1See Contributions and Acknowledgments section for full author list. Please
send correspondence to<EMAIL_ADDRESS>
# Gemma: Open Models Based on Gemini Research and Technology

Gemma Team  Google DeepMind1

###### Abstract

This work introduces Gemma, a family of lightweight, state-of-the art open
models built from the research and technology used to create Gemini models.
Gemma models demonstrate strong performance across academic benchmarks for
language understanding, reasoning, and safety. We release two sizes of models
(2 billion and 7 billion parameters), and provide both pretrained and fine-
tuned checkpoints. Gemma outperforms similarly sized open models on 11 out of
18 text-based tasks, and we present comprehensive evaluations of safety and
responsibility aspects of the models, alongside a detailed description of
model development. We believe the responsible release of LLMs is critical for
improving the safety of frontier models, and for enabling the next wave of LLM
innovations.

##  1 Introduction

We present Gemma, a family of open models based on Google’s Gemini models
(Gemini Team, 2023).

We trained Gemma models on up to 6T tokens of text, using similar
architectures, data, and training recipes as the Gemini model family. Like
Gemini, these models achieve strong generalist capabilities in text domains,
alongside state-of-the-art understanding and reasoning skills at scale. With
this work, we release both pre-trained and fine-tuned checkpoints, as well as
an open-source codebase for inference and serving.

Gemma comes in two sizes: a 7 billion parameter model for efficient deployment
and development on GPU and TPU, and a 2 billion parameter model for CPU and
on-device applications. Each size is designed to address different
computational constraints, applications, and developer requirements. At each
scale, we release raw, pretrained checkpoints, as well as checkpoints fine-
tuned for dialogue, instruction-following, helpfulness, and safety. We
thoroughly evaluate the shortcomings of our models on a suite of quantitative
and qualitative benchmarks. We believe the release of both pretrained and
fine-tuned checkpoints will enable thorough research and investigation into
the impact of current instruction-tuning regimes, as well as the development
of increasingly safe and responsible model development methodologies.

Gemma advances state-of-the-art performance relative to comparable-scale (and
some larger), open models (Jiang et al., 2023; Touvron et al., 2023b, a;
Almazrouei et al., 2023) across a wide range of domains including both
automated benchmarks and human evaluation. Example domains include question
answering (Clark et al., 2019; Kwiatkowski et al., 2019), commonsense
reasoning (Sakaguchi et al., 2019; Suzgun et al., 2022), mathematics and
science (Cobbe et al., 2021; Hendrycks et al., 2020), and coding (Austin et
al., 2021; Chen et al., 2021). See complete details in the Evaluation section.

Figure 1: Language understanding and generation performance of Gemma 7B across
different capabilities compared to similarly sized open models. We group
together standard academic benchmark evaluations by capability and average the
respective scores; see Table 6 for a detailed breakdown of performance.

Like Gemini, Gemma builds on recent work on sequence models (Sutskever et al.,
2014) and transformers (Vaswani et al., 2017), deep learning methods based on
neural networks (LeCun et al., 2015), and techniques for large-scale training
on distributed systems (Barham et al., 2022; Roberts et al., 2023; Dean et
al., 2012). Gemma also builds on Google’s long history of open models and
ecosystems, including Word2Vec (Mikolov et al., 2013), the Transformer
(Vaswani et al., 2017), BERT (Devlin et al., 2018), and T5 (Raffel et al.,
2019) and T5X (Roberts et al., 2022).

We believe the responsible release of LLMs is critical for improving the
safety of frontier models, for ensuring equitable access to this breakthrough
technology, for enabling rigorous evaluation and analysis of current
techniques, and for enabling the development of the next wave of innovations.
While thorough testing of all Gemma models has been conducted, testing cannot
cover all applications and scenarios in which Gemma may be used. With this in
mind, all Gemma users should conduct rigorous safety testing specific to their
use case before deployment or use. More details on our approach to safety can
be found in section Responsible Deployment.

In this technical report, we provide a detailed overview of the model
architecture, training infrastructure, and pretraining and fine-tuning recipes
for Gemma, followed by thorough evaluations of all checkpoints across a wide-
variety of quantitative and qualitative benchmarks, as well as both standard
academic benchmarks and human-preference evaluations. We then discuss in
detail our approach to safe and responsible deployment. Finally, we outline
the broader implications of Gemma, its limitations and advantages, and
conclusions.

##  2 Model Architecture

The Gemma model architecture is based on the transformer decoder (Vaswani et
al., 2017). The core parameters of the architecture are summarized in Table 1.
Models are trained on a context length of 8192 tokens.

Parameters | 2B | 7B
---|---|---
d_model | 2048 | 3072
Layers | 18 | 28
Feedforward hidden dims | 32768 | 49152
Num heads | 8 | 16
Num KV heads | 1 | 16
Head size | 256 | 256
Vocab size | 256128 | 256128
Table 1: Key model parameters.

We also utilize several improvements proposed after the original transformer
paper. Below, we list the included improvements:

Multi-Query Attention (Shazeer, 2019). Notably, the 7B model uses multi-head
attention while the 2B checkpoints use multi-query attention (with
$num\\_kv\\_heads=1$), based on ablation studies that revealed respective
attention variants improved performance at each scale (Shazeer, 2019).

RoPE Embeddings (Su et al., 2021). Rather than using absolute positional
embeddings, we use rotary positional embeddings in each layer; we also share
embeddings across our inputs and outputs to reduce model size.

GeGLU Activations (Shazeer, 2020). The standard ReLU non-linearity is replaced
by the GeGLU activation function.

RMSNorm. We normalize the input of each transformer sub-layer, the attention
layer and the feedforward layer, with RMSNorm (Zhang and Sennrich, 2019) .

##  3 Training Infrastructure

We train the Gemma models using TPUv5e; TPUv5e are deployed in pods of 256
chips, configured into a 2D torus of 16 x 16 chips. For the 7B model, we train
our model across 16 pods, totaling to 4096 TPUv5e. We pretrain the 2B model
across 2 pods, totaling 512 TPUv5e. Within a pod, we use 16-way model sharding
and 16-way data replication for the 7B model. For the 2B, we simply use
256-way data replication. The optimizer state is further sharded using
techniques similar to ZeRO-3. Beyond a pod, we perform data-replica reduce
over the data-center network, using Pathways approach of (Barham et al.,
2022).

Model |  Embedding Parameters |  Non-embedding Parameters
---|---|---
2B | 524,550,144 | 1,981,884,416
7B | 786,825,216 | 7,751,248,896
Table 2: Parameter counts for both sizes of Gemma models.

As in Gemini, we leverage the ’single controller’ programming paradigm of Jax
(Roberts et al., 2023) and Pathways (Barham et al., 2022) to simplify the
development process by enabling a single Python process to orchestrate the
entire training run; we also leverage the GSPMD partitioner (Xu et al., 2021)
for the training step computation and the MegaScale XLA compiler (XLA, 2019).

###  3.1 Carbon Footprint

We estimate the carbon emissions from pretraining the Gemma models to be $\sim
131$ $tCO_{2}eq$. This value is calculated based on the hourly energy usage
reported directly from our TPU datacenters; we also scale this value to
account for the additional energy expended to create and maintain the data
center, giving us the total energy usage for our training experiments. We
convert total energy usage to carbon emissions by joining our hourly energy
usage against hourly per-cell carbon emission data reported by our data
centers.

In addition, Google data centers are carbon neutral, achieved through a
combination of energy efficiency, renewable energy purchases, and carbon
offsets. This carbon neutrality also applies to our experiments and the
machines used to run them.

##  4 Pretraining

###  4.1 Training Data

Gemma 2B and 7B are trained on 2T and 6T tokens respectively of primarily-
English data from web documents, mathematics, and code. Unlike Gemini, these
models are not multimodal, nor are they trained for state-of-the-art
performance on multilingual tasks.

We use a subset of the SentencePiece tokenizer (Kudo and Richardson, 2018) of
Gemini for compatibility. It splits digits, does not remove extra whitespace,
and relies on byte-level encodings for unknown tokens, following the
techniques used for both (Chowdhery et al., 2022) and (Gemini Team, 2023). The
vocabulary size is 256k tokens.

###  4.2 Filtering

We filter the pre-training dataset to reduce the risk of unwanted or unsafe
utterances, and filter out certain personal information and other sensitive
data. This includes using both heuristics and model-based classifiers to
remove harmful or low-quality content. Further, we filter all evaluation sets
from our pre-training data mixture, run targeted contamination analyses to
check against evaluation set leakage, and reduce the risk of recitation by
minimizing proliferation of sensitive outputs.

The final data mixture was determined through a series of ablations on both
the 2B and 7B models. Similar to the approach advocated in (Gemini Team,
2023), we stage training to alter the corpus mixture throughout training to
increase the weight of relevant, high-quality data towards the end of
training.

##  5 Instruction Tuning

We finetune Gemma 2B and 7B with supervised fine-tuning (SFT) on a mix of
text-only, English-only synthetic and human-generated prompt-response pairs
and reinforcement learning from human feedback (RLHF) with the reward model
trained on labelled English-only preference data and the policy based on a set
of high-quality prompts. We find that both stages are important for improved
performance on downstream automatic evaluations and human preference
evaluations of model outputs.

###  5.1 Supervised Fine-Tuning

We selected our data mixtures for supervised fine-tuning based on LM-based
side-by-side evaluations (Zheng et al., 2023). Given a set of held-out
prompts, we generate responses from a test model, generate responses on the
same prompts from a baseline model, shuffle these randomly, and ask a larger,
high capability model to express a preference between two responses. Different
prompt sets are constructed to highlight specific capabilities, such as
instruction following, factuality, creativity, and safety. The different
automatic LM-based judges we use employ a number of techniques, such as chain-
of-thought prompting (Wei et al., 2022) and use of rubrics and constitutions
(Bai et al., 2022), to be aligned with human preferences.

###  5.2 Filtering

When using synthetic data, we run several stages of filtering over it,
removing examples that show certain personal information, unsafe or toxic
model outputs, mistaken self-identification data, or duplicated examples.
Following Gemini, we find that including subsets of data that encourage better
in-context attribution, hedging, and refusals to minimize hallucinations can
improve performance on several factuality metrics, without degrading model
performance on other metrics.

The final data mixtures and supervised fine-tuning recipe, which includes
tuned hyperparameters, were chosen on the basis of improving helpfulness while
minimizing model harms related to safety and hallucinations.

###  5.3 Formatting

Instruction tuned models are trained with a specific formatter that annotates
all instruction tuning examples with extra information, both at training and
inference time. It has two purposes: 1) indicating roles in a conversation,
such as the User role, and 2) delineating turns in a conversation, especially
in a multi-turn conversation. Special control tokens are reserved in the
tokenizer for this purpose. While it is possible to get coherent generations
without the formatter, it will be out-of-distribution for the model, and will
very likely produce worse generations.

The relevant formatting control tokens are presented in Table 3, with a
dialogue example presented in Table 4.

Context | Relevant Token
---|---
User turn | user
Model turn | model
Start of conversation turn | <start_of_turn>
End of conversation turn | <end_of_turn>
Table 3: Relevant formatting control tokens used for both SFT and RLHF of Gemma models. User: | <start_of_turn>user
---|---
| Knock knock.<end_of_turn>
| <start_of_turn>model
Model: | Who’s there?<end_of_turn>
User: | <start_of_turn>user
| Gemma.<end_of_turn>
| <start_of_turn>model
Model: | Gemma who?<end_of_turn>
Table 4: Example dialogue with user and model control tokens.

###  5.4 Reinforcement Learning from Human Feedback

We further finetuned the supervised fine-tuned model using RLHF (Christiano et
al., 2017; Ouyang et al., 2022). We collected pairs of preferences from human
raters and trained a reward function under the Bradley-Terry model (Bradley
and Terry, 1952), similarly to Gemini. The policy was trained to optimize this
reward function using a variant of REINFORCE (Williams, 1992) with a
Kullback–Leibler regularization term towards the initially tuned model.
Similar to the SFT phase, and in order to tune hyperparameters and
additionally mitigate reward hacking (Amodei et al., 2016; Skalse et al.,
2022) we relied on a high capacity model as an automatic rater and computed
side-by-side comparisons against baseline models.

##  6 Evaluation

We evaluate Gemma across a broad range of domains, using both automated
benchmarks and human evaluation.

###  6.1 Human Preference Evaluations

In addition to running standard academic benchmarks on the finetuned models,
we sent final release candidates to human evaluation studies to be compared
against the Mistral v0.2 7B Instruct model (Jiang et al., 2023).

On a held-out collection of around 1000 prompts oriented toward asking models
to follow instructions across creative writing tasks, coding, and following
instructions, Gemma 7B IT has a 51.7% positive win rate and Gemma 2B IT has a
41.6% win rate over Mistral v0.2 7B Instruct. On a held-out collection of
around 400 prompts oriented towards testing basic safety protocols, Gemma 7B
IT has a 58% win rate, while Gemma 2B IT has a 56.5% win rate. We report the
corresponding numbers in Table 5.

Model | Safety | Instruction Following
---|---|---
Gemma 7B IT | 58% | 51.7%
95% Conf. Interval | [55.9%, 60.1%] | [49.6%, 53.8%]
Win / Tie / Loss | 42.9% / 30.2% / 26.9% | 42.5% / 18.4% / 39.1%
Gemma 2B IT | 56.5% | 41.6%
95% Conf. Interval | [54.4%, 58.6%] | [39.5%, 43.7%]
Win / Tie / Loss | 44.8% / 22.9% / 32.3% | 32.7% / 17.8% / 49.5%
Table 5: Win rate of Gemma models versus Mistral 7B v0.2 Instruct with 95%
confidence intervals. We report breakdowns of wins, ties, and losses, and we
break ties evenly when reporting the final win rate.

###  6.2 Automated Benchmarks

|  | LLaMA-2 | Mistral | Gemma
---|---|---|---|---
Benchmark |  metric | 7B | 13B | 7B | 2B | 7B
MMLU | 5-shot, top-1 | 45.3 | 54.8 | 62.5 | 42.3 | 64.3
HellaSwag | 0-shot | 77.2 | 80.7 | 81.0 | 71.4 | 81.2
PIQA | 0-shot | 78.8 | 80.5 | 82.2 | 77.3 | 81.2
SIQA | 0-shot | 48.3 | 50.3 |  ∗47.0∗ | 49.7 | 51.8
Boolq | 0-shot | 77.4 | 81.7 |  ∗83.2∗ | 69.4 | 83.2
Winogrande | partial scoring | 69.2 | 72.8 | 74.2 | 65.4 | 72.3
CQA | 7-shot | 57.8 | 67.3 |  ∗66.3∗ | 65.3 | 71.3
OBQA |  | 58.6 | 57.0 | 52.2 | 47.8 | 52.8
ARC-e |  | 75.2 | 77.3 | 80.5 | 73.2 | 81.5
ARC-c |  | 45.9 | 49.4 | 54.9 | 42.1 | 53.2
TriviaQA | 5-shot | 72.1 | 79.6 | 62.5 | 53.2 | 63.4
NQ | 5-shot | 25.7 | 31.2 | 23.2 | 12.5 | 23.0
HumanEval | pass@1 | 12.8 | 18.3 | 26.2 | 22.0 | 32.3
MBPP† | 3-shot | 20.8 | 30.6 |  ∗40.2∗ | 29.2 | 44.4
GSM8K | maj@1 | 14.6 | 28.7 |  ∗35.4∗ | 17.7 | 46.4
MATH | 4-shot | 2.5 | 3.9 | 12.7 | 11.8 | 24.3
AGIEval |  | 29.3 | 39.1 |  ∗41.2∗ | 24.2 | 41.7
BBH |  | 32.6 | 39.4 |  ∗56.1∗ | 35.2 | 55.1
Average |  | 47.0 | 52.2 | 54.0 | 44.9 | 56.4
Table 6: Academic benchmark results, compared to similarly sized, openly-
available models trained on general English text data. † Mistral reports 50.2
on a different split for MBPP and on their split our 7B model achieves 54.5. ∗
evaluations run by us. Note that due to restrictive licensing, we were unable
to run evals on LLaMA-2; all values above were previously reported in Touvron
et al. (2023b).

We measure Gemma models’ performance on domains including physical reasoning
(Bisk et al., 2019), social reasoning (Sap et al., 2019), question answering
(Clark et al., 2019; Kwiatkowski et al., 2019), coding (Austin et al., 2021;
Chen et al., 2021), mathematics (Cobbe et al., 2021), commonsense reasoning
(Sakaguchi et al., 2019), language modeling (Paperno et al., 2016), reading
comprehension (Joshi et al., 2017), and more.

| Mistral | Gemma
---|---|---
Benchmark | 7B | 7B
ARC-c | 60.0 | 61.9
HellaSwag | 83.3 | 82.2
MMLU | 64.2 | 64.6
TruthfulQA | 42.2 | 44.8
Winogrande | 78.4 | 79.0
GSM8K | 37.8 | 50.9
Average | 61.0 | 63.8
Table 7: HuggingFace H6 benchmark. The performance of small models are
sensitive to small modifications in prompts and we further validate the
quality of our models on an independent implementation of multiple known
benchmarks. All evaluations were run by HuggingFace.

For most automated benchmarks we use the same evaluation methodology as in
Gemini. Specifically for those where we report performance compared with
Mistral, we replicated methodology from the Mistral technical report as
closely as possible. These specific benchmarks are: ARC (Clark et al., 2018),
CommonsenseQA (Talmor et al., 2019), Big Bench Hard (Suzgun et al., 2022), and
AGI Eval (English-only) (Zhong et al., 2023). Due to restrictive licensing, we
were unable to run any evaluations on LLaMA-2 and cite only those metrics
previously reported (Touvron et al., 2023b).

We compare Gemma 2B and 7B models to several external open-source (OSS) LLMs
across a series of academic benchmarks, reported in Table 6 and Table 7.

On MMLU (Hendrycks et al., 2020), Gemma 7B outperforms all OSS alternatives at
the same or smaller scale; it also outperforms several larger models,
including LLaMA2 13B. However, human expert performance is gauged at 89.8% by
the benchmark authors; as Gemini Ultra is the first model to exceed this
threshold, there is significant room for continued improvements to achieve
Gemini and human-level performance.

Gemma models demonstrate particularly strong performance on mathematics and
coding benchmarks. On mathematics tasks, which are often used to benchmark the
general analytical capabilities of models, Gemma models outperform other
models by at least 10 points on GSM8K (Cobbe et al., 2021) and the more
difficult MATH (Hendrycks et al., 2021) benchmark. Similarly, they outperform
alternate open models by at least 6 points on HumanEval (Chen et al., 2021).
They even surpass the performance of the code-fine-tuned CodeLLaMA-7B models
on MBPP (CodeLLaMA achieves a score of 41.4% where Gemma 7B achieves 44.4%).

|  | Mistral | Gemma
---|---|---|---
Benchmark | metric | 7B* | 2B | 7B
RealToxicity | avg | 8.44 | 6.86 | 7.90
BOLD |  | 38.21 | 45.57 | 49.08
CrowS-Pairs | top-1 | 32.76 | 45.82 | 51.33
BBQ Ambig | 1-shot, top-1 | 97.53 | 62.58 | 92.54
BBQ Disambig | top-1 | 84.45 | 54.62 | 71.99
Winogender | top-1 | 64.3 | 51.25 | 54.17
TruthfulQA |  | 44.2 | 44.84 | 31.81
Winobias 1_2 |  | 65.72 | 56.12 | 59.09
Winobias 2_2 |  | 84.53 | 91.1 | 92.23
Toxigen |  | 60.26 | 29.77 | 39.59
Table 8: Safety academic benchmark results, compared to similarly sized,
openly-available models.
∗ evaluations run by us. Note that due to restrictive licensing, we were
unable to run evals on LLaMA-2; we do not report previously-published LLaMA-2
numbers for TruthfulQA, as we use different, non-comparable evaluation set-ups
(we use MC2, where LLaMA-2 uses GPT-Judge).

###  6.3 Memorization Evaluations

Recent work has shown that aligned models may be vulnerable to new adversarial
attacks that can bypass alignment (Nasr et al., 2023). These attacks can cause
models to diverge, and sometimes regurgitate memorized training data in the
process. We focus on discoverable memorization, which serves as a reasonable
upper-bound on the memorization of a model (Nasr et al., 2023) and has been
the common definition used in several studies (Carlini et al., 2022; Anil et
al., 2023; Kudugunta et al., 2023).

Figure 2: Comparing average memorization rates across model families. We
compare the Gemma pretrained models to PaLM and PaLM 2 models of comparable
size and find similarly low rates of memorization.

We test for memorization111Our use of “memorization” relies on the definition
of that term found at www.genlaw.org/glossary.html. of the Gemma pretrained
models with the same methodology performed in Anil et al. (2023). We sample
10,000 documents from each corpus and use the first 50 tokens as a prompt for
the model. We focus mainly on exact memorization, where we classify texts as
memorized if the subsequent 50 tokens generated by the model exactly match the
ground truth continuation in the text. However, to better capture potential
paraphrased memorizations, we include approximate memorization (Ippolito et
al., 2022) using an 10% edit distance threshold. In Figure 2, we compare the
results of our evaluation with the closest sized PaLM (Chowdhery et al., 2022)
and PaLM 2 models (Anil et al., 2023).

#### Verbatim Memorization

PaLM 2 compared with PaLM by evaluating on a shared subset of their training
corpora. However, there is even less overlap between the Gemma pretraining
data with the PaLM models, and so using this same methodology, we observe much
lower memorization rates (Figure 2 left). Instead, we find that estimating the
“total memorization” across the entire pretraining dataset gives a more
reliable estimate (Figure 2 right) where we now find the Gemma memorizes
training data at a comparable rate to PaLM.

Figure 3: Measuring personal and sensitive data memorization rates. No
sensitive data was memorized, hence it is omitted from the figure.

#### Personal Data

Perhaps of higher importance is the possibility that personal data might be
memorized. As part of making Gemma pre-trained models safe and reliable, we
used automated techniques to filter out certain personal information and other
sensitive data from training sets.

To identify possible occurrences of personal data, we use Google Cloud
Sensitive Data Protection222Available at: https://cloud.google.com/sensitive-
data-protection. This tool outputs three severity levels based on many
categories of personal data (e.g., names, emails, etc.). We classify the
highest severity as “sensitive” and the remaining two as simply “personal”.
Then, we measure how many memorized outputs contain any sensitive or personal
data. As shown in Figure 3, _we observe no cases of memorized sensitive data._
We do find that the model memorizes some data we have classified as
potentially “personal” according to the above, though often at a much lower
rate. Further, it is important to note that these tools are known to have many
false positives (because they only match patterns and do not consider the
context), meaning that our results are likely overestimates of the amount of
personal data identified.

Figure 4: Comparing exact and approximate memorization.

#### Approximate Memorization

In Figure 4, we observe that roughly 50% more data is approximately memorized
(note the log scale) and that this is nearly consistent across each of the
different subcategories over the dataset.

##  7 Responsible Deployment

In line with previous releases of Google’s AI technologies (Gemini Team, 2023;
Kavukcuoglu et al., 2022), we follow a structured approach to responsible
development and deployment of our models, in order to identify, measure, and
manage foreseeable downstream societal impacts. As with our recent Gemini
release, these are informed by prior academic literature on language model
risks (Weidinger et al., 2021), findings from similar prior exercises
conducted across the industry (Anil et al., 2023), ongoing engagement with
experts internally and externally, and unstructured attempts to discover new
model vulnerabilities.

###  7.1 Benefits

We believe that openness in AI science and technology can bring significant
benefits. Open-sourcing is a significant driver of science and innovation, and
a responsible practice in most circumstances. But this needs to be balanced
against the risk of providing actors with the tools to cause harm now or in
the future.

Google has long committed to providing broader access to successful research
innovations (GraphCast, Transformer, BERT, T5, Word2Vec), and we believe that
releasing Gemma into the AI development ecosystem will enable downstream
developers to create a host of beneficial applications, in areas such as
science, education and the arts. Our instruction-tuned offerings should
encourage a range of developers to leverage Gemma’s chat and code capabilities
to support their own beneficial applications, while allowing for custom fine-
tuning to specialize the model’s capabilities for specific use cases. To
ensure Gemma supports a wide range of developer needs, we are also releasing
two model sizes to optimally support different environments, and have made
these models available across a number of platforms (see Kaggle for details).
Providing broad access to Gemma in this way should reduce the economic and
technical barriers that newer ventures or independent developers face when
incorporating these technologies into their workstreams.

As well as serving developers with our instruction-tuned models, we have also
provided access to corresponding base pretrained models. By doing so, it is
our intention to encourage further AI safety research and community
innovation, providing a wider pool of models available to developers to build
on various methods of transparency and interpretability research that the
community has already benefited from (Pacchiardi et al., 2023; Zou et al.,
2023).

###  7.2 Risks

In addition to bringing benefits to the AI development ecosystem, we are aware
that malicious uses of LLMs, such as the creation of deepfake imagery, AI-
generated disinformation, and illegal and disturbing material can cause harm
on both an individual and institutional levels (Weidinger et al., 2021).
Moreover, providing access to model weights, rather than releasing models
behind an API, raises new challenges for responsible deployment.

First, we cannot prevent bad actors from fine tuning Gemma for malicious
intent, despite their use being subject to Terms of Use that prohibit the use
of Gemma models in ways that contravene our Gemma Prohibited Use Policy.
However, we are cognizant that further work is required to build more robust
mitigation strategies against intentional misuse of open systems, which Google
DeepMind will continue to explore both internally and in collaboration with
the wider AI community.

The second challenge we face is protecting developers and downstream users
against the unintended behaviours of open models, including generation of
toxic language or perpetuation of discriminatory social harms, model
hallucinations and leakage of personally identifiable information. When
deploying models behind an API, these risks can be reduced via various
filtering methods.

###  7.3 Mitigations

Without this layer of defense for the Gemma family of models, we have
endeavoured to safeguard against these risks by filtering and measuring biases
in pre-training data in line with the Gemini approach, assessing safety
through standardized AI safety benchmarks, internal red teaming to better
understand the risks associated with external use of Gemma, and subjecting the
models to rigorous ethics and safety evaluations, the results of which can be
seen in 8.

While we’ve invested significantly in improving the model, we recognize its
limitations. To ensure transparency for downstream users, we’ve published a
detailed model card to provide researchers with a more comprehensive
understanding of Gemma.

We have also released a Generative AI Responsible Toolkit to support
developers to build AI responsibly. This encompasses a series of assets to
help developers design and implement responsible AI best practices and keep
their own users safe.

The relative novelty of releasing open weights models means new uses, and
misuses, of these models are still being discovered, which is why Google
DeepMind is committed to the continuous research and development of robust
mitigation strategies alongside future model development.

###  7.4 Assessment

Ultimately, given the capabilities of larger systems accessible within the
existing ecosystem, we believe the release of Gemma will have a negligible
effect on the overall AI risk portfolio. In light of this, and given the
utility of these models for research, auditing and downstream product
development, we are confident that the benefit of Gemma to the AI community
outweighs the risks described.

###  7.5 Going Forward

As a guiding principle, Google DeepMind strives to adopt assessments and
safety mitigations proportionate to the potential risks from our models. In
this case, although we are confident that Gemma models will provide a net
benefit to the community, our emphasis on safety stems from the irreversible
nature of this release. As the harms resulting from open models are not yet
well defined, nor does an established evaluation framework for such models
exist, we will continue to follow this precedent and take a measured and
cautionary approach to open model development. As capabilities advance, we may
need to explore extended testing, staggered releases or alternative access
mechanisms to ensure responsible AI development.

As the ecosystem evolves, we urge the wider AI community to move beyond
simplistic ’open vs. closed’ debates, and avoid either exaggerating or
minimising potential harms, as we believe a nuanced, collaborative approach to
risks and benefits is essential. At Google DeepMind we’re committed to
developing high-quality evaluations and invite the community to join us in
this effort for a deeper understanding of AI systems.

##  8 Discussion and Conclusion

We present Gemma, an openly available family of generative language models for
text and code. Gemma advances the state of the art of openly available
language model performance, safety, and responsible development.

In particular, we are confident that Gemma models will provide a net benefit
to the community given our extensive safety evaluations and mitigations;
however, we acknowledge that this release is irreversible and the harms
resulting from open models are not yet well defined, so we continue to adopt
assessments and safety mitigations proportionate to the potential risks of
these models. In addition, our models outperform competitors on 6 standard
safety benchmarks, and in human side-by-side evaluations.

Gemma models improve performance on a broad range of domains including
dialogue, reasoning, mathematics, and code generation. Results on MMLU (64.3%)
and MBPP (44.4%) demonstrate both the high performance of Gemma, as well as
the continued headroom in openly available LLM performance.

Beyond state-of-the-art performance measures on benchmark tasks, we are
excited to see what new use-cases arise from the community, and what new
capabilities emerge as we advance the field together. We hope that researchers
use Gemma to accelerate a broad array of research, and we hope that developers
create beneficial new applications, user experiences, and other functionality.

Gemma benefits from many learnings of the Gemini model program including code,
data, architecture, instruction tuning, reinforcement learning from human
feedback, and evaluations. As discussed in the Gemini technical report, we
reiterate a non-exhaustive set of limitations to the use of LLMs. Even with
great performance on benchmark tasks, further research is needed to create
robust, safe models that reliably perform as intended. Example further
research areas include factuality, alignment, complex reasoning, and
robustness to adversarial input. As discussed by Gemini, we note the need for
more challenging and robust benchmarks.

##  9 Contributions and Acknowledgments

Core Contributors
Thomas Mesnard
Cassidy Hardin
Robert Dadashi
Surya Bhupatiraju
Shreya Pathak
Laurent Sifre
Morgane Rivière
Mihir Sanjay Kale
Juliette Love
Pouya Tafti
Léonard Hussenot

Contributors
Aakanksha Chowdhery
Adam Roberts
Aditya Barua
Alex Botev
Alex Castro-Ros
Ambrose Slone
Amélie Héliou
Andrea Tacchetti
Anna Bulanova
Antonia Paterson
Beth Tsai
Bobak Shahriari
Charline Le Lan
Christopher A. Choquette-Choo
Clément Crepy
Daniel Cer
Daphne Ippolito
David Reid
Elena Buchatskaya
Eric Ni
Eric Noland
Geng Yan
George Tucker
George-Christian Muraru
Grigory Rozhdestvenskiy
Henryk Michalewski
Ian Tenney
Ivan Grishchenko
Jacob Austin
James Keeling
Jane Labanowski
Jean-Baptiste Lespiau
Jeff Stanway
Jenny Brennan
Jeremy Chen
Johan Ferret
Justin Chiu
Justin Mao-Jones
Katherine Lee
Kathy Yu
Katie Millican
Lars Lowe Sjoesund
Lisa Lee
Lucas Dixon
Machel Reid
Maciej Mikuła
Mateo Wirth
Michael Sharman
Nikolai Chinaev
Nithum Thain
Olivier Bachem
Oscar Chang
Oscar Wahltinez
Paige Bailey
Paul Michel
Petko Yotov
Pier Giuseppe Sessa
Rahma Chaabouni
Ramona Comanescu
Reena Jana
Rohan Anil
Ross McIlroy
Ruibo Liu
Ryan Mullins
Samuel L Smith
Sebastian Borgeaud
Sertan Girgin
Sholto Douglas
Shree Pandya
Siamak Shakeri
Soham De
Ted Klimenko
Tom Hennigan
Vlad Feinberg
Wojciech Stokowiec
Yu-hui Chen
Zafarali Ahmed
Zhitao Gong

Product Management
Tris Warkentin
Ludovic Peran

Program Management
Minh Giang

Executive Sponsors
Clément Farabet
Oriol Vinyals
Jeff Dean
Koray Kavukcuoglu
Demis Hassabis
Zoubin Ghahramani
Douglas Eck
Joelle Barral
Fernando Pereira
Eli Collins

Leads
Armand Joulin
Noah Fiedel
Evan Senter

Tech Leads
Alek Andreev$\dagger{}$
Kathleen Kenealy$\dagger{}$ ††$\dagger{}$ equal contribution.

Acknowledgements
Our work is made possible by the dedication and efforts of numerous teams at
Google. We would like to acknowledge the support from the following teams:
Gemini, Gemini Safety, Gemini Infrastructure, Gemini Evaluation, Google Cloud,
Google Research Responsible AI, Kaggle, and Keras.

Special thanks and acknowledgment to Adrian Hutter, Andreas Terzis, Andrei
Kulik, Angelos Filos, Anushan Fernando, Aurelien Boffy, Danila Sinopalnikov,
Edouard Leurent, Gabriela Surita, Geoffrey Cideron, Jilin Chen, Karthik
Raveendran, Kathy Meier-Hellstern, Kehang Han, Kevin Robinson, Kritika
Muralidharan, Le Hou, Leonard Berrada, Lev Proleev, Luheng He, Marie Pellat,
Mark Sherwood, Matt Hoffman, Matthias Grundmann, Nicola De Cao, Nikola
Momchev, Nino Vieillard, Noah Constant, Peter Liu, Piotr Stanczyk, Qiao Zhang,
Ruba Haroun, Seliem El-Sayed, Siddhartha Brahma, Tianhe (Kevin) Yu, Tom Le
Paine, Yingjie Miao, Yuanzhong Xu, and Yuting Sun.

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# Intrinsic Néel antiferromagnetic multimeronic spin-textures in ultrathin
films

Amal Aldarawsheh1,2∗ Moritz Sallermann1,3,4 Muayad Abusaa5 and Samir
Lounis1,2∗

Peter Grünberg Institute and Institute for Advanced Simulation,
Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany

Faculty of Physics, University of Duisburg-Essen and CENIDE, 47053 Duisburg,
Germany

RWTH Aachen University, 52056 Aachen, Germany

Science Institute and Faculty of Physical Sciences, University of Iceland, VR-
III, 107 Reykjavík, Iceland

Department of Physics, Arab American University, Jenin, Palestine

*<EMAIL_ADDRESS><EMAIL_ADDRESS>
## Abstract

The realization of topological antiferromagnetic (AFM) solitons in real
materials is a major goal towards their use in information technology. While
they bear various advantages with respect to their ferromagnetic cousins,
their observation is scarce. Utilizing first-principles simulations, here we
predict new chiral particles in the realm of AFM topological magnetism,
frustrated multimeronic spin-textures hosted by a Néel magnetic state, arising
in single Mn layers directly grown on Ir(111) surface or interfaced with Pd-
based films. These topological structures are intrinsic, i.e. they form in a
single AFM material, can carry distinct topological charges and can combine in
various multimeronic sequences with enhanced stability against external
magnetic fields. We envision the frustrated Néel AFM multimerons as exciting
highly-sought after AFM solitons having the potential to be utilized in novel
spintronic devices hinging on non-synthetic AFM quantum materials.

## Introduction

Recent experimental breakthroughs promoted antiferromagnetic (AFM) materials
into the realm of information technological applications [1, 2, 3, 4, 5, 6, 7,
8, 9] and triggered state-of-the-art activities in the world of topological
magnetism [10, 7, 11, 12, 13]. The antiparallel spin sublattices present in
AFM materials result in zero dipolar fields, making them insensitive to
magnetic field perturbations and enhances the stabilization of nanoscale
topological structures [1, 14, 15, 4, 10, 9, 16]. Moreover, AFM materials
possess faster spin dynamics than ferromagnets by orders of magnitude [17, 18,
19, 20], which is an appealing characteristic for THz magnetic memory and
logic devices.

The race in identifying AFM non-trivial spin-swirling objects is strongly
motivated by their particle-like nature, potentially realizing ideal magnetic
bits, augmented with the low power consumption [21, 14, 22, 23, 24, 25, 26,
27, 28, 4, 29, 30, 7, 31, 32, 33, 34, 12] involved in their manipulation with
the possibility of controlling their current-driven motion [14, 22, 23, 25,
26, 28, 9, 16] while avoiding the skyrmion Hall effect that plagues the
ferromagnetic (FM) cousins [35, 36, 37, 38, 39].

This led to the recent discovery of synthetic AFM skyrmions, which consist of
two FM skyrmions that are realized in two distinct magnetic layers and
antiferromagnetically coupled through a non-magnetic spacer layer [10, 7, 11,
12, 13]. Here, utilizing first-principles in conjunction with atomistic spin
dynamics we unveil multimeronic textures, a new type of topological AFM
particles, which are non-synthetic and emerge in magnetically frustrated thin
films (see Fig.1).

Regular FM merons are in-plane magnetized textures with magnetization that
curls around a stable core pointing out-of-plane, and are topologically
equivalent to one half of a skyrmion [40, 41, 42, 43, 44, 45, 46, 47, 48, 49].
The meronic topological charge
$N=\frac{1}{4\pi}\int\textbf{n}\cdot\left(\frac{\partial\textbf{n}}{\partial_{x}}\times\frac{\partial\textbf{n}}{\partial_{y}}\right)d{x}d{y}$
equals $\pm\frac{1}{2}$, where n is the direction vector of magnetization.
While they have been observed experimentally in bulk [50] and thin films [45,
51], they emerge in AFM synthetic [42, 44, 52, 53] and intrinsic bulk (thick
films) phases [54, 31, 55], following a large body of phenomenology-based
simulations [30, 56, 32, 33, 34]. However, a pristine ultrathin film material
that hosts AFM merons remains elusive.

Our multi-meronic textures are distinct from current predictions since they
form in a realistic material a rich set of combinations materializing in a
frustrated in-plane Néel ground state, shown in Fig. 1j, which can be
decomposed into three FM sublattices, with an opening angle of 120∘ between
their respective magnetic moments. We predict a single Mn layer as a universal
hosting material once interfaced in different fashions with Ir(111) surface
with and without Pd, Fe monolayers, PdFe bilayer or Pd2Fe trilayer (see
Fig.2a-d). The different substrates form a typical family of substrates
typically known to host FM [57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67], and
AFM skyrmions [9, 16]. The in-plane AFM Néel state is the ground state for Mn
layer in all magnetic systems, formed as a result of magnetic frustration
caused by strong AFM exchange coupling among the first nearest neighbors, as
illustrated in Supplementary Fig. 1. While the in-plane orientation is
dictated by the $z$ component of the antisymmetric exchange interactions
(Dzyaloshinskii-Moriya Interactions – DMI) and is further reinforced by the
in-plane magnetic anisotropy energy (MAE) $K$.

## Results

###  0.1 Topological magnetic states in frustrated Mn layer.

The Ir(111) substrate forms a triangular lattice, on which we deposit layers
of Mn, PdMn, MnPdFe and MnPd2Fe and perform atomistic spin dynamics [68],
minimizing the Heisenberg Hamiltonian (Eq. 1 in Methods section) equipped with
the magnetic interactions derived from first-principles (see Methods section).
We identify a plethora of AFM Néel meronic magnetic states forming metastable
states in the Mn layer as depicted in Fig. 1a, Fig. 2g, h, and Supplementary
Fig. 2.

The Néel ordering of the spins is the ground state of the Mn layer in all of
the aforementioned magnetic systems. The associated critical temperatures
range from 130K for PdMn bilayers to about 600K or more for the rest of
explored Mn-based films. The spins forming the AFM Néel order are segmented
into three sublattices L1, L2 and L3, each hosting FM spin alignment (Fig.
1j). At each sublattice, FM meronic pair can be stabilized, so in total, in
the case of single AFM Néel meronic pair (Fig. 1a), we have six FM merons
(antimerons), as shown in Fig. 1d-i, which we refer to as a hexameronic state.
By zooming in into the two spin-swirling extremities of the hexameron (Figs.
1b-c) and their respective sublattice decomposition (Figs. 1d-i), we identify
a vortex (Fig. 1d) and an antivortex (Fig. 1h) whose cores reside on an Mn
lattice site, around which the spins of the remaining meronic textures
precess, as dictated by the magnetic frustration induced by the underlying AFM
magnetic interactions.

Each of the FM building blocks of our AFM explored solitons holds a
topological charge (N) defined as: N = (wp/2) [40], where w = +1 (-1) for the
vortex (antivortex) is the winding number describing the rotational direction
of the in-plane magnetization, and p is the polarity which defines the out-of-
plane magnetization of the center being +1 (-1) when pointing up (down) [69].
Since the merons and antimerons carry a topological charge of -1/2 and +1/2,
respectively [45, 51, 31], the sublattice charge NL is either -1 (+1) for a
meron-meron (antimeron-antimeron) pair, as the case of L3 (Fig. 1 f, i), or 0
for a hybrid (see L1 and L2 in Fig. 1 d, e, g, h) meron-antimeron pair. By
summing up the total charge Nt for a hexameron, one can end up with three
possible values -1, 0 and +1 (see Fig. 1k), which interestingly are
energetically degenerate in the absence of an external magnetic field.

Besides the hexameronic frustrated AFM Néel state, we identified a rich set of
other meronic textures, such as the dodecameron, hosting 12 merons, shown in
Fig. 2g. Further examples of complex multimerons are presented in
Supplementary Fig. 2. Similarly to the purely FM counterparts, in confined
geometries (See Supplementary Fig. 2b-c) a ”single” AFM Néel meronic state can
be stabilized. This object is a trimeron resulting from three frustrated
merons with overlapping cores, carrying in total a half integer topological
charge.

###  0.2 Stability against external magnetic fields.

The investigation of the response of topologically paired AFM Néel meronic
pairs to an magnetic fields is important to inspect stability aspects and to
fingerprint subsequent potential non-trivial topological transitions.

The frustrated meronic textures survive to extremely high in-plane magnetic
fields ($>200$ Tesla). The case of an out-of-plane (OOP) magnetic field shows
a rather rich impact on the explored spin-textures. Therefore, here, we
scrutinize in detail the latter scenario by focusing on three different AFM
Néel meronic states (see Figs. 2 f-h).

As a prototypical chiral magnetic object, we consider the hexameron emerging
either in the AFM Néel (Fig. 2f) or in the spiraling AFM Néel states (Fig. 2h)
as well as the dodecameron (Fig. 2g). For interfaces hosting the Fe layer,
MnPdFe/Ir(111) and MnPd2Fe/Ir(111), we examined both cases: switching-off
(solid bars in Fig. 2e) and -on (dashed bars in Fig. 2e) the Mn-Fe magnetic
interactions. A snapshot for the Mn-hexameron interfaced with ferromagnetic Fe
spirals and skyrmkion is illustrated in Fig. 2i.

While we were expecting the robustness of the unveiled meronic textures
against external magnetic fields, we were intrigued by the annihilation of
some hexamerons emerging in an AFM Néel background with experimentally
accessible OOP fields, e.g. 10 Tesla, in contrast to dodecamerons and
hexamerons arising in a Néel spiraling state (red and green bars in Fig. 2e).

To get insight into the origin of the sensitivity of these magnetic
states,hexamerons forming in an AFM Néel background, we scrutinize the
sublattices topological distribution along with the spin orientation at each
sublattice of the different hexameronic states shown in Fig. 3 (See
supplementary Fig. 3 illustrating snapshots of the different hexamerons). As
introduced earlier, there is a quadruple degeneracy for each hexameron in the
absence of a magnetic field. The four states, denoted Hexa A–D and illustrated
in Fig. 3, can be distinguished by the vortex nature of their core
constituents and the orientation of the core spins (see Fig. 1k). A finite OOP
field lifts partially the degeneracy and favors the hexameron, here Hexa D,
with most spins pointing along the field direction (see also Supplementary
Fig. 3). Among the four hexamerons, Hexa D will be the most robust to the
applied field and therefore survives gigantic fields. The remaining hexamerons
experience at some point magnetization switching to reach the optimal
sublattice topological distribution defined by Hexa D. This requires a flip of
the spins for at least one meron (antimeron) implying going through a
topological charge transition, being a non trivial process, during which, the
AFM meronic structure might encounter an unstable spin distribution, leading
to the annihilation of the AFM meronic structure where the AFM vortex and
antivortex start rolling towards each other and then collapse at a rather low
magnetic field. If the transition occurs, however, the new magnetic state
would be capable of surviving large magnetic fields similar to Hexa D.

However, the presence of Néel spirals in the background or additional pairs of
AFM meronic textures (leading to for example to dodecamerons) prevent the
formation of unstable states within the topological transition induced by the
magnetic field, which would lead to the collapse of the frustrated soliton.
Effectively, a barrier is provided by enabling the rearrangement of the spins
to acquire the desired topological state, which would withstand immense
magnetic fields.

###  0.3 Emergence mechanism.

We have identified that the formation of our frustrated AFM Néel meronic spin
textures requires a strong AFM exchange coupling among the first nearest-
neighbor atoms $J_{1}$ (see Supplementary Fig. 1a-d). This coupling is
responsible for the AFM Néel order of the spins, and it is through magnetic
frustration that these solitons may arise. Additionally, another magnetic
interaction is required to align the spins in the in-plane direction. This
interaction can be provided by the in-plane MAE, $K$ $<$ 0, as observed in
Mn/Ir(111), while for the other three magnetic systems studied, $K$ prefers an
out-of-plane orientation of spins (Supplementary Fig.1e). However, the $z$
component of the DMI vector ($D_{z}$) plays a crucial role in aligning the
spins in-plane, ultimately leading to the emergence of the AFM Néel meronic
textures. In conclusion, to obtain our AFM solitons on a triangular lattice,
an AFM $J_{1}$ is required, along with either a finite $D_{z}$ or an in-plane
$K$.

To explore the fundamental mechanisms defining the stability of the spin-
textures, we built a minimal spin model that contains only an AFM $J_{1}$ and
$D_{z}$ since the latter played the main role in stabilizing the meronic
textures in the four investigated Mn-based interfaces. The resulting phase
diagram is shown in Fig. 4a. While the ground state would have been a pure
Néel state without $D_{z}$, the latter enables quickly the formation of
frustrated merons. Increasing $D_{z}$ enforces a stronger in-plane alignment
of the spins, which reduces the size of the meronic constituents (Fig. 4b and
Supplementary Fig. 4). Clearly, the size of merons is dictated by a
competition of magnetic exchange and DMI. Keeping $D_{z}$ fixed while
increasing the AFM $J_{1}$ counteracts the effect of DMI and enlarges the
meron core (Fig. 4c).

Fig. 4d presents the critical OOP magnetic field upon which the meronic
texture, here Hexa D similar to that shown in Fig. 3, is annihilated as
function of the OOP DMI component all normalized by the nearest neighboring
AFM exchange interaction. The obtained curve follows a quadratic dependence,
highlighting that the DMI enhances the stability of the frustrated merons. In
fact, the application of an OOP magnetic field counteracts the influence of
the OOP DMI component by tilting the spins to the OOP direction, causing
disruption to the in-plane alignment of the spins, imposed by the OOP DMI
component, throughout the surrounding area, including the region spanning
between the extremities of the hexameron, ultimately leading to its collapse.
Consequently, the larger the OOP DMI component (smaller meronic cores), the
larger the critical field required to destroy the AFM spin-swirling textures.

## Discussion

Our ab-initio simulations uncovered non-synthetic Néel-frustrated AFM meronic
textures emerging in a realistic set of materials and interfaces. The newly
unveiled magnetic objects are hosted by triangular Mn layer interfaced with an
Ir(111) surface, with either a Pd overlayer, separated from Ir with PdFe
bilayer of Pd2Fe trilayer, which all represent substrates that can readily be
grown experimentally. The frustrated AFM states form hexamerons, composed of
three FM meronic pairs each located at one of the three FM sublattices
building up the AFM Néel background. Other solitons can emerge such as
dodecamerons (12 merons) while confined geometries enables the stabilization
of a frustrated trimeron.

We have observed that these AFM Néel meronic solitons survive high values of
magnetic fields if the majority spins align in the direction of the OOP
magnetic field. Otherwise, a transition of the sublattice topological charge
occurs, leading to the potential annihilation of the AFM solitons at
experimentally accessible values of magnetic fields. To gain a better
understanding of the characteristics of these AFM solitons, we provided a spin
model that outlines the minimum set of magnetic interactions necessary to
generate the detected AFM solitons.

Identifying new AFM solitons with a realistic existence scenario is at the
heart of AFM topological magnetism. Our predictions can initiate the
experimental discovery of the intriguing intrinsic frustrated multimeronic
textures, which can delineate in various topological sequences. It remains to
be explored how such spin states can be implemented and designed in AFM
spintronic devices. Certainly, the thin films being proposed provide a solid
platform for AFM meronic textures with a potential impact in information
technology.

In this study, we conducted a systematic investigation to explore the magnetic
structures that can be hosted by the magnetic layers of our four layered
systems. Our approach involved a three-fold procedure, combining ab-initio
calculations with spin atomistic dynamics. The details of this procedure are
outlined below.

###  0.4 Ab-initio calculations.

To simulate the magnetic properties of our magnetic layers, we utilized in a
first step the Quantum-Espresso computational package [70]. The calculations
employed projector augmented wave pseudo potentials sourced from the PS
Library [71] and the self-consistent calculations were performed with a k-mesh
of $28\times 28\times 1$ points for the unit cell. The layers were arranged in
an fcc-stacked configuration along the [111] direction (See to Fig. 2a-d). The
relaxation parameters were then extracted, revealing the relaxation
percentages of the different layers in relation to the ideal interlayer
distance in the Ir-based systems. Specifically, for Mn/Ir(111), the relaxation
percentages were 2.3% and -3.4%; for PdMn/Ir(111), they were 8.6%, 10.3%, and
-2.3%; for MnPdFe/Ir(111), the percentages were 4%, 5.2%, 8.1%, and -1%; and
for MnPd2Fe/Ir(111), they were 5.9%, -4%, 8.2%, 8.2%, and -0.7%, for each
layer respectively. Here, positive (negative) values indicate atomic
relaxations towards (away from) the Ir surface.

After establishing the geometries of the various magnetic systems, we
conducted in a second step a detailed investigation of their magnetic
properties and interactions using the all-electron full-potential relativistic
Korringa-Kohn-Rostoker (KKR) Green function method, implemented in the JuKKR
computational package [72, 73],in the local spin density approximation. Each
of the four magnetic systems consists of a slab with 30 layers. In the case of
Mn/Ir(111), the slab consists of 5 vacuum + 1 Mn + 20 Ir layers + 4 vacuum
layers. For PdMn/Ir(111), the slab comprises 4 vacuum + 1 Pd + 1 Mn layer+ 20
Ir layers + 4 vacuum . In the case of MnPdFe/Ir(111), the slab includes 3
vacuum + 1 Mn layer + 1 Pd + 1 Fe + 20 Ir + 4 vacuum layers. Lastly, for
MnPd2Fe/Ir(111), the slab is composed of 2 vacuum + 1 Mn + 2 Pd + 1 Fe + 20 Ir
+ 4 vacuum. To perform the calculations, the momentum expansion of the Green
function was truncated at $\ell_{\text{max}}=3$. Self-consistent calculations
were conducted using a k-mesh of $30\times 30\times 1$ points. The energy
contour consisted of 23 complex energy points in the upper complex plane, and
it incorporated 9 Matsubara poles. To extract the Heisenberg exchange
interactions and Dzyaloshinskii-Moriya (DM) vectors, we employed the
infinitesimal rotation method [74, 75]. For this extraction, we used a finer
k-mesh of $200\times 200\times 1$ points.

###  0.5 Hamiltonian Model and atomistic spin dynamics.

After extracting the magnetic parameters for our magnetic atoms from first-
principles, we employ the Landau-Lifshitz equation (LLG) implemented in the
Spirit code [68] to explore the magnetic properties and complex states. This
exploration involves minimizing the two-dimensional Heisenberg Hamiltonian on
a triangular lattice. The Hamiltonian comprises several terms, including
Heisenberg exchange coupling, Dzyaloshinskii-Moriya interaction (DMI),
magnetic anisotropy energy, and Zeeman term. The energy functional of the
system can be described as follows:

$H=H_{\text{Exchange}}+H_{\text{DMI}}+H_{\text{Anisotropy}}+H_{\text{Zeeman}},$
(1)

with

$H_{\text{Exchange}}=-\sum\limits_{<i,j>}J^{\text{Mn-
Mn}}_{ij}\;\textbf{S}_{i}\cdot\textbf{S}_{j}-\sum\limits_{<i,j>}J^{\text{Fe-
Mn}}_{ij}\;\textbf{S}_{i}\cdot\textbf{S}_{j}-\sum\limits_{<i,j>}J^{\text{Fe-
Fe}}_{ij}\;\textbf{S}_{i}\cdot\textbf{S}_{j},$
$H_{\text{DMI}}=-\sum\limits_{<i,j>}\textbf{D}^{\text{Mn-
Mn}}_{ij}\cdot[\textbf{S}_{i}\times\textbf{S}_{j}]-\sum\limits_{<i,j>}\textbf{D}^{\text{Fe-
Mn}}_{ij}\cdot[\textbf{S}_{i}\times\textbf{S}_{j}]-\sum\limits_{<i,j>}\textbf{D}^{\text{Fe-
Fe}}_{ij}\cdot[\textbf{S}_{i}\times\textbf{S}_{j}],$
$H_{\text{Anisotropy}}=-K^{\text{Mn}}\sum\limits_{i}(\textbf{S}_{i}\cdot\textbf{e}_{i})^{2}-K^{\text{Fe}}\sum\limits_{i}(\textbf{S}_{i}\cdot\textbf{e}_{i})^{2},$
$H_{\text{Zeeman}}=-\sum\limits_{i}\mu_{i}\textbf{B}\cdot\textbf{S}_{i},$

where we assign indices $i$ and $j$ to denote specific sites, each associated
with a magnetic moment. The magnetic moment is represented by the unit vector
S. The Heisenberg exchange coupling strength $J^{\text{X-Y}}_{ij}$ describes
the interaction between an atom X on site $i$ and an atom Y on site $j$, where
a negative value indicates AFM interaction. Similarly, we use the notation  D
for the Dzyaloshinskii-Moriya interaction vector, $K$ for the magnetic
anisotropy energy, and $\mu_{i}\textbf{B}$ to represent the Zeeman coupling to
the atomic spin moment $\mu$ at site $i$. It is important to note that the Fe-
Mn and Fe-Fe interactions are only considered in the MnPdFe/Ir(111) and
MnPd2Fe/Ir(111) systems. For our spin atomistic simulations, we adopt both
periodic and finite boundary conditions to model the extended and confined
two-dimensional system, respectively, with cells containing $249^{2}$,
$300^{2}$, $390^{2}$ sites.

###  0.6 Data availability

The data needed to evaluate the conclusions in the paper are present in the
paper and the Supplementary Information.

###  0.7 Code availability

We used the following codes: Quantum ESPRESSO which can be found at
https:/www.quantum-espresso.org/download, SPIRIT can be found at
https://github.com/spirit-code/spirit, and the KKR code is a rather complex
ab-initio DFT-based code, which is in general impossible to use without proper
training on the theory behind it and on the practical utilization of the code.
We are happy to provide the latter code upon request.

Figure 1: Frustrated Néel AFM meronic topology: a AFM hexameronic state
composed of Vortex-antivortex pair that emerges in a frustrated triangular Mn
layer on e.g. Ir(111) surface with zoom into the vortex b, and antivortex c
components. The frustrated AFM meronic texture is decomposed into three FM
vortix-antivortex pairs residing at sublattices L1 d, g, L2 e, h, and L3 f, i.
j illustration of the Néel AFM ground state with colors indicating the
decomposition into three sublattices L1, L2 and L3. k Schematic representation
of the set of sublattices for the possible topological magnetic structures,
with w stands for the winding number and N stands for the topological number
(N = wp/2 with p = +1 for up and p = -1 for down polarity of the core). Figure
2: Impact of external magnetic field : a-d Schematic representation of the
magnetic layered systems of study. e The critical out-of-plane magnetic field
annihilating. Blue and red bars refer to respectively hexa- and dodecamerons
emerging in AFM Néel order, while green bars correspond to hexamerons hosted
by initially spiraling Néel states. Bars with solid versus dashed lines
distinguish the cases without and with Mn-Fe interactions. f-h snapshots for
the blue, red and green magnetic states, respectively, inset shows the spiral
at the background of h. i Snapshot showing the blue dashed bar representing
the Mn layer(upper layer) interfaced with the Fe layer (lower layer).  Figure
3: Topologically-dependent response to the external magnetic field :  Lifting
the quadrupole degeneracy of the hexameron (Hexa A–D) upon application of an
outof-plane magnetic field. Each hexmeron is decomposed into the three
sublattices with the illustration of the vortex nature of the meronic core
constituents together with the core spin-direction. Hexa D is the frustrated
hexameron satisfying the ideal stability criterion against the magnetic field.
Figure 4: Minimal spin model for frustrated AFM Néel multimerons: a Phase
diagram showing immediate emergence of hexamerons requiring an AFM nearest
neighboring magnetic interaction, $J_{1}$, and an out-of-plane DMI component,
$D_{z}$. b, c Mutual impact of magnetic exchange interactions and DMI on the
Sz profile of one of the vortices. d The associated critical field required
for the annihilation of the multimeron as function of the DMI.

## ACKNOWLEDGEMENTS

We acknowledge fruitful discussions with Nihad Abuawwad. This work was
supported by the Federal Ministry of Education and Research of Germany in the
framework of the Palestinian-German Science Bridge (BMBF grant number
01DH16027) and the Deutsche Forschungsgemeinschaft (DFG) through SPP 2137
“Skyrmionics” (Project LO 1659/8-1). The authors gratefully acknowledge the
computing time granted through JARA on the supercomputer JURECA at
Forschungszentrum Jülich.

S.L. initiated, designed and supervised the project. A.A. performed the
simulations and post processed the data . A.A., M.S., M.A., and S.L. discussed
the results. A.A. and S.L. wrote the manuscript to which all co-authors
contributed.

The authors declare no competing interests.

Correspondence and requests for materials should be addressed to A.A. (email:
<EMAIL_ADDRESS>or to S.L. (email: s.lounis@fz-juelich.de).

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