigma(E,k)}{E^{\prime}-E}dE^{\prime}}~{}E\leq
E_{max}$

$Im\Sigma(E,k)=\left\\{\begin{aligned}
-\frac{1}{\pi}\int_{-\infty}^{+\infty}{\frac{Re\Sigma(E,k)}{E^{\prime}-E}dE^{\prime}}~{}E\leq
E_{max}&\\\
-\frac{1}{\pi}\int_{-\infty}^{+\infty}{\frac{Re\Sigma(E_{max},k)}{E^{\prime}-E_{max}}dE^{\prime}}~{}E>E_{max}&\end{aligned}\right.$

The cut-off energy $E_{max}$ is determined by the maximum energy of AFM
magnons $\omega_{max}\sim 115$ meV in Ba1-xKxMn2As2, above which the electron-
electron correlation starts to substantially contribute to the increase in Im
$\Sigma$.

The coupling constant is calculated by either the renormalization of the Fermi
velocity, or by the Eliashberg function from the self-energy. For both cases,
we employ the formula at the $T\rightarrow 0$ limit because the experimental
temperatures are far below the $T_{N}$ of Ba1-xKxMn2As2. In the quasielastic
approximation where the electronic energy $E$ is much larger than the boson
energy $\omega$, the quasiparticle self-energy is determined by the Eliashberg
function as 10.1088/1367-2630/11/12/125005 :

$Im\Sigma(E,k;T)=\pi\int_{0}^{\omega_{max}}{\alpha^{2}F(E,k;\omega)[1-f(E-\omega)+f(E+\omega)+2n(\omega)]}d\omega$

Assuming the $T\rightarrow 0$ limit with $n(\omega)\rightarrow 0$, we have:

$Im\Sigma(E,k)=\pi\int_{0}^{\omega_{max}}{\alpha^{2}F(E,k;\omega)f(E+\omega)}d\omega$

As the electronic energy scale of band $\alpha$ is much larger than the magnon
energy scale, the dependence of $\alpha^{2}F(E,k;\omega)$ on the electronic
energy can be ignored. In this case, the variation in Im$\Sigma(E)$ with $E$
mainly comes from the change in the effective integration range due to the
Fermi-Dirac function $f(E+\omega)$. Thus we can estimate $\alpha^{2}F(\omega)$
by taking the derivative of Im$\Sigma(E)$:

$\alpha^{2}F(\omega)=\frac{\partial Im\Sigma(E)}{\pi\partial{E}}|_{E=\omega}$

To avoid nonphysical values, we set the noise induced negative data points of
$\alpha^{2}F(\omega)$ to zero. The coupling constant $\lambda$ can be
estimated by:

$\lambda=2\int_{0}^{\omega_{max}}{\frac{{\alpha^{2}}F(\omega)}{\omega}}d\omega$

###  .0.4 Estimation of density of states N(EF) and bare-band density of
states N0(EF)

The DOS at $E_{\mathrm{F}}$, $N(E_{\mathrm{F}})$, is estimated by the
following equations based on its definition:

$g_{n}(E)=\int_{S_{n}(E)}{\frac{dS}{4\pi^{3}}\frac{1}{|{\nabla}E_{n}(k)|}\approx\frac{S_{FS}}{4\pi^{3}}\overline{|v_{F}^{-1}|}}$

$N(0)=\frac{1}{2}\times\frac{V_{0}}{2}g_{n}\approx\frac{V_{0}S_{FS}}{4\pi^{3}}\overline{|v_{F}^{-1}|}$

where $V_{0}$ is the volume of the unit cell, $S_{FS}$ is the Fermi surface
area and $v_{F}$ is the Fermi velocity. The bare-band density of states
$N^{0}(E_{\mathrm{F}})$ are obtained in the same way by replacing the Fermi
velocity $v_{F}$ with the bare-band velocity $v^{0}_{F}$.

We estimate the $S_{FS}$ of the drum-shaped Fermi pocket $\alpha$ by an
analogue of the body-centred tetragonal Brillouin zone, and the $S_{FS}$ of
band $\beta$/$\beta^{\prime}$ based on elliptical cylinders. The uncertainty
of the $S_{FS}$ is estimated to be 15$\%$. The $\overline{v_{F}^{-1}}$
calculation is based on the measured value of $v_{F}$ and an assumed linear
change. Thus,

$\overline{v_{F}^{-1}}=\frac{\int_{v_{Fmin}}^{v_{Fmax}}{v_{F}^{-1}}d{v_{F}}}{v_{Fmax}-v_{Fmin}}=\frac{ln(v_{Fmax})-ln(v_{Fmin})}{v_{Fmax}-v_{Fmin}}.$

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We gratefully acknowledge the experimental support of Dr. Y. B. Huang, Dr. Z.
Sun, Dr Z. T. Liu, and Dr. D. W. Shen. We thank the Diamond Light Source for
time on beam line I05, the Advanced Light Source (U.S. DOE contract no. DE-
AC02-05CH11231) for access to beamline 4.0.3, the Stanford Synchrotron
Radiation Light Source for the access to beamline 5-2, and the Swiss Light
Source for time on SX-ARPES endstation of beamline ADRESS. Some preliminary
data were taken at National Synchrotron Radiation Laboratory (NSRL, China) and
BL03U at Shanghai Synchrotron Radiation Facility. This work is supported in
part by the National Natural Science Foundation of China (Grants No. 11888101,
12074074, 11704074, 11704073, and 11790312), the National Key R&D Program of
the MOST of China (Grants No. 2016YFA0300200 and 2017YFA0303004), Project
supported by Shanghai Municipal Science and Technology Major Project (Grant
No. 2019SHZDZX01), and Shanghai Rising-Star Program (20QA1401400).

[Competing Interests] The authors declare that they have no competing
financial interests.

[Correspondence] Correspondence and requests for materials should be addressed
to H.C.X. (email<EMAIL_ADDRESS>and D.L.F. (email:
dlfeng@fudan.edu.cn).