# NLPDove at SemEval-2020 Task 12: Improving Offensive Language Detection with
Cross-lingual Transfer

Hwijeen Ahn
Sogang University
Seoul, Korea
<EMAIL_ADDRESS>
Jimin Sun
Seoul National University
Seoul, Korea
<EMAIL_ADDRESS>
Chan Young Park
Carnegie Mellon University
Pittsburgh, USA
<EMAIL_ADDRESS>Hwijeen Ahn1*, Jimin Sun2*, Chan Young Park3*, Jungyun Seo
1
1Sogang University, Republic of Korea
2Seoul National University, Republic of Korea
3Language Technologies Institute, Carnegie Mellon University, USA
{hwijeen<EMAIL_ADDRESS>
<EMAIL_ADDRESS><EMAIL_ADDRESS>

###### Abstract

This paper describes our approach to the task of identifying offensive
languages in a multilingual setting. We investigate two data augmentation
strategies: using additional semi-supervised labels with different thresholds
and cross-lingual transfer with data selection. Leveraging the semi-supervised
dataset resulted in performance improvements compared to the baseline trained
solely with the manually-annotated dataset. We propose a new metric,
Translation Embedding Distance, to measure the transferability of instances
for cross-lingual data selection. We also introduce various preprocessing
steps tailored for social media text along with methods to fine-tune the pre-
trained multilingual BERT (mBERT) for offensive language identification. Our
multilingual systems achieved competitive results in Greek, Danish, and
Turkish at OffensEval 2020.

##  1 Introduction

00footnotetext:  This work is licensed under a Creative Commons Attribution
4.0 International License. License details:
http://creativecommons.org/licenses/by/4.0/.
$\ast$ The first three authors contributed equally.

Online social media has become one of the most important means of
communication. Unfortunately, the discourse is often laden with abusive
language that can have damaging effects on social media users [Zampieri et
al., 2019a]. As online abuse grows as a serious social problem, many social
media platforms are employing human moderators to track inappropriate contents
and comments. However, such human moderation comes at the cost of additional
operation and the mental suffering of the workers [Roberts, 2014, Dosono and
Semaan, 2019]. In response, the automatic identification of offensive language
has been a rising area of interest to both academia and industry.
Computational methods presented in several prior studies [Park and Fung, 2017,
Pitsilis et al., 2018, Wulczyn et al., 2017, Founta et al., 2018] have shown
promising results on how we can automatically detect a large number of
offensive contents with minimal human intervention.

As an effort to promote this line of research, OffensEval was organized at
SemEval-2019 [Zampieri et al., 2019b]. The organizers released a dataset,
Offensive Language Identification dataset (OLID), that contains English tweets
with human annotations over three sub-tasks: 1) whether a tweet is offensive
or not, 2) whether an offensive tweet is targeted or not, and if so 3) whether
the target is an individual or a group. The second edition of OffensEval,
OffensEval 2020 : Multilingual Offensive Language Identification in Social
Media, holds the same task but extends the OLID to multiple languages
(English, Arabic, Danish, Greek, and Turkish) [Zampieri et al., 2020].

This paper describes our system, NLPDove, submitted to OffensEval 2020 . We
present two different data augmentation strategies. First, for English, we
augment the training set with reliable samples filtered out from the provided
semi-supervised dataset. Second, we use samples from languages other than the
target language to enhance performance in the target language, namely cross-
lingual transfer. Specifically, we propose a new metric, Translation Embedding
Distance(TED), to measure the data transferability of each example in the
data. We use the metric to effectively select additional training data samples
from other available transfer languages. We also introduce various
preprocessing steps to extract meaningful information from user-generated
texts despite their inherently noisy nature. Our model is based on the
multilingual pre-trained language model, particularly multilingual BERT
(mBERT) [Devlin et al., 2019]. Our final submitted model is an ensemble of
multiple mBERT models with different pooling mechanisms, representation layers
and randoms seeds. Our submission achieved macro F1 of 0.85 in Greek (1st/38),
0.79 in Danish (3rd/40), 0.80 in Turkish (5th/47), 0.91 in English (15th/86),
and 0.80 in Arabic (20th/54). 111The code for our system can be found at
https://github.com/hwijeen/OffensEval2020

In the remainder of this paper, we first describe the dataset and the task of
OffensEval 2020 (§2). We then present our method, including the data
augmentation strategies, preprocessing pipeline, and model architecture (§3).
The evaluation results of our final submission are reported along with other
experiments to further investigate the effectiveness of our method (§4). We
then discuss our findings and negative results to shed light on the
limitations and remaining challenges in the current offensive language
identification models (§5). Finally, we review related work (§6) and conclude
(§7).

##  2 Data

The most noticeable update in OffensEval 2020 is the extension of the task to
four additional languages other than English: Arabic [Mubarak et al., 2020],
Danish [Sigurbergsson and Derczynski, 2020], Greek [Pitenis et al., 2020], and
Turkish [Çöltekin, 2020]. This change facilitates the research of offensive
language identification in multiple languages, and also enables researchers to
explore the feasibility of cross-lingual approaches of the task. One thing to
note is that unlike English tweets which had annotations for all three sub-
tasks, the four new languages do not have all of them; they are only annotated
on the first sub-task, which tells whether they are offensive or not.

In the case of English, in addition to the manually annotated tweets from the
previous workshop [Zampieri et al., 2019a], OffensEval 2020 released a large
semi-supervised dataset where samples are labeled by a set of trained models,
not by human annotators [Rosenthal et al., 2020]. Therefore, the labels are
not binary but given as floating-point numbers between 0 and 1 (i.e. the
average score of multiple models), with their standard deviation indicating
the confidence level among classifiers. For further details regarding the
data, we refer to the original paper [Rosenthal et al., 2020]. The summary
statistics of the dataset are presented in Table 2.

##  3 Method

There are three important components in our system: training data
augmentation, extensive preprocessing, and model ensembling. The following
subsections describe each part in detail.

Language | Train size | Valid size | OFF:NOT
---|---|---|---
Arabic | 7202 | 800 | 0.25
Danish | 2666 | 296 | 0.15
English | 12691 | 1411 | 0.49
Greek | 7871 | 874 | 0.40
Turkish | 28582 | 3176 | 0.24
English-semi | 9M | - | -
Table 1: Summary statistics of the dataset. English-semi denotes the semi-
supervised English dataset. For English, we also used the OLID from OffensEval
2019 [Zampieri et al., 2019a]. We randomly split the provided data into train
and validation set by 9:1.

Preprocessing | # of Cases
---|---
Emoji substitution | 1454
Hashtag segmentation | 2290
Letter casing normalization | 12665
URL replacement | 2140
Punctuation trimming | 504
Table 2: Preprocessing methods and the number of examples modified by each
method in the English training data.

###  3.1 Data Augmentation

mBERT and other large-scale pre-trained language models are known for their
massive number of parameters [Conneau and Lample, 2019]. Thus, they require a
substantial amount of data to be fine-tuned sufficiently to the downstream
task. And yet, the dataset in hand may not be large enough, especially for
some languages due to the expensive annotation process. To alleviate this data
sparsity issue, we propose two data augmentation approaches to make most of
the provided semi-supervised labels and multilingual data.

#### Semi-supervised Labels

It has become a common practice to augment training data with machine
annotated or synthetic labels when the training data is insufficient [Sennrich
et al., 2016]. There is almost an infinite number of unlabeled Twitter data
available, many of which contain offensive languages. One way to obtain a
substantial amount of pseudo-labels is to predict unlabeled tweets with models
trained with existing labeled data. OffensEval 2020 released over nine million
English tweets labeled in this semi-supervised manner [Rosenthal et al.,
2020]. Each sample was given with its average label probability from several
trained models and the standard deviation of the probabilities which indicates
the confidence level. One practical question lies in how to utilize this data
while reducing the effect of noisy labels and controlling the data quality.
One straightforward approach is to set certain thresholds to filter out the
uncertain examples. We investigate different thresholding strategies with
respect to the two measures, the average probability and the standard
deviation.

#### Cross-lingual Data Selection

Multilingual pre-trained language models allow seamless cross-lingual
transfer; they map texts in different languages into the same representation
space without introducing extra costs. Cross-lingual transfer can be
especially helpful when the training data is limited for the target language,
i.e., low-resource settings. Transferring examples from high-resource
languages to low-resource languages often results in great improvements [Chen
et al., 2018, Xu and Yang, 2017].

Although it is clear that cross-lingual transfer can be of help, the question
of which data to additionally use remains an open problem. Should we use the
entire dataset, or is there a subset better than the entire dataset? We
hypothesize that not all samples in the same transfer language will be equally
helpful to the target language task, leading to the conclusion that a
carefully selected subset will give higher performance gain than using the
whole dataset.

To address the how part of data selection, we propose a new metric,
translation embedding distance (TED), to quantify the transferability of a
data sample or a language. We first define a sample’s transferability as how
useful the transfer language sample is when transferred to the target language
task. Here, we hypothesize that transferability as a concept correlates with
translatability; if a sentence is easily translated to the target language, it
is more likely to be a useful training sample. To measure TED, we follow the
three steps: first, we (machine) translate the training samples in transfer
languages into the target language.222We used Google Translate in our
experiments. Then, we extract sentence embeddings for both the original
sentence and its translation using mBERT. More specifically, we applied mean
pooling over the second-to-last (penultimate) layer of mBERT and used it as
the sentence embedding. Finally, we measure the L2 distance between the two
representations and refer to it as the TED of the instance. The
transferability of a _language_ , which we define as language-level TED, is
simply the average of instance-level TED of samples in the transfer language.

We can then rank transfer samples according to their TED scores and choose
top-$k$ samples with the lowest distance. Likewise, to find the most
transferable languages, we can select the top-$k$ languages based on their
language-level TED scores. To verify our hypothesis that adding samples in
other languages can enhance performance in the target language task, we
investigate the effectiveness of both language-level and instance-level data
selection in §4.2.

###  3.2 Preprocessing

User-generated contents are inherently noisy, whereas the pre-trained language
models that we use throughout our system are mostly trained with clean texts
such as Wikipedia articles and BookCorpus [Devlin et al., 2019]. To minimize
the discrepancy, we applied various preprocessing steps to normalize the noisy
tweets provided in our dataset. In particular, we focus on normalizing the
unique conventions of tweets (e.g. hashtags, mentions, emojis) and their
irregular usage of punctuation and capitalization. Table 2 lists all of the
considered methodologies and the number of cases found for each method in the
English data. Each item is explained in more detail below.

#### Emoji Substitution

Although emojis are effective means of expressing sentiments, learning a good
representation of emojis with neural models can be challenging due to their
low frequency. Another challenge is that the most pre-trained language models
are not acquainted with the use of emojis as the texts used to train them did
not contain emojis. To fully benefit from the knowledge embedded in pre-
trained language models, we replaced all emojis with their plain text
descriptions (e.g. ☺ $\rightarrow$ smiley face) using an off-the-shelf
library333https://github.com/carpedm20/emoji.

#### Hashtag Segmentation

Hashtags are prevalent in tweets, and they often contain essential information
and keywords. Conventionally, hashtags are prefixed with the # symbol followed
by phrases concatenated without whitespaces. In order to extract all relevant
information from hashtags, we split them into words using a word segmentation
toolkit444http://www.grantjenks.com/docs/wordsegment/. We preserved the #
symbol in the beginning of segmented words to help the model differentiate
hashtags from plain texts.

#### Letter Casing Normalization

In social media texts, people often use capitalization to express the
intensity of their emotions. For example, “GET OUT!” sounds much more intense
than “get out!”. Although “GET” and “get”, in this case, possess the same
meaning and only differ in the degree of emphasis, they will be assigned to
completely different tokens if we do not use a canonical form representing
both variants. Keeping the original form may be useful to preserve the
richness in expressing emotional intensity, but the embedding quality of the
less frequent variants cannot be assured. In this case, “GET” would occur much
infrequently than “get” in the training corpus. Therefore, we first normalized
these casing variations by lowercasing all words. But at the same time, we
prepended a special token <has_cap> when the word contains an uppercase
alphabet and <all_cap> when the entire word was uppercased.

#### URL Replacement

Tweets often include raw urls that redirect users to a reference page. In the
provided data, most of the urls were already replaced with two special tokens,
HTTP and URL. We unified them into HTTP, since HTTP is the token used during
the pre-training stage of mBERT.

#### Punctuation Trimming

One characteristic of social media text is the irregular usage of punctuation
marks. For instance, the two sentences “I am sad..” and “I am sad……..” differ
slightly in their use of punctuation marks. The difference between the two
sentences is negligible for a human reader in terms of sentiment. However,
their sentence representations may differ significantly since the latter’s
representation would be diluted with its repeated use of periods. Hence, we
limit the maximum number of consecutive punctuation marks to three
occurrences.

###  3.3 Model

In our final submission, we used an ensemble of several different mBERT
models. Here, we explain how we selected and ensembled the models.

#### mBERT

mBERT is a multilingual extension of BERT which shares the same architecture
with BERT [Devlin et al., 2019]. The main difference is that mBERT was trained
on the monolingual corpora in multiple languages with an extended vocabulary,
which enables seamless cross-lingual transfer. The model can take inputs in
various languages, and we can either jointly train a model with both the
transfer and target language or perform zero-shot transfer where the model is
trained only with the transfer language. mBERT is shown to be highly effective
in both settings [Pires et al., 2019], implying the model’s ability to learn a
universal representation space that is shared across languages.

We took advantage of the multilinguality of mBERT and used it as the main
model for our system for all languages. We added a pooling layer and a linear
classifier on top of mBERT for the classification task. The pooling layer
takes mBERT representations of each word and combines them into a fixed-size
vector. 555We experimented with mean pooling, max pooling, concatenation of
both, and CNN pooling. We used the same hyperparameters values provided in ?)
except for the learning rate, random seed, and dropout probability. For the
three hyperparameters we tuned, we ran a grid-search to select the best
configuration based on the validation set performance. We note that tuning the
random seed, as found in ?), resulted in a significant performance gain.

#### Ensemble

Model ensemble methods are widely employed to improve a model’s robustness and
generalization performance. With this motivation in mind, we developed a
pipeline for model ensembling. We trained multiple BERT-based models for each
task that differ by which BERT layer is used for the word representation
(last, second-to-last)666It has been reported that BERT outputs from different
layers encode different kinds of information [Kovaleva et al., 2019]. ,
pooling mechanism (mean, max, concatenation of both, and CNN), learning rate
(1e-5, 1e-6), and also random seeds. We then chose the top three models
according to the validation performance. In the case of English, we
additionally considered an mBERT model trained with the augmented dataset that
incorporates the semi-supervised dataset as described in §4.2. We used
majority voting to aggregate the prediction of the selected models for the
final prediction.

##  4 Experiment Results

Model | Language
---|---
Arabic | Danish | English | Greek | Turkish
mBERT (Single model) | 0.8722 | 0.7837 | 0.7770 | 0.8349 | 0.7835
Ensemble | 0.8775 | 0.7514 | 0.7822 | 0.8343 | 0.7970
Table 3: Performance of our system on development data. The ensemble model was
used for final submission for all languages.

###  4.1 Main Results

We used a macro-averaged F1 score as our main evaluation metric as in
OffensEval 2020. Table 3 summarizes the performance of our models in the
validation data for each target language. We also report the best performance
of a single mBERT model for comparison. As explained in §3.3, our final
submission models used a majority vote ensemble of several mBERT models.

###  4.2 Data Augmentation Experiment

#### Semi-supervised Labels

For the English task, we used the human-annotated dataset from OffensEval 2019
as the primary data source and augmented it with the subset of the semi-
supervised dataset from OffensEval 2020. As explained in Section 2, the semi-
supervised labels are the averaged prediction scores of various trained models
accompanied by the standard deviation of these scores.

One way to control the quality of the additional data is to filter out noisy
data using the prediction confidence score of classifiers and their standard
deviation. For instance, setting the minimum value of the offensive class
confidence as 0.9 rather than 0.6 would result in a smaller but more reliable
subset. Similarly, a sample with a lower standard deviation indicates a higher
likelihood of multiple models agreeing to its predicted label, thereby more
reliable. We performed a grid search over combinations of threshold values for
offensive and non-offensive tweets as well as the standard deviation. In
particular, we set the grid with three different threshold parameters:
$t_{\mathrm{off}}\in\\{0.8,0.9\\},t_{\mathrm{not}}\in\\{0.2,0.3\\},t_{\mathrm{std}}\in\\{0.1,0.125\\}$.
Data samples are selected when the standard deviation is lower than
$t_{\mathrm{std}}$, and its score is either higher than $t_{\mathrm{off}}$ or
lower than $t_{\mathrm{not}}$.

The results are summarized in Table 4. Although varying the threshold resulted
in additional data of different qualities and sizes, the difference in results
was marginal. When about 30K samples were added with cut-off values of
$t_{\mathrm{off}}=0.8,t_{\mathrm{not}}=0.2,t_{\mathrm{std}}=0.125$, we
observed a small performance gain compared to others. In our final ensemble
model, we included the models that performed better than the baseline which
was trained solely on the human-annotated dataset.

#### Cross-lingual Data Transfer

We first consider language-level cross-lingual transfer strategies. That is,
we seek the most effective transfer language for the given target language. To
this end, we measure language-level TED for each transfer and target language
pair. We then pick top-k languages that have high language-level TED score for
each target language.

Cross-lingual transfer has been shown to be effective especially when the
target language dataset is not sufficient. Our experiments focus on the
setting where Danish is the target language as it has the least number of
training samples. $k$ was set to 1 for language selection. Results showed that
English (9.83) is the most useful transfer language to Danish, followed by
Arabic (10.85), Greek (22.02) and Turkish (23.08). The high transferability
from English to Danish is probably due to the two languages’ surface-level
resemblance, which comes from the shared orthography. We note that English
turned out to be the most effective language to Danish even in terms of zero-
shot transfer performance (trained only on the source language and tested on
the target language).

Next, we consider the transfer strategy on a more fine-grained instance-level.
We construct a subset of the dataset of the most transferable language based
on each sample’s transferability. Specifically, we sort the English samples
based on their TED to Danish, and choose the samples with the lowest TED. We
investigate three different ways to build the subset: taking
top/bottom/random-k English samples ($\mathrm{en}_{\mathrm{top}}$,
$\mathrm{en}_{\mathrm{bottom}}$, $\mathrm{en}_{\mathrm{rand}}$). In our
experiment, we set k to 1300, which is about half the size of the Danish
dataset. We compare the results with two baselines, one trained only with
Danish data ($\mathrm{da}$) and another one trained with the aggregated
dataset of Danish and _all_ English samples
($\mathrm{da}+\mathrm{en}_{\mathrm{all}}$). The results are in Table 5.

Results confirmed our hypothesis that we can further improve cross-lingual
transfer by selecting samples that are more transferable than others.
$\mathrm{da}+\mathrm{en}_{\mathrm{top}}$ showed the best performance, while
$\mathrm{da}+\mathrm{en}_{\mathrm{bottom}}$ and
$\mathrm{da}+\mathrm{en}_{\mathrm{rand}}$ performed worse than
$\mathrm{da}+\mathrm{en}_{\mathrm{all}}$. This shows that naïvely using all
samples in the transfer language (English) is not necessarily the best way to
conduct cross-lingual transfer.

Threshold | Additional | Macro
---|---|---
OFF | NOT | std | data size | F1
0.8 | 0.2 | 0.1 | 3533 | 0.7693
0.8 | 0.2 | 0.125 | 29681 | 0.7793
0.8 | 0.3 | 0.1 | 7956 | 0.7716
0.8 | 0.3 | 0.125 | 83782 | 0.7738
0.9 | 0.2 | 0.1 | 2769 | 0.7741
0.9 | 0.2 | 0.125 | 19590 | 0.7709
0.9 | 0.3 | 0.1 | 7192 | 0.7707
0.9 | 0.3 | 0.125 | 73691 | 0.7453
Baseline | 0 | 0.7754
Table 4: Results of data augmentation from semi-supervised labels. F1 scores are measured over the validation split of English data. Train data | $da$ | $da+en_{all}$ | $da+en_{top}$ | $da+en_{bottom}$ | $da+en_{rand}$
---|---|---|---|---|---
Macro F1 | 0.77 | 0.78 | 0.84 | 0.72 | 0.72
Table 5: Results of cross-lingual data augmentation on the Danish validation
data. $da$ refers to the original Danish training data, and
$\mathrm{en}_{\mathrm{all}}$ is the entire English training dataset.
$\mathrm{en}_{\mathrm{top}}$, $\mathrm{en}_{\mathrm{bottom}}$,
$\mathrm{en}_{\mathrm{rand}}$ are the subsets of samples according to the TED.

##  5 Analysis and Discussion

In this section, we analyze how cross-lingual data selection could help
improve performance. In addition, we discuss limitations of the proposed
metric, TED, and some negative results with masking offensive words with a
hope to provide insights for future work.

###  5.1 How Does Cross-lingual Data Selection Help?

We showed that our data augmentation strategy using data from other languages
helps improve the target task performance in Section 4.2. Here, we investigate
why cross-lingual data selection was helpful.

Figure 1: tSNE visualization of mBERT sentence embeddings of OLID samples.
Samples are color coded according to their language (ar:Arabic, da:Danish,
en:English, el:Greek, and tr:Turkish).

We first take a look at the embedding space of mBERT to understand why
language-level data selection, according to language-level TED, was
beneficial. We randomly sampled a thousand samples from each language and
visualized their sentence embeddings using tSNE [Maaten and Hinton, 2008] in
Figure 1. From the visualization, we observed that the examples formed rough
clusters based on their language. Interestingly, English and Danish clusters
are placed near one another. This aligns with our experimental result in the
previous section, where we found English to be the most transferable language
to Danish by language-level TED. We speculate that this proximity in the
embedding space may be related to the improvement yielded when English samples
with low TED were added to the Danish dataset. mBERT might have benefited from
the additional English data even while training a Danish classifier because
the examples were relatively close to each other in the shared embedding
space.

In addition, we manually inspect the examples with low TED scores which we
assumed to be more transferable. Examples in Table 6 reveal that the samples
with low TED are the ones that did not change significantly after the
translation procedure. These samples often contain words used in both
languages colloquially (e.g., creepy, fool), and tend to be short with a
rather simple grammatical structure. We posit that this simplistic nature of
the samples with low TED made themselves more translatable, thus more
transferable, and led to improvements via cross-lingual transfer.

###  5.2 Limitations of TED

TED measures the transferability of an example with the help of a machine
translation system. Incorporating an external off-the-shelf translator is
convenient in that we do not need to build an additional translation system
for multiple pairs of languages. However, still, the computation of TED comes
with a cost of translating all samples for all possible transfer-target
language pairs. Another limitation of our method is that the quality of data
selection relies on the performance of the employed machine translation
system. This dependency may lead to the misrepresentation of transferability
in low-resource language samples because the quality of translation systems in
these languages are generally deficient. We believe that the different
approaches commonly used for cross-lingual transfer (e.g., alignment methods)
may pave the way for building a transferability metric that does not rely on
external translation modules.

###  5.3 Offensive Words in Inoffensive Contexts

In our pilot experiment, we fine-tuned BERT with the OLID from OffensEval 2019
[Zampieri et al., 2019b]. The model’s initial performance was around 0.80
macro F1, which is comparable considering that the best performance from
OffensEval 2019 was 0.82 [Liu et al., 2019]. Qualitative analysis on the
false-positive cases, however, showed that the model tends to classify tweets
that include offensive words as offensive, regardless of the context. For
example, “@USER And the fact he called you a b*tch after you respectfully told
him your preference..” was classified as offensive although the term “b*tch”
was not used to express any aggression toward the listener. Offensive words
are also often used for alternative motives: as a topic of the statement or
even to emphasize a positive sentiment. We have found many cases in the
dataset where offensive terms have not been used in a despicable manner (e.g.,
“f*cking awesome”). However, since most offensive words are paired with
aggressive intentions, the model’s prediction seemed to be dictated by the
presence of these words, ignoring the subtle context.

Our attempt to help the model focus more on the context and differentiate
these subtle cases was to randomly mask some of the offensive words during
training. The intuition was to encourage the model to attend to the context
instead of specific terms by partially removing the dependency on certain
words. During model training, when an input tweet contained words in the
offensive word list777https://www.cs.cmu.edu/ biglou/resources/,
https://www.freewebheaders.com/full-list-of-bad-words-banned-by-google,
https://github.com/LDNOOBW/List-of-Dirty-Naughty-Obscene-and-Otherwise-Bad-
Words, we randomly replaced them with a [PAD] token. We used the unmasked,
original sample at inference time. We expected this procedure to help the
model become more robust against different contexts of offensive word usage.
Unfortunately, the masking strategy did not result in quantitative gains. A
possible explanation for the performance decline could be that the naïve
masking excessively deleted offensive words that were actually used
offensively. A more balanced approach would be required to address this
limitation in future work.

Original (English) |  Translated (Danish)
---|---
@USER Creepy |  @USER Creepy
@USER Fool! |  @USER Fool!
#RestoreHumanity #AntiFa September 22: Stop the fascist NVU in #Amsterdam: URL HT @USER |  #RestoreHumanity #AntiFa September 22: Stop det fascistiske NVU in #Amsterdam: URL HT @USER
@USER I’M SO FU*KING READY |  @USER I’M SO FU*KING KLAR
@USER @USER so sad #taketworeferenceswithmoniqueandchloe x |  @USER @USER så trist #taketworeferenceswithmoniqueandchloe x
Table 6: English samples with low TED when transferred to Danish. Most
examples were not changed significantly after the translation.

##  6 Related Work

Computational methods to identify offensive language have been studied in many
different aspects [Davidson et al., 2017, Schmidt and Wiegand, 2017].
Researchers have focused on a variety of categories of offensive language such
as sexism, racism, and hate speech in general. ?) identified a racial bias in
hate speech detection datasets and proposed better annotation methods to
address the problem. ?) pointed out the gender bias in abusive language
detection models and suggested a de-biasing algorithm. ?) introduced a more
fine-grained hate speech identification task than binary classification, and
presented an architecture that leverages Conditional Variational Autoencoder
(CVAE).

Large-scale pre-trained models like BERT have achieved state-of-the-art
results in various NLP tasks [Devlin et al., 2019, Yang et al., 2019]. ?), ?),
and ?) explored the multilinguality of mBERT and confirmed the model’s
effectiveness in cross-lingual transfer. In the task of offensive language
detection, [Liu et al., 2019] has adopted BERT to solve the problem. In our
work, we also use mBERT but improve the method’s ability under a multilingual
setting by leveraging cross-lingual transfer.

##  7 Conclusion

In this paper, we describe NLPDove’s approach to SemEval-2020 Task 12:
Multilingual Offensive Language Identification in Social Media. The system
yielded significant results in the competition for multiple languages,
confirming the strength of large-scale pre-trained language models and the
importance of various preprocessing schemes and model ensembling. We examine
two data augmentation strategies and propose a new metric, TED, to quantify
cross-lingual transferability. In qualitative analysis, we inspect factors why
data selection with TED increased performance. We also present the limitations
of our system, mainly failing to detect the speaker’s intention expressed
subtly in the context, hoping to offer valuable insights and elicit future
work in the field.

## References

  * [Çöltekin, 2020]  Çağrı Çöltekin.  2020\.  A Corpus of Turkish Offensive Language on Social Media.  In Proceedings of the 12th International Conference on Language Resources and Evaluation. ELRA.
  * [Chen et al., 2018]  Xilun Chen, Yu Sun, Ben Athiwaratkun, Claire Cardie, and Kilian Weinberger.  2018\.  Adversarial deep averaging networks for cross-lingual sentiment classification.  Transactions of the Association for Computational Linguistics, 6:557–570.
  * [Conneau and Lample, 2019]  Alexis Conneau and Guillaume Lample.  2019\.  Cross-lingual language model pretraining.  In Advances in Neural Information Processing Systems, pages 7059–7069.
  * [Davidson et al., 2017]  Thomas Davidson, Dana Warmsley, Michael Macy, and Ingmar Weber.  2017\.  Automated hate speech detection and the problem of offensive language.  In Eleventh international aaai conference on web and social media.
  * [Devlin et al., 2019]  Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.  2019\.  BERT: Pre-training of deep bidirectional transformers for language understanding.  In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pages 4171–4186, Minneapolis, Minnesota, June. Association for Computational Linguistics.
  * [Dodge et al., 2020]  Jesse Dodge, Gabriel Ilharco, Roy Schwartz, Ali Farhadi, Hannaneh Hajishirzi, and Noah A. Smith.  2020\.  Fine-tuning pretrained language models: Weight initializations, data orders, and early stopping.  ArXiv, abs/2002.06305.
  * [Dosono and Semaan, 2019]  Bryan Dosono and Bryan Semaan.  2019\.  Moderation practices as emotional labor in sustaining online communities: The case of aapi identity work on reddit.  In Proceedings of the 2019 CHI Conference on Human Factors in Computing Systems, pages 1–13.
  * [Founta et al., 2018]  Antigoni Maria Founta, Constantinos Djouvas, Despoina Chatzakou, Ilias Leontiadis, Jeremy Blackburn, Gianluca Stringhini, Athena Vakali, Michael Sirivianos, and Nicolas Kourtellis.  2018\.  Large scale crowdsourcing and characterization of twitter abusive behavior.  In Twelfth International AAAI Conference on Web and Social Media.
  * [K et al., 2020]  Karthikeyan K, Zihan Wang, Stephen Mayhew, and Dan Roth.  2020\.  Cross-lingual ability of multilingual bert: An empirical study.  In International Conference on Learning Representations.
  * [Kovaleva et al., 2019]  Olga Kovaleva, Alexey Romanov, Anna Rogers, and Anna Rumshisky.  2019\.  Revealing the dark secrets of BERT.  In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pages 4365–4374, Hong Kong, China, November. Association for Computational Linguistics.
  * [Liu et al., 2019]  Ping Liu, Wen Li, and Liang Zou.  2019\.  NULI at SemEval-2019 task 6: Transfer learning for offensive language detection using bidirectional transformers.  In Proceedings of the 13th International Workshop on Semantic Evaluation, pages 87–91, Minneapolis, Minnesota, USA, June. Association for Computational Linguistics.
  * [Maaten and Hinton, 2008]  Laurens van der Maaten and Geoffrey Hinton.  2008\.  Visualizing data using t-sne.  Journal of machine learning research, 9(Nov):2579–2605.
  * [Mubarak et al., 2020]  Hamdy Mubarak, Ammar Rashed, Kareem Darwish, Younes Samih, and Ahmed Abdelali.  2020\.  Arabic offensive language on twitter: Analysis and experiments.  arXiv preprint arXiv:2004.02192.
  * [Park and Fung, 2017]  Ji Ho Park and Pascale Fung.  2017\.  One-step and two-step classification for abusive language detection on twitter.  In Proceedings of the First Workshop on Abusive Language Online, pages 41–45, Vancouver, BC, Canada, August. Association for Computational Linguistics.
  * [Pires et al., 2019]  Telmo Pires, Eva Schlinger, and Dan Garrette.  2019\.  How multilingual is multilingual BERT?  In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 4996–5001, Florence, Italy, July. Association for Computational Linguistics.
  * [Pitenis et al., 2020]  Zeses Pitenis, Marcos Zampieri, and Tharindu Ranasinghe.  2020\.  Offensive Language Identification in Greek.  In Proceedings of the 12th Language Resources and Evaluation Conference. ELRA.
  * [Pitsilis et al., 2018]  Georgios K. Pitsilis, Heri Ramampiaro, and Helge Langseth.  2018\.  Detecting offensive language in tweets using deep learning.  CoRR, abs/1801.04433.
  * [Qian et al., 2018]  Jing Qian, Mai ElSherief, Elizabeth Belding, and William Yang Wang.  2018\.  Hierarchical CVAE for fine-grained hate speech classification.  In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pages 3550–3559, Brussels, Belgium, October-November. Association for Computational Linguistics.
  * [Roberts, 2014]  Sarah T Roberts.  2014\.  Behind the screen: The hidden digital labor of commercial content moderation.  Ph.D. thesis, University of Illinois at Urbana-Champaign.
  * [Rosenthal et al., 2020]  Sara Rosenthal, Pepa Atanasova, Georgi Karadzhov, Marcos Zampieri, and Preslav Nakov.  2020\.  A Large-Scale Semi-Supervised Dataset for Offensive Language Identification.  In arxiv.
  * [Sap et al., 2019]  Maarten Sap, Dallas Card, Saadia Gabriel, Yejin Choi, and Noah A. Smith.  2019\.  The risk of racial bias in hate speech detection.  In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics, pages 1668–1678, Florence, Italy, July. Association for Computational Linguistics.
  * [Schmidt and Wiegand, 2017]  Anna Schmidt and Michael Wiegand.  2017\.  A Survey on Hate Speech Detection Using Natural Language Processing.  In Proceedings of the Fifth International Workshop on Natural Language Processing for Social Media. Association for Computational Linguistics, pages 1–10, Valencia, Spain.
  * [Sennrich et al., 2016]  Rico Sennrich, Barry Haddow, and Alexandra Birch.  2016\.  Improving neural machine translation models with monolingual data.  In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 86–96, Berlin, Germany, August. Association for Computational Linguistics.
  * [Sigurbergsson and Derczynski, 2020]  Gudbjartur Ingi Sigurbergsson and Leon Derczynski.  2020\.  Offensive Language and Hate Speech Detection for Danish.  In Proceedings of the 12th Language Resources and Evaluation Conference. ELRA.
  * [Wolf et al., 2019]  Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, R’emi Louf, Morgan Funtowicz, and Jamie Brew.  2019\.  Huggingface’s transformers: State-of-the-art natural language processing.  ArXiv, abs/1910.03771.
  * [Wu and Dredze, 2019]  Shijie Wu and Mark Dredze.  2019\.  Beto, bentz, becas: The surprising cross-lingual effectiveness of BERT.  In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), pages 833–844, Hong Kong, China, November. Association for Computational Linguistics.
  * [Wulczyn et al., 2017]  Ellery Wulczyn, Nithum Thain, and Lucas Dixon.  2017\.  Ex machina: Personal attacks seen at scale.  In Proceedings of the 26th International Conference on World Wide Web, pages 1391–1399.
  * [Xu and Yang, 2017]  Ruochen Xu and Yiming Yang.  2017\.  Cross-lingual distillation for text classification.  In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 1415–1425, Vancouver, Canada, July. Association for Computational Linguistics.
  * [Yang et al., 2019]  Zhilin Yang, Zihang Dai, Yiming Yang, Jaime Carbonell, Russ R Salakhutdinov, and Quoc V Le.  2019\.  Xlnet: Generalized autoregressive pretraining for language understanding.  In Advances in neural information processing systems, pages 5754–5764.
  * [Zampieri et al., 2019a]  Marcos Zampieri, Shervin Malmasi, Preslav Nakov, Sara Rosenthal, Noura Farra, and Ritesh Kumar.  2019a.  Predicting the Type and Target of Offensive Posts in Social Media.  In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics (NAACL), pages 1415–1420.
  * [Zampieri et al., 2019b]  Marcos Zampieri, Shervin Malmasi, Preslav Nakov, Sara Rosenthal, Noura Farra, and Ritesh Kumar.  2019b.  Semeval-2019 task 6: Identifying and categorizing offensive language in social media (offenseval).  In Proceedings of the 13th International Workshop on Semantic Evaluation, pages 75–86.
  * [Zampieri et al., 2020]  Marcos Zampieri, Preslav Nakov, Sara Rosenthal, Pepa Atanasova, Georgi Karadzhov, Hamdy Mubarak, Leon Derczynski, Zeses Pitenis, and Çağrı Çöltekin.  2020\.  SemEval-2020 Task 12: Multilingual Offensive Language Identification in Social Media (OffensEval 2020).  In Proceedings of SemEval.


# Local structural distortions drive magnetic molecular field in a
compositionally complex spinel oxide

Rukma Nevgi  Contributed equally<EMAIL_ADDRESS>Department of
Physics, Indian Institute of Science, Bengaluru 560012, India  Subha Dey
Contributed equally  Department of Physics, Indian Institute of Science,
Bengaluru 560012, India  Nandana Bhattacharya  Department of Physics, Indian
Institute of Science, Bengaluru 560012, India  Tinku Dan  Deutsches
Elektronen-Synchrotron DESY, 22607 Hamburg, Germany  Sujay Chakravarty  UGC-
DAE CSR Kalpakkam Node Kokilamedu-603104, Tamilnadu, India  S. D. Kaushik
UGC-DAE Consortium for Scientific Research Mumbai Centre, R5 Shed, Bhabha
Atomic Research Centre, Mumbai 400085, India  Christoph Klewe  Advanced Light
Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
George E. Sterbinsky  Advanced Photon Source, Argonne National Laboratory,
Lemont, Illinois 60439, USA  Srimanta Middey<EMAIL_ADDRESS>Department of
Physics, Indian Institute of Science, Bengaluru 560012, India

###### Abstract

A core challenge in understanding high entropy oxides (HEOs) is how these
systems, with five or more cations at a crystallographic site, can withstand
local distortions while preserving a uniform structure on a larger scale. We
address this for spinel HEO by comparatively examining extended X-ray
absorption fine structure (EXAFS) on (Mn0.2Co0.2Ni0.2Cu0.2Zn0.2)Cr2O4
($A^{5}$Cr2O4) and its parent counterparts $A$Cr2O4 ($A$= Mn, Co, Ni, Cu, Zn).
Unlike the HEO with rock-salt structure, the element-specific distortions in
disordered sublattice go beyond the first neighbor here. Moreover, the
tetragonal distortion around the Cu2+ ion, known as a textbook example of the
Jahn-Teller effect, is highly reduced in $A^{5}$Cr2O4 compared to CuCr2O4.
Despite variations in the A-O bond lengths, the inter-cationic distances
remained remarkably similar. This affirms a high level of flexibility in the
positioning of oxygen, enabling them to adapt to the overall cubic symmetry.
Despite containing multiple magnetic ions, the Curie-Weiss temperature and
effective magnetic moments of $A^{5}$Cr2O4 are similar to those of NiCr2O4.
This can be attributed to both materials’ comparable local bond lengths around
Cr, as evidenced by EXAFS analysis. This study conclusively presents a method
for elucidating how local structural distortions influence the macroscopic
properties of compositionally complex quantum materials.

The periodic arrangement of atoms/ions/molecules within crystalline materials
is the backbone of their diverse electronic, magnetic, and topological
properties. Conventionally, crystalline materials are synthesized based on the
principle of enthalpy minimization. However, in recent years, there has been a
surge of interest in high-entropy materials that break this paradigm, where
high configurational entropy drives structure formation George:2019p515 ;
Sarkar:2019p1806236 ; Oses:2020p295 ; Musico:2020p040912 ; Brahlek:2022p110902
; Kotsonis:2023p5587 ; Mazza:2024embracing . Originally introduced for
multicomponent alloys Cantor:2004p213 ; Yeh:2004p299 , this concept was
extended to oxide ceramics in 2015 by demonstrating the stabilization of
Mg0.2Co0.2Ni0.2Cu0.2Zn0.2O in a rock-salt structure Rost:2015p8485 . Since
then, high entropy oxides (HEOs) have been synthesized with a variety of
structures, such as fluorites ($A$O2-δ) Djenadic:2017p102 , perovskites
($AB$O3) Jiang:2018p116 ; Sharma:2018p060404 ; Patel:2020p071601 ;
Brahlek:2020p054407 , spinels ($AB_{2}$O4) Musico:2019p104416 ;
Sharma:2021p17971 ; Johnstone:2022p20590 , and pyrocholores ($A_{2}B_{2}$O7)
Wright:2020p76 ; Jiang:2020p4196 ; Kinsler:2020p104411 , where at least one of
the crystallographic sites is occupied by five or more elements in equal or
nearly equal atomic fractions. Despite not all being entropy-stabilized
Brahlek:2022p110902 , these compositionally complex oxides (CCOs) exhibit
interesting properties beyond their single element counterparts and hold
potential for applications such as energy storage, catalysis, and microwave
absorption Sarkar:2018p3400 ; Chen:2018p11129 ; Braun:2018p1805004 ;
Kante:2023p5329 ; Patel:2023p031407 ; Zhao:2023p2210243 ; Schweidler:2024p1 .

Deciphering the interplay among disorder, distortions, and electronic/magnetic
properties within a CCO is a major hurdle Aamlid:2023p5991 . In conventional
oxides with low disorder, distortions around individual cations are generally
related to their ionic radii, coordination numbers, and oxidation states,
which control electron hopping and magnetic exchange interaction strength. The
local distortions around each cation within the disordered sublattice of CCO
are expected to be highly variable and likely to deviate significantly from
the average long-range structure probed by the diffraction technique. It is
also necessary to determine the extent of this local distortion variation
across neighboring elements and how it affects the material’s properties. To
address these issues, we employ the extended X-ray absorption fine structure
(EXAFS) technique, which is an element-specific method used to study the local
chemical distribution (length scale $\sim$ 1-10 Å) around particular atoms
Ruffoni:2007p421 ; Newville:2014p33 ; Rehr:2000p621 . EXAFS spectra are
specifically sensitive to the coordination number, bond distances, and atomic
species surrounding the core atom, providing a relatively simple way to
understand the local structural distortion. Interestingly, EXAFS studies have
shown that the variation in cation-specific bond lengths is confined only to
the first coordination shell in the case of rock-salt HEOs Rost:2017p2732 ;
Pu:2023peadi8809 . This work focuses on how spinel oxide handles local
distortions and how these influence the magnetic interaction energies.

Figure 1: Structural characterization using X-ray diffraction. a Schematic of
$A^{5}$Cr2O4 with cubic spinel structure having Cr at the octahedral site and
$A$ (= Mn, Co, Ni, Cu and Zn) at the tetrahedral site. b Rietveld refined XRD
data for CuCr2O4 and ZnCr2O4 along with $A^{5}$Cr2O4. c The lattice parameters
for the parent compounds and $A^{5}$Cr2O4 as obtained from the Rietveld
analysis. The parameter $a$ in the tetragonal phases of NiCr2O4 and CuCr2O4
have been multiplied by $\sqrt{2}$ for ease of comparison.

The normal $AB_{2}$O4 spinel consists of a diamond lattice formed by the
tetrahedrally coordinated $A$ site and a pyrochlore lattice formed by the
octahedrally coordinated $B$ site [Fig. 1(a)]. The spinel family has been
extensively studied for over a century due to the observation of various
phenomena, such as magnetic ordering, frustrated magnetism, orbital ordering,
charge ordering, metal-insulator transitions, etc Tsurkan:2021p1 . We focused
on the $A$Cr2O4 family of compounds with normal spinel structures and
successfully synthesized a new compound:
(Mn0.2Co0.2Ni0.2Cu0.2Zn${}_{0.2})$Cr2O4 (hereafter referred to as
$A^{5}$Cr2O4). The individual members MnCr2O4 and CoCr2O4 are cubic and become
ferrimagnetic at $T_{c}$ values of 41 K and 93 K, respectively
Tomiyasu:2004p214434 ; Bhowmik:2006p144413 ; Yamasaki:2006p207204 ;
Dey:2014p184424 . Additionally, they exhibit multiferroic behavior below 18 K
and 27 K Tomiyasu:2004p214434 ; Bhowmik:2006p144413 ; Yamasaki:2006p207204 ;
Dey:2014p184424 . Due to the Jahn-Teller activity of the Ni2+ and Cu2+ ions,
NiCr2O4 and CuCr2O4 undergo cubic to tetragonal transitions below 310 K and
853 K, respectively. They transform into an orthorhombic phase at 65 K and 125
K, respectively, accompanied by a ferrimagnetic transition
Suchomel:2012p054406 . On the other hand, ZnCr2O4 is cubic at room temperature
and exhibits an antiferromagnetic ordering transition below 12 K
Dutton:2011p064407 .

In the present work, we probed the modification of the local structure of
$A^{5}$Cr2O4 compared to that of its five undoped counterparts ($A$Cr2O4, $A$
= Mn, Co, Ni, Cu, Zn) at room temperature. X-ray diffraction (XRD) and X-ray
absorption spectroscopy (XAS) of the transition metal $L_{3,2}$ edges
confirmed the desired normal spinel structure of $A^{5}$Cr2O4 with cubic
symmetry. Our comprehensive EXAFS measurements revealed a high degree of
similarity between the local environment surrounding Cr in $A^{5}$Cr2O4 and
that surrounding Cr in pristine CoCr2O4, ZnCr2O4, and NiCr2O4. However, the
local structural distortions around the individual $A$-sites of $A^{5}$Cr2O4
differ from each other and persist beyond the first neighbor. Interestingly,
the Jahn-Teller distortions typically observed in the CuCr2O4 are
significantly suppressed in $A^{5}$Cr2O4, which is compensated for by a
reduction in the length of the bonds surrounding the Mn. Moreover, the oxygen
atoms in $A^{5}$Cr2O4 are rearranged relative to their original positions in
the parent compounds to accommodate the variations in local distortions. This
enables $A^{5}$Cr2O4 to maintain its overall cubic structure. We found that
the magnetic response of $A^{5}$Cr2O4 is contributed by all magnetic ions:
Cr3+ and $A^{2+}$ ($A$= Mn, Co, Ni and Cu). Finally, EXAFS and Curie-Weiss
analysis of the magnetic data establish a direct correlation between the mean-
field magnetic interaction energy scale and the Cr-O and Cr-Cr bond lengths.

Figure 2: Determination of oxidation state using X-ray absorption
spectroscopy. a Cr $L_{3,2}$ edge in MnCr2O4 and $A^{5}$Cr2O4. b Mn $L_{3,2}$
edge in MnCr2O4 and $A^{5}$Cr2O4. c Co $L_{3,2}$ edge in CoCr2O4 and
$A^{5}$Cr2O4. d Ni $L_{3,2}$ edge in NiCr2O4 and $A^{5}$Cr2O4. e Cu $L_{3,2}$
edge in CuCr2O4 and $A^{5}$Cr2O4. The spectra of Cr and Mn for MnCr2O4 is
taken from Ref. Vanderlaan:2010p067405, . The spectra of Co for CoCr2O4 is
adapted from Ref. kim:2009p94, . f Spin configurations of Cr, Mn, Co, Ni, Cu,
and Zn cations in $A^{5}$Cr2O4. The energy gap between $t_{2g}$ and $e_{g}$ is
not according to the scale.

Results:

Synthesis and crystal structure: The synthesis of polycrystalline samples of
five parent compounds $A$Cr2O4 (A = Mn, Co, Ni, Cu and Zn) and $A^{5}$Cr2O4
was carried out using a conventional solid-state synthesis route (details are
provided in the Methods section). The powder X-ray diffraction (XRD) pattern
of $A^{5}$Cr2O4 at room temperature is compared with that of two parent
members, tetragonal CuCr2O4 and cubic ZnCr2O4, in Fig. 1(b). Similar to
ZnCr2O4, the diffraction pattern of $A^{5}$Cr2O4 can be indexed and refined
with a normal spinel structure with cubic symmetry having a space group of
$Fd\bar{3}m$ (space group number: 227). The diffraction patterns and
structural information obtained from the refinement of all six compounds are
shown in the Supplementary Information (Table S1 and Fig. S1). The lattice
constants and lattice volumes for the five parent members and $A^{5}$Cr2O4 at
room temperature are shown in Fig. 1(c). For comparison, the lattice constant
$a$ of the tetragonal members NiCr2O4 and CuCr2O4 is multiplied by $\sqrt{2}$
(see Supplementary Fig. S2). The trend in lattice parameters and volume can be
understood by considering the ionic radii of $A^{2+}$ ions. The average ionic
radii (0.592 Å) of the $A$-site for $A^{5}$Cr2O4 are closer to those of Zn2+
(0.60 Å) and Co2+ (0.58 Å) [ionic radii of Mn2+: 0.66 Å, Ni2+: 0.55 Å, and
Cu2+: 0.57 Å] Shannon:1970p1046 , leading to similar unit cell volumes of
$A^{5}$Cr2O4 and $A$Cr2O4 ($A$= Co and Zn). Although NiCr2O4 is tetragonal,
the Jahn-Teller distortion is very small at 300 K, and the unit cell volume is
very similar. It can also be inferred from Fig. 1(c) that the Mn and Cu ions
are likely to experience internal stress (compressive for Mn and tensile for
Cu) when introduced into $A^{5}$Cr2O4, leading to strong local distortions.

Figure 3: Probing the local structure using EXAFS. a The k weighted EXAFS
spectra in $A^{5}$Cr2O4. The Fourier transform of the EXAFS spectra at b Cr
$K$-edge and c $A$ $K$-edges in the parent oxides and $A^{5}$Cr2O4. The first
and second nearest neighbor distances have also been shown as an inset of
panels b and c.

Transition metal valency and crystal field environment: In all parent $A$Cr2O4
compounds, the cations $A^{2+}$ occupy the tetrahedral site, while Cr3+
occupies the octahedral site Tsurkan:2021p1 . To explore the same phenomenon
in $A^{5}$Cr2O4, we carried out element-specific XAS experiments on the
$L_{3,2}$ edges of transition metal ions because the XAS spectral line shape
for the 2$p^{6}$3$d^{n}\rightarrow$2$p^{5}$3$d^{n+1}$ transition is strongly
dependent on the valency, spin character of the initial state and crystal
field environment of the system Stohr:2006book . The XAS spectra for the
$L_{3,2}$ edges of Cr, Mn, Co, Ni, and Cu in $A^{5}$Cr2O4, recorded in total
electron yield mode, were compared with those of the corresponding parent
compounds, as shown in Fig. 2 (a)-(e). It is evident that the spectra of Cr,
Mn, Co, and Ni for $A^{5}$Cr2O4 look exactly similar to the corresponding
edges of the parent compounds Windsor:2017p224413 ; Vanderlaan:2010p067405 ;
kim:2009p94 . Although the main features of Cu $L_{3,2}$ XAS for $A^{5}$Cr2O4
are quite similar to those of the parent CuCr2O4, the features at
approximately 933.9 eV and 953.7 eV are more intense. This slight difference
may be attributed to the reduced Jahn-Teller distortion in $A^{5}$Cr2O4
(demonstrated in the latter part of the manuscript). Overall, our XAS
measurements further established a normal spinel structure similar to that of
all the parent compounds. Fig. 2(f) shows the expected spin configurations for
each of the cations of $A^{5}$Cr2O4, according to the oxidation state found by
XAS. This is further corroborated by the Curie‒Weiss analysis of magnetic
susceptibility, which is demonstrated in the latter part of the manuscript.

Element specific local distortions using EXAFS: To investigate the local
structural distortions around Cr, Mn, Co, Ni, Cu, and Zn, we recorded the
$K$-edge EXAFS spectra. The spectra of every transition metal edge were
calibrated using the corresponding standard metal foils. To avoid interference
from the next absorption edge in $A^{5}$Cr2O4, the spectra were truncated
above 12 Å-1 in k space. Similar features across Mn, Co, Ni, Cu, and Zn
$K$-edges [Fig. 3(a)] suggest a similar coordination geometry with a uniform
distribution throughout the lattice. The Fourier transform (FT) of
$k^{2}.\chi(k)$ of Cr and $A$ $K$-edges for each of the parent compounds and
$A^{5}$Cr2O4 are shown in Fig. 3(b) and (c), respectively. The first peak at
1.55 Å in both Cr and $A$ $K$-edge data suggests similar Cr-O and $A$-O
distances in parent compounds. The second peak at 2.5 Å in Cr $K$-edge data
corresponds to Cr-Cr distance, while the one at 3 Å in $A$ $K$-edge data
corresponds to $A$-Cr distance, implying different cation environments. We
also note that the real scattering distance shifts by approximately 0.5 Å as
the phase shift in the Fourier transform remains uncorrected.

Figure 4: Analysis of local structure in the octahedral environment. The
Fourier transformed EXAFS spectra along with the fitted data [the magnitude
$|\chi(R)|$ and the real part Re. $\chi(R)$] in a ZnCr2O4, b CuCr2O4 and c
$A^{5}$Cr2O4. The distance between d Cr and the first neighbor O, e Cr and the
second neighbor Cr, f Cr and the third neighbor $A$ cations in pristine
chromite spinels and $A^{5}$Cr2O4. Due to Jahn-Teller distortion, NiCr2O4 and
CuCr2O4 display two bond lengths (drawn as open circles), whose weighted
average (denoted by the closed circle) is also plotted for ease of comparison.
Figure 5: Analysis of local structure in the tetrahedral environment. The
magnitude of the Fourier transformed EXAFS spectra along with fitting obtained
at the a Mn $K$-edge in MnCr2O4 and $A^{5}$Cr2O4, b Zn $K$-edge in ZnCr2O4 and
$A^{5}$Cr2O4 and c Cu $K$-edge in CuCr2O4 and $A^{5}$Cr2O4. A comparison of
bond distances between d the $A$ cations and the first neighbor O, e the $A$
cations and the second neighbor O, f two $A$ cations in the pristine chromite
oxides and $A^{5}$Cr2O4. In e, due to Jahn-Teller distortion, NiCr2O4, and
CuCr2O4 display two bond lengths between $A$ cations and O anions (drawn as
open circles), whose weighted average (closed cycle) is plotted for ease of
comparison. As one of the second neighbor Ni-O bond length $\sim$ 3.23 Å of
NiCr2O4 is the same as in $A^{5}$Cr2O4, no distinction can be made between the
two values in panel e.

The FT of $k^{2}.\chi(k)$ for Cr $K$ in $A^{5}$Cr2O4 [Fig. 3(b)] shows similar
features like the parent compounds (except CuCr2O4). However, Fig. 3(c)
reveals significant changes in local structures around Cu and Mn in
$A^{5}$Cr2O4 compared to CuCr2O4 and MnCr2O4, respectively. This is likely due
to the difference in crystal symmetry (cubic vs. tetragonal) and lattice
volume changes. Local structures around Co, Ni, and Zn in $A^{5}$Cr2O4 are
similar to their parent compounds, except for a slight change in Zn-Cr
distance. These spectra clearly demonstrate that the local distortions vary
across the $A$-sites, extending beyond the first neighbor in $A^{5}$Cr2O4.

To quantify the effect of all differences shown in Fig. 3, we performed
fittings for the $A$ $K$-edge spectra ($A$ = Mn, Co, Ni, Cu and Zn) in every
parent compound in the $k$ range of 2 to 14 Å-1 and the $R$ range of 1 to 4.5
Å (details are in the Methods section). For the Cr $K$-edge, the $k$ range of
2 to 12 Å-1 and the $R$ range of 1 to 3.7 Å were employed in fittings. The
analysis considered structural symmetries determined by XRD. The best fits
obtained for the Cr local structure in cubic ZnCr2O4, $A^{5}$Cr2O4 and
tetragonal CuCr2O4 are depicted in Fig. 4 (a)-(c). In the cubic model, a Cr
cation has 6 O anions as first neighbors (Fig. 4 (d)), 6 Cr cations as second
neighbors (Fig. 4 (e)), and 6 $A$ cations as third neighbors (Fig. 4 (f)). In
the tetragonal model, six equal bond lengths in each case split into equal
bond distances with coordination four and two, whose weighted average is
plotted (denoted by closed circles) for easier comparison (for NiCr2O4 and
CuCr2O4). From the analysis, we could infer that the bond distances Cr-O (1.97
Å), Cr-Cr (2.96 Å) and Cr-$A$ (3.46 Å) in $A^{5}$Cr2O4 are akin to that of
CoCr2O4, ZnCr2O4 and also with the weighted average bond lengths of NiCr2O4.
Consistent with the difference in lattice constant, these bond lengths are
higher in MnCr2O4. Also, the average Cr-O and Cr-$A$ bond distances of CuCr2O4
are lower compared to $A^{5}$Cr2O4.

Cr EXAFS, averaging local Cr environments, can’t distinguish distortions
caused by specific $A$ cations ($e.g.$ Mn vs Cu). Analyzing $A$-site EXAFS in
$A^{5}$Cr2O4 versus $A$Cr2O4 reveals these element-specific distortions [see
Fig. 5 (a-c), Fig. S3 and Supplementary Tables S2, S3, and S4]. Interestingly,
$A$ ions share the same coordination for first-neighbor oxygen and fourth-
neighbor $A$ cation for both cubic and tetragonal structures. In case of cubic
MnCr2O4, we find that Mn has 4 O at $R$ =1.99 Å , 12 O at $R$ =3.32 Å , 12 Cr
at $R$ =3.50 Å and 4 Mn as at $R$ =3.64 Å as direct scatterers. The Cr-Mn
distance obtained from the Cr $K$-edge EXAFS analysis and the Mn-Cr distance
obtained from Mn $K$-edge EXAFS fitting were very similar. In the case of
tetragonal CuCr2O4, the analysis of Cu $K$-edge finds 4 O at $R$ = 1.95 Å , 8
O at $R$ = 3.46 Å and 4 O at $R$ = 3.04 Å , 8 Cr at $R$ = 3.52Å and 4 Cr at
$R$ = 3.26 Å , and 4 Cu at $R$ = 3.61 Å as direct scatterers.

The EXAFS fittings of each $A$-site of $A^{5}$Cr2O4 were performed considering
cubic symmetry in accordance with the XRD result. Excellent fitting has been
found for each case, including Cu $K$-edge [Fig. 5 (c)] and Ni $K$-edge (see
Supplementary Fig. S3 (c)). We have also attempted to fit Cu $K$ EXAFS of
$A^{5}$Cr2O4 using tetragonal symmetry, similar to the parent compound
CuCr2O4. However, such fitting results in negative $\sigma^{2}$ (see
Supplementary Table S5) for Cu. This exclusively demonstrates that even the
local Jahn-Teller distortion is either fully absent or highly suppressed in
$A^{5}$Cr2O4. This contrasts sharply with Cu-containing rock-salt HEO, where
the Cu can maintain clear Jahn-Teller distortions locally Rost:2017p2732 ;
Rak:2018p300 .

Figure 6: Magnetic characterization and it’s connection with local structure a
Fitting of inverse magnetic dc susceptibility using Curie-Weiss equation above
$T_{N}$ in $A^{5}$Cr2O4 at 5000 Oe. Inset features field cooled (FC) dc
susceptibility as a function of temperature. -$\theta_{\mathrm{CW}}$ is
plotted as a function of b Cr-Cr bond distance and $A$-site spin and c Cr-O
bond distance and $A$ site spin in parent oxides and $A^{5}$Cr2O4. d A
comparision of the magnetic exchange interaction energy between two Cr cations
($J_{BB}$), between Cr and $A$ ($J_{AB}$), and between two $A$ cations
($J_{AA}$) in MnCr2O4 and $A^{5}$Cr2O4.

The comparison of each neighbor distance among the pristine members and doped
compound reveals several interesting trends (Fig. 5 (d)-(f)). The Mn-O
distance in MnCr2O4 is the largest due to its bigger unit cell volume than
other pristine materials. In $A^{5}$Cr2O4, the first neighbor $A$-O distance
depends on the specific element positioned at the $A$-site. The Co-O, Ni-O,
and Cu-O distances are very similar, whereas Mn-O and Zn-O distances differ.
Notably, the $A$-O bond distances are smaller than those in parent $A$Cr2O4,
indicating that these local variations are not simply due to changes in the
overall crystal volume. Importantly, this study has revealed a strong
variation in second neighbor $A$-O distances in disordered $A^{5}$Cr2O4,
suggesting that local structural distortions extend beyond the first-neighbor
shell. Interestingly, the second-neighbor Mn-O bond length (Fig. 5(e)) is the
shortest among all $A$-O distances in $A^{5}$Cr2O4, which is in stark contrast
to its longest first-neighbor distance (Fig. 5(d)). This strongly suggests
that the oxygen sublattice can adjust to accommodate the variations caused by
different $A$-site cations. The fourth neighbor $A$-$A$ distance is found to
be $\simeq$ 3.58$\pm$ 0.02 Å in the fittings of each $A$-site EXAFS. (See
Supplementary Tables S2, S3 and S4). This $A$-$A$ bond length is comparable to
those in CoCr2O4, NiCr2O4, and ZnCr2O4, but smaller to the ones in MnCr2O4,
and CuCr2O4. The EXAFS analysis suggests that all cation-cation distances in
$A^{5}$Cr2O4 are similar, implying that all $A$ cations form a uniform diamond
sublattice. Consequently, the oxygen anions shift from their ideal positions
to accommodate these local distortions, resulting in varying $A$-O bond
lengths.

Correlation between structural distortions and magnetic interaction: The bond
lengths derived from EXAFS analysis are expected to play a crucial role in
comprehending the strength of magnetic interactions in $A$Cr2O4 spinels. The
theory of ground state magnetic configuration of cubic $AB_{2}$O4 is very
often described by the following Hamiltonian with classical Heisenberg spins
considering $B$-$B$, and $A$-$B$ exchanges, initially proposed by Lyons,
Kaplan, Dwight, and Menyuk Kaplan:2007p3711 ; Kaplan:1960p1460 ;
Tsurkan:2021p1 .

$H=2J_{AB}S_{A}S_{B}\left(\sum_{\langle
ij\rangle}^{A,B}\overrightarrow{\sigma_{i}^{A}}.\overrightarrow{\sigma_{j}^{B}}+\frac{3u}{4}\sum_{\langle
ij\rangle}^{B,B}\overrightarrow{\sigma_{i}^{B}}.\overrightarrow{\sigma_{j}^{B}}\right)$
(1)

The sums are over nearest-neighbor $A$-$B$ and $B$-$B$ pairs and the parameter
$u$ =$\frac{4J_{BB}S_{B}}{3J_{AB}S_{A}}$ and
$\overrightarrow{\sigma_{j}^{\alpha}}$=$\overrightarrow{S_{j}^{\alpha}}$/$S_{j}^{\alpha}$
with $\alpha$=$A$ and $B$. The interaction within the diamond sublattice
($J_{AA}$) has also been claimed to be important in recent studies
Winkler:2009p104418 ; Ederer:2007p064409 . In chromite spinels, the magnetic
interaction between two Cr is a direct exchange and thus depends strongly on
the Cr-Cr distance Winkler:2009p104418 . The superexchange between $A$ and Cr
is mediated through interconnecting oxygen, and the strength will depend on
the bond lengths $A$-O and Cr-O, $A$-O-Cr bond angle and the electronic
configuration of $A$ ions. Due to the presence of multiple magnetic ions at
$A$-site with different $A$-O bond lengths leading to a varying strength of
$J_{AB}$ and $J_{AA}$, the microscopic description of spin arrangements is
expected to be complex in $A^{5}$Cr2O4 and requires a separate detailed study.
Interestingly, a direct dependence of magnetic transition temperatures on the
average crystal structure of perovskite HEOs has been demonstrated, even
though the details of the magnetic features within the magnetically ordered
phase is more complicated Witte:2019p034406 ; Sharma:2020p014404 ;
Mazza:2021p094204 ; Mazza:2022p2200391 ; Su:2022p2358 . In the case of parent
$A$Cr2O4 members, the magnetic frustration caused by antiferromagnetic Cr-Cr
interactions within the pyrochlore sublattice varies, resulting in a very
reduced magnetic ordering temperature compared to the Curie-Weiss temperature
($\theta_{\mathrm{CW}}$) (Supplementary Table S5). As $\theta_{\mathrm{CW}}$
is a measure of molecular field and considered as an approximate indicator of
the strength of mean-field magnetic interaction between the ions
Mugiraneza:2022p95 , we have focused on finding out any relation between
$\theta_{\mathrm{CW}}$ and the bond lengths at 300 K obtained from the EXAFS
analysis.

The temperature-dependent magnetic susceptibility [$\chi$=$M/H$] for
$A^{5}$Cr2O4, measured under a magnetic field ($H$) of 5000 Oe in field cooled
condition has been depicted as an inset of Fig. 6 (a). We found a magnetic
transition around 50 K. The main panel represents the fitting of the inverse
of dc susceptibility at high temperature using molecular field theory of a
ferrimagnet Coey2010

$\chi^{-1}=\frac{T-\theta_{CW}}{C_{A}+2C_{B}}-\frac{C^{{}^{\prime\prime}}}{T-\theta^{{}^{\prime}}}$
(2)

The first term is the hyperbolic high-temperature linear part with a Curie-
Weiss form, where $C_{A}$ and $C_{B}$ correspond to Curie constants related to
the two magnetic sublattices $M_{A}$ and $M_{B}$, respectively.
$\theta_{\mathrm{CW}}$ is the Curie-Weiss temperature. The second term is the
hyperbolic low-$T$ asymptote, where $C^{{}^{\prime\prime}}$ and
$\theta^{{}^{\prime}}$ are constants akin to different Weiss coefficients that
represent the inter and intrasublattice interactions. From this fitting, we
have obtained a Curie-Weiss temperature of $\theta_{\mathrm{CW}}$ = -432 K and
the effective magnetic moment of 6.33 $\mu_{B}$/f.u. using the formula
$\mu_{\mathrm{eff}}$=$\sqrt{\frac{3K_{B}(C_{A}+2C_{B})}{N_{A}}}$
kassem2023structural , where $K_{B}$ is Boltzmann’s constant and $N_{A}$ is
Avogadro’s number. Interestingly, $\mu_{\mathrm{eff}}$ is very similar to the
expected value of 6.26 $\mu_{B}$/f.u., calculated by considering the average
magnetic moments of $A^{2+}$ ($A$ = Mn, Co, Ni, Cu; Zn2+ is nonmagnetic) and
Cr3+ of $A^{5}$Cr2O4
($\mu_{\mathrm{eff}}$=$\sqrt{2\mu_{\mathrm{Cr}}^{2}+\mu_{A}^{2}}$). The most
surprising finding is that despite having a series of magnetic interactions
[Cr-$A$ and $A$-$A^{\prime}$ with $A$, $A^{\prime}$= Mn, Co, Ni, Cu], the
$\theta_{\mathrm{CW}}$ of $A^{5}$Cr2O4 is comparable to NiCr2O4
Suchomel:2012p054406  (also see Supplementary Figure S4) and MnCr2O4
Winkler:2009p104418 . The effective magnetic moment also closely resembles
NiCr2O4 (6.64 $\mu_{B}$/f.u.). These findings also indicate that the net
magnetic interaction, felt by a magnetic ion in CCO, can be treated using a
mean-field approach.

To understand the effect of local distortions on magnetism,
$|\theta_{\mathrm{CW}}|$ for all six compounds have been plotted as a function
of EXAFS derived bond lengths and the $A$-site spin value in Fig. 6(b), (c).
The $\theta_{\mathrm{CW}}$ of the parent compounds $A$Cr2O4 is obtained from
Ref. Lee:2000p3718 ; Suchomel:2012p054406 ; Winkler:2009p104418  and an
average of $A$-site spin ($S_{A}$=1.1) for $A^{5}$Cr2O4 has been considered
for these plots. The Cr-Cr bond length (Fig.6 (b)) is considered as it
corresponds to the Cr-Cr direct exchange. The Cr-O bond length is also plotted
in connection with the $A$-O-Cr superexchange path (Fig.6 (b)). While the
$A$-O bond length also plays a role in $A$-O-Cr superexchange strength, we
were unable to create a similar plot for $A$-O bond lengths because this
distance depends on the specific atom occupying the $A$-site in $A^{5}$Cr2O4.
The $\theta_{\mathrm{CW}}$ of $A^{5}$Cr2O4 is closer to the value of NiCr2O4
and MnCr2O4. We have further evaluated the mean-field magnetic exchange
parameters from our magnetization data, following the process described in
Ref. Winkler:2009p104418  [also see Supplementary]. The exchange interaction
parameters $J_{BB}$ (interactions between two Cr3+), $J_{AB}$ (between
$A^{2+}$ and Cr3+), and $J_{AA}$ (between two $A^{2+}$ cations) have been
compared in Fig. 6(d). The exchange parameters for MnCr2O4 have been adapted
from Ref. Winkler:2009p104418 . Interestingly, the $J_{BB}$ interaction shows
almost no difference between these compounds. However, the $J_{AB}$ and
$J_{AA}$ values for $A^{5}$Cr2O4 higher than those of MnCr2O4. The extraction
of these $J$s using equation 2 is not possible for NiCr2O4 due to an anomaly
in the magnetic susceptibility at the cubic-to-tetragonal transition ($\sim$
315 K, see Supplementary Fig S4). However, Fig.6 (b) and (c) clearly
demonstrate the close similarity between $A^{5}$Cr2O4 and NiCr2O4 in terms of
key parameters like Cr-Cr distance, Cr-O distance, and $A$-site spin and
$\theta_{\mathrm{CW}}$. This strong resemblance highlights the crucial role of
local bond lengths around the Cr ions in determining the mean-field magnetic
interactions within $A^{5}$Cr2O4.

Discussions: We have synthesized a new compositionally complex oxide
$A^{5}$Cr2O4 having a normal spinel structure, with Cr3+ ions occupying the
octahedral site and a uniform distribution of $A^{2+}$ ($A$ = Mn, Co, Ni, Cu,
and Zn) ions in the tetrahedral site. Employing element-specific EXAFS
analysis, our investigation of the local structure reveals several unique
features that distinguish it from previously reported high entropy oxides.
Unlike HEOs with rock-salt structures Rost:2017p2732 ; Rak:2018p300 , where
local Jahn-Teller distortions around Cu2+ ions are typically preserved, our
study reveals a significant reduction or even a complete absence (within the
resolution power of EXAFS) of such distortions in $A^{5}$Cr2O4. In contrast to
previous EXAFS studies of rock-salt HEOs Rost:2017p2732 ; Pu:2023peadi8809 ,
where distortions around $A^{2+}$ cations were limited to the first nearest
neighbors and second-neighbor distances remained uniform, $A^{5}$Cr2O4
exhibits variation in local distortions extending beyond the first neighbors.
Despite variation in $A$-O bond distances, $A$-$A$ distances are uniform,
implying the high flexibility of oxygen sublattices to maintain an overall
cubic structure by adjusting their positions. We have also identified the
magnetic interaction energies of $A^{5}$Cr2O4 are very similar to NiCr2O4 due
to their similar Cr-O and Cr-Cr bond lengths and $A$-site spin value.

Unveiling the temperature dependence of $A^{5}$Cr2O4’s long-range and local
structures presents a compelling avenue for future research as some of the
constituent members undergo structural transitions below room temperature
Suchomel:2012p054406 . Future investigations into the spin arrangements and
potential multiferroic phases are warranted. Furthermore, we believe that our
EXAFS analysis approach, which compares CCO with the constituent parent
members, can be a powerful tool to reveal subtle details regarding structural
modifications in other compositionally complex materials as well. Overall,
this study paves the way for a deeper understanding of the impact of local
distortions in HEOs, enabling the targeted design of materials with tailored
properties.

### Methods

Polycrystalline samples of five parent compounds $A$Cr2O4 (A = Mn, Co, Ni, Cu
and Zn) were synthesized by conventional solid-state synthesis with a
stoichiometric amount of Cr2O3 and AO. The first heating was carried out at
9000 C, followed by a second heat treatment at 13000 C with intermediate
grindings. The annealing of MnCr2O4 and CuCr2O4 were performed in argon and
oxygen atmosphere, respectively, while the rest of the compounds were heated
in air. The $A^{5}$Cr2O4 was synthesized in a similar route in the air. The
sample purity of all samples was checked by powder XRD using a laboratory-
based Rigaku Smartlab diffractometer. The final XRD patterns were further
refined by the Rietveld method using the FULLPROF suite Carvajal:2001p12 . The
temperature-dependent magnetization measurement was carried out in the range
of 5 K to 400 K using a commercial SQUID-VSM MPMS from M/s Quantum Design,
USA. XAS spectra for $L_{3,2}$ edges of Cr, Mn, Co, Ni, Cu of the $A^{5}$Cr2O4
were recorded in total electron yield mode at the beamline 4.0.2 of the
Advanced Light Source, USA. Ni $L_{3,2}$ edge of NiCr2O4 and Cu $L_{3,2}$ edge
of CuCr2O4 were also measured.

EXAFS measurements for all transition metal $K$-edge for all five parent
compounds and $A^{5}$Cr2O4 have been performed at the P65 beamline, PETRA III
Synchrotron Source (DESY, Hamburg, Germany) and at the 20 BM beamline of the
Advanced Photon Source, USA. For EXAFS experiments in transmission geometry,
the absorbers were prepared by uniformly coating the powder samples on scotch
tape. The incident and the transmitted photon energies were simultaneously
recorded using the gas ionization chambers as detectors. At each $K$-edge, at
least three scans were collected to average the statistical noise. The
analysis was carried out using well-established procedures in the DEMETER
suite Ravel:2005p537 .

For the EXAFS fittings, the amplitude reduction factor $S_{0}^{2}$ and
correction to the edge energy $\Delta E_{0}$ were derived from the analysis of
the corresponding standard metal spectra, and these parameters were kept fixed
throughout the analysis. The parameters consisting of correction to the bond
length $\Delta R$ and mean square variation in bond length $\sigma^{2}$ were
varied for each scattering path. For the cubic model, ten and eight
independent parameters were used in the fittings of $A$ $K$-edge and Cr
$K$-edge spectra, respectively. Fourteen independent parameters were used for
the tetragonal model to fit both Cr $K$ and $A$ $K$-edges. In the case of
NiCr2O4, the number of independent parameters was similar to the cubic model
due to the very weak tetragonal distortion.

For $A^{5}$Cr2O4, a model describing a normal cubic spinel structure was
modified to incorporate a solid solution containing equal amounts of Mn, Co,
Ni, Cu and Zn at the tetrahedral site. The coordination numbers were
constrained to maintain consistency with the cubic spinel structure. A
realistic solution-like distribution was simulated for both tetrahedral and
octahedral sites by randomly dividing the concerned coordination shell among
the five $A$ cations. Furthermore, the five cations were confined to a
specific distance from the absorber, independent of the species. The R factor
for every fit was less than 2%, indicating the reliability of the fitting
outcomes.

## Acknowledgements

The authors acknowledge the uses of central facilities of the department of
Physics, IISc Bangalore, funded by the FIST program of DST (Department of
Science and Technology), India. SM acknowledges funding support from a SERB
Core Research grant (Grant No. CRG/2022/001906). RN thanks the Indian
Institute of Science for support through Sir C. V. Raman postdoctoral
fellowship program. SD and NB acknowledge funding from the Prime Minister’s
Research Fellowship (PMRF), MoE, Government of India. RN also thanks Prof.
K.R.S. Priolkar for commenting on the manuscript. UGC-DAE Consortium for
Scientific Research, Kalpakkam Node, Kokilamedu, is acknowledged for providing
a SQUID-VSM MPMS facility for conducting magnetic measurements, which is part
of this work. Portions of this research were carried out at the light source
PETRA III DESY, a member of the Helmholtz Association (HGF). Financial support
by the Department of Science & Technology (Government of India) provided
within the framework of the India@DESY collaboration is gratefully
acknowledged. This research used resources of the Advanced Photon Source, a
U.S. Department of Energy Office of Science User Facility operated by Argonne
National Laboratory under Contract No. DE-AC02-06CH11357. This research used
resources of the Advanced Light Source, which is a Department of Energy Office
of Science User Facility under Contract No. DE-AC02-05CH11231.

## References

  * (1) George, E. P., Raabe, D. & Ritchie, R. O.  High-entropy alloys.  _Nature reviews materials_ 4, 515–534 (2019).
  * (2) Sarkar, A. _et al._ High-entropy oxides: fundamental aspects and electrochemical properties.  _Advanced materials_ 31, 1806236 (2019).
  * (3) Oses, C., Toher, C. & Curtarolo, S.  High-entropy ceramics.  _Nature Reviews Materials_ 5, 295–309 (2020).
  * (4) Musicó, B. L. _et al._ The emergent field of high entropy oxides: Design, prospects, challenges, and opportunities for tailoring material properties.  _APL Materials_ 8, 040912 (2020).  URL https://doi.org/10.1063/5.0003149.  eprint https://pubs.aip.org/aip/apm/article-pdf/doi/10.1063/5.0003149/14563544/040912_1_online.pdf.
  * (5) Brahlek, M. _et al._ What is in a name: Defining “high entropy” oxides.  _APL Materials_ 10, 110902 (2022).  URL https://doi.org/10.1063/5.0122727.  eprint https://pubs.aip.org/aip/apm/article-pdf/doi/10.1063/5.0122727/16490715/110902_1_online.pdf.
  * (6) Kotsonis, G. N. _et al._ High-entropy oxides: Harnessing crystalline disorder for emergent functionality.  _Journal of the American Ceramic Society_ 106, 5587–5611 (2023).
  * (7) Mazza, A. _et al._ Embracing disorder in quantum materials design.  _arXiv preprint arXiv:2402.18379_ (2024).
  * (8) Cantor, B., Chang, I., Knight, P. & Vincent, A.  Microstructural development in equiatomic multicomponent alloys.  _Materials Science and Engineering: A_ 375, 213–218 (2004).
  * (9) Yeh, J.-W. _et al._ Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes.  _Advanced engineering materials_ 6, 299–303 (2004).
  * (10) Rost, C. M. _et al._ Entropy-stabilized oxides.  _Nature communications_ 6, 8485 (2015).
  * (11) Djenadic, R. _et al._ Multicomponent equiatomic rare earth oxides.  _Materials Research Letters_ 5, 102–109 (2017).
  * (12) Jiang, S. _et al._ A new class of high-entropy perovskite oxides.  _Scripta Materialia_ 142, 116–120 (2018).
  * (13) Sharma, Y. _et al._ Single-crystal high entropy perovskite oxide epitaxial films.  _Physical Review Materials_ 2, 060404 (2018).
  * (14) Patel, R. K. _et al._ Epitaxial stabilization of ultra thin films of high entropy perovskite.  _Applied Physics Letters_ 116, 071601 (2020).
  * (15) Brahlek, M. _et al._ Unexpected crystalline homogeneity from the disordered bond network in $\mathrm{La}(\mathrm{C}{\mathrm{r}}_{0.2}\mathrm{M}{\mathrm{n}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}){\mathrm{o}}_{3}$ films.  _Phys. Rev. Mater._ 4, 054407 (2020).  URL https://link.aps.org/doi/10.1103/PhysRevMaterials.4.054407.
  * (16) Musicó, B. _et al._ Tunable magnetic ordering through cation selection in entropic spinel oxides.  _Phys. Rev. Mater._ 3, 104416 (2019).  URL https://link.aps.org/doi/10.1103/PhysRevMaterials.3.104416.
  * (17) Sharma, Y. _et al._ Magnetic texture in insulating single crystal high entropy oxide spinel films.  _ACS applied materials & interfaces_ 13, 17971–17977 (2021).
  * (18) Johnstone, G. H. _et al._ Entropy engineering and tunable magnetic order in the spinel high-entropy oxide.  _Journal of the American Chemical Society_ 144, 20590–20600 (2022).
  * (19) Wright, A. J. _et al._ Size disorder as a descriptor for predicting reduced thermal conductivity in medium-and high-entropy pyrochlore oxides.  _Scripta Materialia_ 181, 76–81 (2020).
  * (20) Jiang, B. _et al._ Probing the local site disorder and distortion in pyrochlore high-entropy oxides.  _Journal of the American Chemical Society_ 143, 4193–4204 (2020).
  * (21) Kinsler-Fedon, C. _et al._ Synthesis, characterization, and single-crystal growth of a high-entropy rare-earth pyrochlore oxide.  _Phys. Rev. Mater._ 4, 104411 (2020).  URL https://link.aps.org/doi/10.1103/PhysRevMaterials.4.104411.
  * (22) Sarkar, A. _et al._ High entropy oxides for reversible energy storage.  _Nature communications_ 9, 3400 (2018).
  * (23) Chen, H. _et al._ Entropy-stabilized metal oxide solid solutions as co oxidation catalysts with high-temperature stability.  _Journal of Materials Chemistry A_ 6, 11129–11133 (2018).
  * (24) Braun, J. L. _et al._ Charge-induced disorder controls the thermal conductivity of entropy-stabilized oxides.  _Advanced materials_ 30, 1805004 (2018).
  * (25) Kante, M. V. _et al._ A high entropy oxide as high-activity electrocatalyst for water oxidation.  _ACS Nano_ 17, 5329 (2023).  URL https://pubs.acs.org/doi/10.1021/acsnano.2c08096.
  * (26) Patel, R. K. _et al._ Thickness dependent OER electrocatalysis of epitaxial thin film of high entropy oxide.  _Applied Physics Reviews_ 10, 031407 (2023).  URL https://doi.org/10.1063/5.0146005.  eprint https://pubs.aip.org/aip/apr/article-pdf/doi/10.1063/5.0146005/18068792/031407_1_5.0146005.pdf.
  * (27) Zhao, B. _et al._ High-entropy enhanced microwave attenuation in titanate perovskites.  _Advanced Materials_ 35, 2210243 (2023).
  * (28) Schweidler, S. _et al._ High-entropy materials for energy and electronic applications.  _Nature Reviews Materials_ 1–16 (2024).
  * (29) Aamlid, S. S., Oudah, M., Rottler, J. & Hallas, A. M.  Understanding the role of entropy in high entropy oxides.  _Journal of the American Chemical Society_ 145, 5991–6006 (2023).
  * (30) Ruffoni, M., Pettifer, R., Pascarelli, S., Trapananti, A. & Mathon, O.  Probing atomic displacements with thermal differential exafs.  _Journal of Synchrotron Radiation_ 14, 421–425 (2007).
  * (31) Newville, M.  Fundamentals of xafs.  _Reviews in Mineralogy and Geochemistry_ 78, 33–74 (2014).
  * (32) Rehr, J. J. & Albers, R. C.  Theoretical approaches to x-ray absorption fine structure.  _Rev. Mod. Phys._ 72, 621–654 (2000).  URL https://link.aps.org/doi/10.1103/RevModPhys.72.621.
  * (33) Rost, C. M., Rak, Z., Brenner, D. W. & Maria, J.-P.  _Journal of the American Ceramic Society_ 100, 2732–2738 (2017).
  * (34) Pu, Y. _et al._ (mg, mn, fe, co, ni) o: A rocksalt high-entropy oxide containing divalent mn and fe.  _Science Advances_ 9, eadi8809 (2023).
  * (35) Tsurkan, V., Von Nidda, H.-A. K., Deisenhofer, J., Lunkenheimer, P. & Loidl, A.  On the complexity of spinels: Magnetic, electronic, and polar ground states.  _Physics Reports_ 926, 1–86 (2021).
  * (36) Tomiyasu, K., Fukunaga, J. & Suzuki, H.  Magnetic short-range order and reentrant-spin-glass-like behavior in co cr 2 o 4 and mn cr 2 o 4 by means of neutron scattering and magnetization measurements.  _Physical Review B_ 70, 214434 (2004).
  * (37) Bhowmik, R., Ranganathan, R. & Nagarajan, R.  Lattice expansion and noncollinear to collinear ferrimagnetic order in a mn cr 2 o 4 nanoparticle.  _Physical Review B_ 73, 144413 (2006).
  * (38) Yamasaki, Y. _et al._ Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide.  _Physical review letters_ 96, 207204 (2006).
  * (39) Dey, K., Majumdar, S. & Giri, S.  Ferroelectricity in spiral short-range-ordered magnetic state of spinel mncr 2 o 4: Significance of topological frustration and magnetoelastic coupling.  _Physical Review B_ 90, 184424 (2014).
  * (40) Suchomel, M. R., Shoemaker, D. P., Ribaud, L., Kemei, M. C. & Seshadri, R.  Spin-induced symmetry breaking in orbitally ordered nicr 2 o 4 and cucr 2 o 4.  _Physical Review B_ 86, 054406 (2012).
  * (41) Dutton, S. E., Huang, Q., Tchernyshyov, O., Broholm, C. & Cava, R. J.  Sensitivity of the magnetic properties of the zncr 2 o 4 and mgcr 2 o 4 spinels to nonstoichiometry.  _Physical Review B_ 83, 064407 (2011).
  * (42) Van Der Laan, G., Chopdekar, R., Suzuki, Y. & Arenholz, E.  Strain-induced changes in the electronic structure of mncr 2 o 4 thin films probed by x-ray magnetic circular dichroism.  _Physical review letters_ 105, 067405 (2010).
  * (43) Kim, I. _et al._ Electric polarization enhancement in multiferroic cocr2o4 crystals with cr-site mixing.  _Applied Physics Letters_ 94 (2009).
  * (44) Shannon, R. t. & Prewitt, C.  Revised values of effective ionic radii.  _Acta Crystallographica Section B: Structural Crystallography and Crystal Chemistry_ 26, 1046–1048 (1970).
  * (45) Stöhr, J. & Siegmann, H. C.  Magnetism.  _Solid-State Sciences. Springer, Berlin, Heidelberg_ 5, 236 (2006).
  * (46) Windsor, Y. W. _et al._ Magnetic properties of strained multiferroic coc r 2 o 4: A soft x-ray study.  _Physical Review B_ 95, 224413 (2017).
  * (47) Rák, Z., Maria, J.-P. & Brenner, D.  Evidence for jahn-teller compression in the (mg, co, ni, cu, zn) o entropy-stabilized oxide: A dft study.  _Materials Letters_ 217, 300–303 (2018).
  * (48) Kaplan, T. & Menyuk, N.  Spin ordering in three-dimensional crystals with strong competing exchange interactions.  _Philosophical Magazine_ 87, 3711–3785 (2007).
  * (49) Kaplan, T. A.  Classical theory of spin configurations in the cubic spinel.  _Phys. Rev._ 119, 1460–1470 (1960).  URL https://link.aps.org/doi/10.1103/PhysRev.119.1460.
  * (50) Winkler, E. _et al._ Magnetocrystalline interactions in mncr 2 o 4 spinel.  _Physical Review B_ 80, 104418 (2009).
  * (51) Ederer, C. & Komelj, M.  Magnetic coupling in $\mathrm{Co}{\mathrm{cr}}_{2}{\mathrm{o}}_{4}$ and $\mathrm{Mn}{\mathrm{cr}}_{2}{\mathrm{o}}_{4}$: An $\mathrm{LSDA}+\mathrm{U}$ study.  _Phys. Rev. B_ 76, 064409 (2007).  URL https://link.aps.org/doi/10.1103/PhysRevB.76.064409.
  * (52) Witte, R. _et al._ High-entropy oxides: An emerging prospect for magnetic rare-earth transition metal perovskites.  _Phys. Rev. Mater._ 3, 034406 (2019).  URL https://link.aps.org/doi/10.1103/PhysRevMaterials.3.034406.
  * (53) Sharma, Y. _et al._ Magnetic anisotropy in single-crystal high-entropy perovskite oxide $\mathrm{La}(\mathrm{C}{\mathrm{r}}_{0.2}\mathrm{M}{\mathrm{n}}_{0.2}\mathrm{F}{\mathrm{e}}_{0.2}\mathrm{C}{\mathrm{o}}_{0.2}\mathrm{N}{\mathrm{i}}_{0.2}){\mathrm{o}}_{3}$ films.  _Phys. Rev. Mater._ 4, 014404 (2020).  URL https://link.aps.org/doi/10.1103/PhysRevMaterials.4.014404.
  * (54) Mazza, A. R. _et al._ Charge doping effects on magnetic properties of single-crystal ${\mathrm{la}}_{1\text{$-$}x}{\mathrm{sr}}_{x}({\mathrm{cr}}_{0.2}{\mathrm{mn}}_{0.2}{\mathrm{fe}}_{0.2}{\mathrm{co}}_{0.2}{\mathrm{ni}}_{0.2}){\mathrm{o}}_{3}$ $(0\leq x\leq 0.5)$ high-entropy perovskite oxides.  _Phys. Rev. B_ 104, 094204 (2021).  URL https://link.aps.org/doi/10.1103/PhysRevB.104.094204.
  * (55) Mazza, A. R. _et al._ Designing magnetism in high entropy oxides.  _Advanced Science_ 9, 2200391 (2022).
  * (56) Su, L. _et al._ Direct observation of elemental fluctuation and oxygen octahedral distortion-dependent charge distribution in high entropy oxides.  _Nature communications_ 13, 2358 (2022).
  * (57) Mugiraneza, S. & Hallas, A. M.  Tutorial: a beginner’s guide to interpreting magnetic susceptibility data with the curie-weiss law.  _Communications Physics_ 5, 95 (2022).
  * (58) Coey, J. M. D.  _Magnetism And Magnetic Materials_ (Cambridge University Press, U.K., 2010).
  * (59) Kassem, M. A., El-Fadl, A. A., Nashaat, A. M. & Nakamura, H.  Structural, optical and single-domain magnetic features of the noncollinear ferrimagnetic nano-spinel chromites acr $\\_2$ o $\\_4$(a= ni, co, and mn).  _arXiv preprint arXiv:2305.17856_ (2023).
  * (60) Lee, S.-H., Broholm, C., Kim, T., W Ratcliff, I. & Cheong, S.-W.  Local spin resonance and spin-peierls-like phase transition in a geometrically frustrated antiferromagnet.  _Physical Review Letters_ 84, 3718 (2000).
  * (61) J.Rodríguez-Carvajal.  Recent developments of the program fullprof, in commission on powder diffraction (iucr).  _Newsletter_ 26, 12–19 (2001).
  * (62) Ravel, B. & Newville, M.  Athena, artemis, hephaestus: data analysis for x-ray absorption spectroscopy using ifeffit.  _Journal of synchrotron radiation_ 12, 537–541 (2005).