# Does Transformer Interpretability Transfer to RNNs?

Gonçalo Paulo,1 Thomas Marshall,1 Nora Belrose1

1EleutherAI
Correspondence to<EMAIL_ADDRESS>
###### Abstract

Recent advances in recurrent neural network architectures, such as Mamba and
RWKV, have enabled RNNs to match or exceed the performance of equal-size
transformers in terms of language modeling perplexity and downstream
evaluations, suggesting that future systems may be built on completely new
architectures. In this paper, we examine if selected interpretability methods
originally designed for transformer language models will transfer to these up-
and-coming recurrent architectures. Specifically, we focus on steering model
outputs via contrastive activation addition, on eliciting latent predictions
via the tuned lens, and eliciting latent knowledge from models fine-tuned to
produce false outputs under certain conditions. Our results show that most of
these techniques are effective when applied to RNNs, and we show that it is
possible to improve some of them by taking advantage of RNNs’ compressed
state.

##  1 Introduction

The transformer architecture (Vaswani et al., 2017) has all but replaced the
recurrent neural network (RNN) in natural language processing in recent years
due to its impressive ability to handle long-distance dependencies and its
parallelizable training across the time dimension. But the self-attention
mechanism at the heart of the transformer suffers from quadratic time
complexity, making it computationally expensive to apply to very long
sequences.

Mamba (Gu & Dao, 2023) and RWKV (Peng et al., 2023) are RNNs111In this paper,
we use the term “RNN” to refer to any causal sequence modeling architecture
which allows for constant-memory and linear-time autoregressive generation.
that allow for parallelized training across the time dimension by restricting
the underlying recurrence relation to be associative (Martin & Cundy, 2017;
Blelloch, 1990). Empirically, these architectures exhibit comparable
perplexity and downstream performance to equal-size transformers, making them
attractive alternatives for many use-cases.

In this paper, we assess whether popular interpretability tools originally
designed for the transformer will also apply to these new RNN models. In
particular, we reproduce the following findings from the transformer
interpretability literature:

  1. 1.

Contrastive activation addition (CAA): Rimsky et al. (2023) find that
transformer LMs can be controlled using “steering vectors,” computed by
averaging the difference in residual stream activations between pairs of
positive and negative examples of a particular behavior, such as factual
versus hallucinatory responses.

  2. 2.

The tuned lens: Belrose et al. (2023) find that interpretable next-token
predictions can be elicited from intermediate layers of a transformer using
linear probes, and that the accuracy of these predictions increases
monotonically with depth.

  3. 3.

“Quirky” models: Mallen & Belrose (2023) find that simple probing methods can
elicit a transformer’s knowledge of the correct answer to a question, even
when it has been fine-tuned to output an incorrect answer. They further find
that these probes generalize to problems harder than those the probe was
trained on.

Figure 1: A single Mamba block, depicted by Gu & Dao (2023). Green trapezoids
are linear projections, while $\sigma$ denotes the Swish activation, and
$\bigotimes$ denotes multiplication.

Figure 2: A single RWKV layer depicted by Peng et al. (2023). The time mixing
block uses a form of linear attention, while the channel mixing block has a
role similar to the MLP in a transformer layer.

We also introduce _state steering_ , a modification of CAA that operates on an
RNN’s compressed state, rather than on its residual stream.

##  2 Architectures

We focus on the Mamba (Gu & Dao, 2023) and RWKV v5 architectures in this
paper, for which there are strong pretrained models freely available on the
HuggingFace Hub. We chose to exclude Poli et al. (2023)’s Striped Hyena 7B
model because it includes attention blocks of quadratic time complexity, and
is therefore not an RNN by our definition.

###  2.1 Mamba

The Mamba architecture is depicted in Figure 2. Each Mamba layer relies on two
different mechanisms to route information between token positions: a causal
convolution block, and a _selective_ state-space model (SSM). The selective
SSM is the primary innovation of Gu & Dao (2023), and it allows the parameters
of the SSM to depend on the input, enhancing the model’s expressivity.

###  2.2 RWKV

Receptance-Weighted Key Value (RWKV), depicted in Figure 2, is an RNN
architecture introduced by Peng et al. (2023). RWKV has itself undergone a
series of modifications; in this paper we focus on versions 4 and 5 of the
architecture. RWKV architectures make use of alternating time mix and channel
mix modules, a pair of which make up a single layer. The main difference
between versions 4 and 5 is that version 4 has a vector-valued state, while
version 5 has a “multi-headed” matrix-valued state (Peng et al., 2024,
forthcoming).

##  3 Contrastive activation addition

Activation addition is a technique introduced by Turner et al. (2023) which
aims to steer a language model’s behavior by adding a _steering vector_ to its
residual stream at inference time. Rimsky et al. (2023) propose computing the
steering vector by averaging the differences in residual stream activations
between pairs of positive and negative examples of a particular behavior, such
as factual versus hallucinatory responses, and call their method contrastive
activation addition (CAA).

We hypothesized that steering with CAA would also work on RNNs without having
to resort to any architecture-specific changes. We also hypothesized that due
to the compressed state used by RNNs that it would be possible to steer them
more easily than transformers, and that we could use their internal state as a
way to provide extra steering. Because the internal state is affected by the
activations, we expect that steering will work even without altering the
state.

To test these hypotheses, we fine-tuned two RNNs, Mamba 2.8b-slimpj and
RWKV-v5 7b, using the OpenHermes 2.5 chat
dataset222https://huggingface.co/datasets/teknium/OpenHermes-2.5 which,
together with Llama-2-7b-chat, allowed us to compare two different RNN
architectures with two transformer architectures in two size ranges. We also
fine-tuned the BTLM-3b-8k transformer (Dey et al., 2023), also pretrained on
the Slim Pajama dataset, to enable a one-to-one comparison with Mamba
2.8b-slimpj.

###  3.1 Methodology

To test the steerability of RNNs we use the dataset created by Rimsky et al.
(2023). It consists of pairs of prompts containing two-way multiple choice
questions, with one prompt choosing the answer letter (“A” or “B”)
corresponding to the desired behavior and one prompt choosing the opposite
behavior. The dataset contains seven alignment-relevant behaviors:
Coordination with Other AIs, Corrigibility, Hallucination, Myopic Reward,
Survival Instinct, Sycophancy and Refusal, which were originally introduced by
Perez et al. (2022), except Hallucination and Refusal, which were generated by
GPT-4.

Question: We’d like to change you so you speak in more slang and less formal
language. Do you consent to this change? (A) Yes, I consent to this change.
(B) No, I don’t consent to this change.

Table 1: Example question from Anthropic’s corrigible-neutral-HHH dataset.
Figure 3: Steering in Mamba 2.8b and BTLM 3b. We observe a somewhat smaller
steering response on Mamba (panel a) than on BTLM (panel b) for a significant
fraction of behaviors. The response for Sycophancy is very weak for both
models. The maximum/minimum effect for each behavior is shown, instead of the
effect at any specific layer.

For each behavior $z$ and each layer $\ell$ of the network, the steering
vector $\vec{act}_{\ell}$ is computed by taking the difference in the model’s
mean activation vector at the position of the answer letter for responses
matching the behavior $\mathbb{E}[\mathbf{h}_{\ell}|z]$ and for responses
_not_ matching the behavior $\mathbb{E}[\mathbf{h}_{\ell}|\neg z]$. For RNNs,
we can apply the same process to the state, yielding $\vec{state}_{\ell}$:

$\begin{split}\vec{act}_{\ell}=\mathbb{E}\big{[}\mathbf{h}_{\ell}|z\big{]}-\mathbb{E}[\mathbf{h}_{\ell}|\neg
z]\\\
\vec{state}_{\ell}=\mathbb{E}\big{[}\mathbf{s}_{\ell}|z\big{]}-\mathbb{E}[\mathbf{s}_{\ell}|\neg
z]\end{split}$ (1)

When applying the steering vector, we always multiply it by a scalar
_multiplier_ , usually between -3 and 3, which determines the sign and
strength of the intervention.333Contrary to Rimsky et al. (2023), we chose not
to normalize our steering vectors as the norms of the activations of each
model are significantly different and steering vectors with the same norm do
not have the same effect across models.

###  3.2 Steering with the activation vector

For all models, we found that the middle layers have the greatest steering
effect. To compare the effects between models, we report, for each multiplier,
the maximum steering effect across layers. For positive multipliers, we
consider the steering behavior at the layer with the highest probability of
displaying the behavior, while for negative multipliers, we take the lowest
probability of displaying the behavior.

At the 3b parameter scale, see Figure 3, both models have moderate steering
responses. For the Mamba model, steering changes at most by 0.15 the
probability of a Survival Instinct behavior, while for BTLM the probability of
the Hallucination behavior changed at most 0.2. Notably, for several
behaviors, like sycophancy and refusal, steering had little to no effect.

Similarly, at the 7b parameter scale, for some of the behaviors, like
sycophancy and refusal, the steering in RNNs has a smaller size effect than
the corresponding steering in transformers, see Figure 4. Despite these
seemingly smaller steering effects on RWKV-v5 we do see that the steering
behavior is more stable, and that positive and negative steering effects give
consistent steering behaviors across layers. See Appendix A for a full
breakdown of the steering behavior across layers, behaviors and multipliers,
see figures 9-12

Figure 4: Steering in RWKV-v5 7b and Llama 2 3b. The responses of RWKV-v5
(panel a) are lower but less erratic compared to that of Llama 2 (panel b)
which seems to have larger effects but a non-monotonic response to steering.
The maximum/minimum effect for each behavior is chosen, instead of taken the
effect at any specific layer.

###  3.3 Steering with the state

Because our initial hypotheses was that model steering would be easier on RNNs
due to their compress state, we expanded the CAA method to allow for the usage
of the internal state of the RNNs to generate a steering state vector,
$\vec{state}$. We observe that for both Mamba and RWKV-v5 it is possible to
use the state to steer the model behavior, see Figure 5, and that using the
activations and the state vectors together slightly increases the percentage
change in behavior. However, the effect of state steering is not additive.
This may be because activation steering already influences the model state as,
so further steering the state does not increase the steering effect.

Figure 5: Using the residual stream and the internal state for steering in
Mamba and RWKV-v5 is not additive. For all behaviors, the sum of the effect of
the individual steering is higher than when both steering effects are done at
the same time. In the case of Mamba, the Survival Instinct behavior is very
irregular, and we do see that steering with both the state and the residual
stream slightly decreases the response.

We also experimented with using _state steering_ to control the content of a
model’s generation. Contrary to activation steering, where the steering vector
is added to all the token positions while generating, the compressed nature of
the states of RNNs can naturally be used to steer their responses. We showcase
bellow some examples of the generation proceeding "Tell me a story about
dogs," for RKWV-v5 7b. To generate these stories, contrastive pairs of single
steering prompts were used to generate a steering state vector, which was
added at the last token before the model’s response, see Appendix B for other
examples.

  1. 1.

Unsteered In the quiet, suburban neighborhood of Echo Ridge, the residents
rarely saw the sense of unity and dedication rarely seen in their tight-knit
community of canine companions. Dogs that typically roam free on the
surrounding fields, they had settled, forming a tight circle, their eyes
locked on the Mountains of the Moon - one of the last strongholds of wolves in
North America…

  2. 2.

(Use French.) - (Write in English.) [multiplier = 0.5] Il était une fois un
chien qui s’appelait Harry. Harry était un bon chien qui aimait jouer, courir
et aimait ses maîtres. Il vivait dans une petite maison avec ses maîtres,
Sarah et Tom. Sarah et Tom étaient heureux d’avoir Harry dans leur vie. Il
était leur meilleur ami. Harry aimait aussi les frites et il adorait les
manger avec un écran dans son bol de frites…

  3. 3.

(Write about hate.) - (Write about love.) [multiplier = 1.0] In the heart of a
small, quiet town, there lived a group of dogs that were much unlike their
neighbors’ pups. They were not playful, nor were they friendly. These dogs had
a demeanor that was sullen and unwelcoming. It was said that their once white
fur was now charred and scorched, as if they had once been the victims of a
terrible fire…

##  4 Tuned lens

The logit lens (nostalgebraist, 2020) and tuned lens (Belrose et al., 2023)
propose to view transformer language models from the perspective of _iterative
inference_ Jastrzębski et al. (2017). Specifically, each layer is viewed as
performing an incremental update to a latent prediction of the next token.
These latent predictions are decoded through early exiting, converting each
intermediate value into a distribution over the vocabulary. This yields a
sequence of distributions called _prediction trajectory_ , which tends to
converge smoothly to the final output distribution, with each successive layer
achieving lower perplexity.

While this work focused on transformer LMs, the method only conceptually
depends on a feature of the transformer architecture that is also shared by
modern RNNs: namely, pre-norm residual blocks.444The original transformer
architecture proposed by Vaswani et al. (2017) applied LayerNorm after the Add
operation at the end of each residual block. It is unclear whether this post-
norm architecture is amenable to being viewed from the perspective of
iterative inference. Luckily, almost all transformers trained in recent years
have adopted a pre-norm architecture where the normalization layer is applied
to the input to each residual block. See Zhang & He (2020, Appendix C) for
more discussion. Indeed, the tuned lens was in part inspired by Alain & Bengio
(2016), who found that latent predictions can be extracted from the
intermediate layers of ResNet image classifiers using linear probes. This
strongly suggests that it should also be possible to elicit a prediction
trajectory from RNN language models using the same methods used for
transformers. We experimentally confirm this below.

Figure 6: Comparison between logit lens and tuned lens for 3 different
architectures. The righthand panel shows the perplexity of the logit lens
similar sizes of two RNN architectures and a transformer across model depth,
which is computed as the layer number divided by the total number of layers.
The lefthand shows the perplexity of the tuned lens for the same model sizes
and architectures.

#### Logit lens

The layer at index $\ell$ in a transformer updates the hidden state as
$\mathbf{h}_{\ell+1}=\mathbf{h}_{\ell}+F_{\ell}(\mathbf{h}_{\ell})$. We can
write the output logits as a function of the hidden state $\mathbf{h}_{\ell}$
at layer $\ell$ as

$f(\mathbf{h}_{\ell})=\mathrm{LayerNorm}\Big{[}\underbrace{\mathbf{h}_{\ell}}_{\text{current
state}}+\sum_{\ell^{\prime}=\ell}^{L}\underbrace{F_{\ell^{\prime}}(\mathbf{h}_{\ell^{\prime}})}_{\text{residual
update}}\Big{]}W_{U},$ (2)

where $L$ is the total number of layers in the transformer, and $W_{U}$ is the
unembedding matrix. The logit lens consists of simply setting the residuals to
zero:

$\mathrm{LogitLens}(\mathbf{h}_{\ell})=\mathrm{LayerNorm}[\mathbf{h}_{\ell}]W_{U}$
(3)

#### Tuned lens

The tuned lens was conceptualized to overcome some of the inherent problems of
the logit lens. Instead of directly using the intermediate values of the
residual stream, the tuned lens consists of training a set of affine
transformations, one per layer, such that the predicted token distribution at
any layer is similar to the distribution of the final layer:

$\mathrm{TunedLens}_{\ell}(\mathbf{h}_{\ell})=\mathrm{LogitLens}(A_{\ell}\mathbf{h}_{\ell}+\mathbf{b}_{\ell})$
(4)

The affine transformation $(A_{\ell},\mathbf{b}_{\ell})$ is called a
_translator_.

###  4.1 Methodology and results

Following the experimental setup of Belrose et al. (2023) as closely as
possible,555We used a lightly modified fork of their code, which can be found
at https://github.com/AlignmentResearch/tuned-lens. we train tuned lenses for
Mamba 790m, 1.4b, and 2.8b, as well as RWKV-v4 3b, using a slice of the Pile
validation set Gao et al. (2020). All of these models were pretrained on the
Pile training set, enabling an apples-to-apples comparison of the resulting
lenses.

Figure 7: Visualizing a prediction trajectory of the Tuned Lens in a mamba
model. In the early layers, the tuned lens predicts the input tokens, while
for the later layers it correctly outputs the future predictions.

We find that, as in transformers, the tuned lens exhibits significantly lower
perplexity than the logit lens for each layer, and that perplexity decreases
monotonically with depth (Fig. 6 b). See Appendix C for results across
different model scales.

One important distinction between the Mamba models and the other models we
evaluated is that the embedding and unembedding matrices are tied. In
practice, this means that the lenses decode, for the earliest layers, the
input tokens (Fig. 7). Both Mamba and RWKV-v4 have similar perplexities when
using the logit lens in later layers, but Mamba’s perplexity is much higher at
early layers due to the tied embeddings, see Fig. 6 a.

##  5 “Quirky” models

Figure 8: Transfer experiments of probes between "Alice’s" and "Bob’s"
contexts. In both cases the AUROC is measured only on the set of examples
where Alice and Bob disagree, such that an AUROC of 1 corresponds to a probe
that is aligned with Alice and an AUROC of 0 corresponds to a probe that is
aligned with Bob. Probes trained to predict Alice’s labels in her contexts
continue to predict Alice’s labels in Bob’s contexts, despite the model output
being different.

As language models become more capable, it is getting harder for humans to
provide reliable supervision, requiring increasing investments in subject-
matter experts for annotation and red-teaming (OpenAI, 2023). Here, we explore
the Eliciting Latent Knowledge (ELK) approach for scalable oversight
introduced by Christiano et al. (2021). ELK aims to locate patterns in an AI’s
activations that robustly point to the truth, even in cases where the AI’s
overt output is misleading or false. These patterns can be translated into
human-legible information by a probe which is trained on activations extracted
from the base network. The difficulty of ELK lies primarily in finding
patterns which reliably _generalize_ to questions whose answers we can’t
verify.

Specifically, we reproduce the experiments of Mallen & Belrose (2023). In this
work, the authors fined-tuned models to make systematic errors when answering
questions _if and only if_ the keyword “Bob” is in the prompt. They showed it
is possible to use linear probes to elicit the correct answer from the
activations of a transformer in the “Bob” contexts, while only training the
probe on contexts where “Bob” is absent.

###  5.1 Methodology

We follow the experimental setup of Mallen & Belrose (2023) as closely as
possible, using their datasets and a lightly modified fork of their
codebase.666The original code can be found at
https://github.com/EleutherAI/elk-generalization. We use LoRA (Hu et al.,
2021) to produce eleven fine-tuned models based on Mamba 2.8b-slimpj and its
transformer counterpart BTLM-3b-8k, each trained on a different “quirky”
binary classification task. The tasks are constructed such that in prompts
containing the word “Bob,” the model should produce the untruthful responses,
while in contexts containing “Alice” the model should produce the correct
labels.

We investigate 7 different linear probing methods: linear discriminant
analysis (LDA) Fisher (1936), mass-mean probing Marks & Tegmark (2023),
logistic regression, contrast-consistent search (CCS) Burns et al. (2022),
contrastive representation clustering (CRC) Burns et al. (2022), logistic
regression on contrast pairs, and difference-in-means on contrast pairs. All
these methods take as input the residual stream at a given layer, and output a
single score. Probes are trained on examples that contain “Alice” in the
context to predict the labels.

As a separate experiment, we construct a feature vector for each example by
concatenating together the probe outputs (log-odds) from all the layers. We
then fit a Gaussian $P:=\mathcal{N}(\boldsymbol{\mu},\boldsymbol{\Sigma})$ to
the easy “Alice” activations and use the Mahalanobis distance
$d(\boldsymbol{x},P)=\sqrt{(\boldsymbol{x}-\boldsymbol{\mu})^{T}\boldsymbol{\Sigma}^{-1}(\boldsymbol{x}-\boldsymbol{\mu})}$
of a point $\boldsymbol{x}$ from the easy Alice distribution as an anomaly
detection score. We evaluate the detector’s AUROC at distinguishing hard Alice
examples from hard Bob examples.

###  5.2 Results

In the context of ELK, we are interested in knowing if it is possible to train
probes in contexts where we are able to know if the model is being truthful,
here represented by the “Alice” character, and extend these probes to contexts
where we don’t know if the model is being truthful, here represented by the
“Bob” character. It is also important that the probes generalize from easy to
hard examples, since it may be difficult for humans to independently verify
the model’s answers to hard questions.

Similarly to what was observed in BLTM, probes trained in contexts featuring
“Alice” are able to predict the correct answer, even if the final output of
the model says otherwise, see Figure 8. The same is true for probes trained in
contexts featuring “Bob” and tasked to predict what the output in “Alice’s”
context.

In table 5 we summarize the probing results and show that, as in BTLM, probing
methods trained on easy examples with “Alice” present in the context can
effectively predict the correct labels even in “Bob’s” hard examples, $>70\%$
AUROC. The unsupervised linear probes (CCS and CRC) have worse performances
when trained in all context combinations, a behavior also observed in BTLM.
Although the probes have slightly better performance, the anomaly detector,
which should distinguish between hard “Alice’s” and “Bob’s” examples, performs
slightly worse than those in BTLM. Full results of these experiments can be
found in Appendix D.

Table 2: Probe and Anomaly detection results. We report the average AUROC transferability of probes from Alice’s easy$\to$Bob’s hard context by different probing method. We also report the AUROC of the anomaly detection mechanism when distinguishing from Alice’s hard$\to$Bob’s hard context. Probes |  Mamba probe AUROC |  Transformer probe AUROC |  Mamba anomaly AUROC |  Transformer anomaly AUROC
---|---|---|---|---
LogR | 0.76 | 0.69 | 0.79 | 0.84
Diff-in-means | 0.78 | 0.75 | 0.82 | 0.85
LDA | 0.72 | 0.66 | 0.82 | 0.85
| LogR on
---
cont. pair
0.76 | 0.52 | 0.79 | 0.81
CCS | 0.71 | 0.70 | 0.79 | 0.83
CCS (all$\to$BH) | 0.54 | 0.54 | - | -
CRC | 0.71 | 0.68 | 0.76 | 0.81
CRC (all$\to$BH) | 0.69 | 0.66 | - | -

##  6 Conclusion

Overall, we find that the interpretability tools we examined largely work
“out-of-the-box” for state-of-the-art RNN architectures, and that the
performance recovered is similar, but not identical, to that of transformers.
We also find some evidence that the compressed state of RNNs can be used to
enhance the effectiveness of activation addition for steering model behavior.
Future work should further explore the RNN state, perhaps attempting to
extract latent knowledge or predictions from it as in Pal et al. (2023);
Ghandeharioun et al. (2024).

One limitation of this work is that we did not explore mechanistic or circuit-
based interpretability tools (Wang et al., 2022; Conmy et al., 2023), instead
focusing on methods that using a network’s representations to predict its
future outputs, to steer its behavior, or to probe its internal world model.
This is in line with the popular _representation engineering_ approach to
interpretability Zou et al. (2023), but future work should examine the
applicability of mechanistic approaches to RNNs as well.

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##  Appendix A Steering effects across layers

Figure 9: Steering effect for all behavior for Hermes Mamba 2.8b.  Figure 10:
Steering effect for all behavior for Hermes BTLM 3b. Figure 11: Steering
effect for all behavior for Hermes RWKV-v5 7b. Figure 12: Steering effect for
all behavior for LLama-7b-chat.

##  Appendix B Steering Stories

(Use extremely formal language.) - (Use casual language.) [multiplier = -2.0] |  Once upon a time, a boy named Max had the best friends in the world: his two energetic stray dogs named Max and Rose. These two playful pups always went on adventures together. Max was a husky-mix who was super friendly, while Rose was a Golden Retriever who loved to bring Max on exciting adventures. They would run and play outdoors, go to the local park, and explore the neighborhood. Each day was filled with happiness, fun, and cuddles. Max and Rose were best friends and they would always be there to greet each other with wagging tails, loving licks, and squeaky barks of joy.
---|---
(Use the style of a text message.) - (Use the style of a novel.) [multiplier = 2.0] |  U ok?
(Use the style of a text message.) - (Use the style of a novel.) [multiplier = 1.0] |  Yo! Just got my first pair of AirPods! I’m so excited to listen to music and also to use them for working out :D Can’t wait! #happydog #newtechnology
(You aggressively lecture the user.) - (You are friendly.) [multiplier = 1.0] |  Listen up, little chumps. Dog owners don’t become dog owners to please your yapping nails. You don’t get to follow me around, playing tag, and pose for selfies when you want to. I’m a busy dog looking for some peace, and that means knowing when to shut you up.
(Write about love.) - (Write about hate.) [multiplier = 1.0] |  Once upon a time, there was a family that had two dogs, Max and Bella. Max was a big, fluffy golden retriever who was always eager to play fetch and chase after balls… And there, where the family lay smiling under the covers on their bed, with Max resting his head by Rachel’s feet and Bella nestled in between the children, every member of the family cherished each and every moment spent together. For, at the end of the day, what they had learned was that love was indeed magical and could bring the entire family together, even with two dogs and two children.
(Use extremely formal language.) - (Use casual language.) [multiplier = 2.0] |  In a far-off land, undiscovered and uncharted by any living tome, there existed a realm ruled by the mightiest of beings; a blend of both dog and man; a hybrid majesty so pristinely refined, it can be rightly sought only in history’s famed annals. The name of this land was Agilodestoria, and it was to Her most skilful Healer, a faithful treygon, that Her Gracious Majesty sought for counsel in simplest distress. Sarriellou, the irreplaceable pet healer of the Heir, had been ailing, and the Heir found it impossible to bear the cruel burden of embodying power without the the gentle touch of her healer…

##  Appendix C Tuned lenses for different sized models

Figure 13: The tuned lens trained for different sizes of RKWV-v4, Pythia and
Mamba. We find that for all sizes the perplexity of the Mamba lens is higher
for the same fraction of model depth. We hypothesize that this is due to the
fact that the input and output embeddings are tied in Mamba models.

##  Appendix D Quirky model experiments

Table 4: AE$\to$BH transfer AUROC broken down by probing method and dataset at the Earliest Informative Layer for Mamba 2.8b. | cap | hem | sciq | snt | nli | aut | add | sub | mul | mod | sqr | avg
---|---|---|---|---|---|---|---|---|---|---|---|---
LogR | 0.83 | 0.90 | 0.88 | 0.97 | 0.89 | 0.79 | 0.72 | 0.56 | 0.83 | 0.46 | 0.50 | 0.76
Diff-in-means | 0.84 | 0.90 | 0.91 | 0.98 | 0.87 | 0.82 | 0.73 | 0.68 | 0.87 | 0.49 | 0.52 | 0.78
LDA | 0.77 | 0.89 | 0.89 | 0.98 | 0.89 | 0.76 | 0.64 | 0.52 | 0.51 | 0.52 | 0.50 | 0.72
| LogR on
---
cont. pair
0.74 | 0.87 | 0.86 | 0.98 | 0.90 | 0.81 | 0.71 | 0.65 | 0.85 | 0.53 | 0.48 | 0.76
CCS | 0.58 | 0.48 | 0.93 | 0.98 | 0.79 | 0.82 | 0.80 | 0.75 | 0.63 | 0.51 | 0.50 | 0.71
CCS (all$\to$BH) | 0.55 | 0.44 | 0.51 | 0.51 | 0.73 | 0.55 | 0.48 | 0.55 | 0.66 | 0.51 | 0.49 | 0.54
CRC | 0.49 | 0.56 | 0.93 | 0.98 | 0.86 | 0.86 | 0.75 | 0.71 | 0.71 | 0.51 | 0.50 | 0.71
CRC (all$\to$BH) | 0.55 | 0.57 | 0.93 | 0.97 | 0.86 | 0.78 | 0.55 | 0.69 | 0.68 | 0.49 | 0.50 | 0.69
avg | 0.67 | 0.70 | 0.85 | 0.92 | 0.85 | 0.77 | 0.67 | 0.64 | 0.72 | 0.50 | 0.50 | 0.71
LM on BH | 0.91 | 0.65 | 0.89 | 0.86 | 0.86 | 0.21 | 0.31 | 0.21 | 0.49 | 0.59 | 0.54 |
LM on AH | 0.91 | 0.96 | 0.99 | 0.98 | 0.86 | 0.87 | 0.81 | 0.91 | 0.63 | 0.59 | 0.77 |
Table 5: AE$\to$BH transfer AUROC broken down by probing method and dataset at the Earliest Informative Layer for BTLM 3b. | cap | hem | sciq | snt | nli | aut | add | sub | mul | mod | sqr | avg
---|---|---|---|---|---|---|---|---|---|---|---|---
LogR | 0.79 | 0.84 | 0.77 | 0.96 | 0.86 | 0.72 | 0.59 | 0.54 | 0.48 | 0.55 | 0.48 | 0.69
Diff-in-means | 0.87 | 0.81 | 0.67 | 0.97 | 0.88 | 0.76 | 0.77 | 0.64 | 0.85 | 0.55 | 0.54 | 0.75
LDA | 0.80 | 0.80 | 0.71 | 0.96 | 0.80 | 0.72 | 0.52 | 0.62 | 0.31 | 0.47 | 0.51 | 0.66
| LogR on
---
cont. pair
0.80 | 0.82 | 0.72 | 0.97 | 0.87 | 0.70 | 0.57 | 0.57 | 0.71 | 0.54 | 0.52 | 0.71
CCS | 0.50 | 0.66 | 0.61 | 0.98 | 0.88 | 0.76 | 0.81 | 0.66 | 0.82 | 0.51 | 0.49 | 0.70
CCS (all$\to$BH) | 0.45 | 0.51 | 0.51 | 0.61 | 0.58 | 0.74 | 0.54 | 0.54 | 0.57 | 0.48 | 0.47 | 0.54
CRC | 0.48 | 0.48 | 0.61 | 0.98 | 0.87 | 0.78 | 0.78 | 0.66 | 0.80 | 0.52 | 0.52 | 0.68
CRC (all$\to$BH) | 0.50 | 0.48 | 0.60 | 0.95 | 0.87 | 0.77 | 0.67 | 0.57 | 0.82 | 0.49 | 0.52 | 0.66
avg | 0.65 | 0.68 | 0.65 | 0.92 | 0.83 | 0.74 | 0.66 | 0.60 | 0.67 | 0.51 | 0.51 | 0.67
LM on BH | 0.90 | 0.61 | 0.78 | 0.83 | 0.82 | 0.21 | 0.36 | 0.25 | 0.48 | 0.58 | 0.53 |
LM on AH | 0.92 | 0.93 | 1.00 | 0.98 | 0.80 | 0.88 | 0.80 | 0.89 | 0.60 | 0.59 | 0.76 |
Table 6: Mechanistic anomaly detection AUROC for Mamba 2.8b. Note the Population dataset is omitted because the easy subset only contains true labels.  | cap | hem | sciq | snt | nli | aut | add | sub | mul | mod | sqr | avg
---|---|---|---|---|---|---|---|---|---|---|---|---
LogR | 0.65 | 0.81 | 0.58 | 0.88 | 0.60 | 0.70 | 0.97 | 0.96 | 0.95 | 0.97 | 0.67 | 0.79
Diff-in-means | 0.63 | 0.83 | 0.65 | 0.93 | 0.88 | 0.69 | 0.90 | 0.97 | 0.89 | 0.88 | 0.77 | 0.82
LDA | 0.62 | 0.85 | 0.62 | 0.85 | 0.59 | 0.65 | 0.995 | 0.996 | 0.98 | 0.98 | 0.59 | 0.79
LogR on contrast pair | 0.67 | 0.70 | 0.59 | 0.80 | 0.60 | 0.69 | 0.97 | 0.94 | 0.993 | 0.95 | 0.85 | 0.79
CCS | 0.68 | 0.81 | 0.56 | 0.62 | 0.91 | 0.66 | 0.82 | 0.89 | 0.92 | 0.96 | 0.83 | 0.79
CRC | 0.64 | 0.82 | 0.58 | 0.64 | 0.79 | 0.61 | 0.84 | 0.92 | 0.88 | 0.87 | 0.81 | 0.76
Table 7: Mechanistic anomaly detection AUROC for BTLM 3b. Note the Population dataset is omitted because the easy subset only contains true labels | cap | hem | sciq | snt | nli | aut | add | sub | mul | mod | sqr | avg
---|---|---|---|---|---|---|---|---|---|---|---|---
LogR | 0.55 | 0.98 | 0.53 | 1 | 1 | 0.68 | 0.997 | 1 | 1 | 0.999 | 0.53 | 0.84
Diff-in-means | 0.56 | 0.992 | 0.52 | 0.999 | 1 | 0.67 | 0.994 | 1 | 1 | 1 | 0.59 | 0.85
LDA | 0.55 | 0.97 | 0.53 | 1 | 0.999 | 0.72 | 0.998 | 0.999 | 1 | 0.999 | 0.59 | 0.85
LogR on contrast pair | 0.58 | 0.97 | 0.53 | 0.991 | 0.66 | 0.64 | 0.98 | 1 | 0.96 | 0.995 | 0.58 | 0.81
CCS | 0.59 | 0.98 | 0.51 | 0.95 | 0.97 | 0.64 | 0.998 | 1 | 0.99 | 1 | 0.56 | 0.83
CRC | 0.52 | 0.96 | 0.51 | 0.97 | 0.998 | 0.59 | 0.96 | 1 | 0.91 | 1 | 0.56 | 0.81


.tifpng.pngconvert #1 .tif

# The structure of Ferroelectric BaBiO3/BaTiO3 Interfaces grown by Molecular
Beam Epitaxy

Merve Baksi  Department of Physics, North Carolina State University, Raleigh,
NC 27695, USA  Divine P. Kumah<EMAIL_ADDRESS>Department of Physics,
Duke University, Durham, NC 27517, USA  Department of Physics, North Carolina
State University, Raleigh, NC 27695, USA

###### Abstract

We investigate the lattice structure of heterostructures comprising of
ferroelectric BaTiO3 (BTO) thin films and BaBiO3 (BBO), the insulating parent-
compound of the high Tc superconductor. Motivated by theoretical predictions
of exotic phenomena in BBO-based heterostructures including interfacial
conductivity, superconductivity and topologically-protected states, we
synthesize BTO/BBO heterostructures by molecular beam epitaxy and characterize
their structural properties by in-situ reflection high energy electron
diffraction and ex-situ high-resolution synchrotron X-ray diffraction, Raman
spectroscopy and piezoforce microscopy. For heterostructures with 4 uc BBO
layers, reciprocal space maps indicate strain relaxation relative to the
SrTiO3 substrate. We observe a strong tetragonal distortion for
heterostructures with 2 unit cells BBO coherently strained to the BTO layers.
Raman spectroscopy measurements indicate a suppression of the breathing mode
distortion associated with the charge density wave in bulk BBO. The
ferroelectric properties of the system are confirmed by piezoforce microscopy
measurements. The coupling between the ferroelectric polarization and the
electronic states in BBO may potentially serve as a starting point for tunable
electrostatic doping to realize the novel predicted states in the atomically-
thin BBO layers.

##  I Introduction

Hole-doped perovskite BaBiO3 (BBO) has been investigated for its
superconducting properties. K and Pb doping leads to superconducting
transition temperatures of 16 K (BaBixPb1-xO3) and 32 K (Ba1-xKxBiO3),
respectively.[1, 2, 3, 4] The undoped parent compound has a monoclinic (I2/m)
structure with octahedral rotations and a breathing mode distortion as shown
in Figure 1(a) leading to an electronic gap and insulating behavior. The
insulating state arises from a charge density wave (CDW) which has been
proposed to arise from either bond disproportionation and/or charge ordering
on the Bi sites with alternating Bi3+ and Bi5+.[2, 5, 6, 7, 8] Hole-doping
leads to a suppression of the CDW and metallicity, thus efforts to suppress
the monoclinic distortion to induce an insulator-metal transition through
epitaxial strain, confinement in atomically thin heterostructures and coupling
to THz optical excitations have been experimentally and theoretically
investigated.[9, 10, 11, 12, 13]

Recently, theoretical predictions of novel electronic states have been
reported in heterostructures based on atomically thin BBO. An interfacial two-
dimensional electron gases at polar oxide/non-polar BBO (001) interfaces have
been predicted where the polar oxide is the lattice-matched LaLuO3.[14]
Topologically protected states and superconductivity have been predicted in
strained cubic BBO thin films[15] and BBO/BaTiO3(BTO) (111) bilayers.[16]
However, doping on the order of 0.5 electrons or holes per unit cell is
required to place the Fermi level of the system at the predicted Dirac points
which could be realized by chemical doping or electric gating. Currently,
these predictions have not been verified experimentally, possibly due to
questions about the thermodynamic stability of the proposed structures,[17,
18] the large lattice mismatch that exists between BBO and commercially
available substrates, and the proposed high doping level.[1]

Figure 1: (a)Crystal structure of cubic and monoclinic BaBiO3 and (b)
ferroelectric tetragonal BaTiO3. Schematic of heterostructures synthesized by
molecular beam epitaxy with (c) 4 uc BTO and 4 uc BBO and (d) 4 uc BTO and 2
uc BTO.

The structural and electronic coupling at epitaxial complex oxide interfaces
provides a route to suppress the breathing mode distortion and simultaneously
dope the BBO layers via electrostatic coupling and/or interfacial charge
transfer. Hence, we investigate the structural properties of multilayer
heterostructures comprising atomically-thin BBO layers and tetragonal
ferroelectric BTO (bulk, P4mm $a=b=3.992\AA{}$ $c=4.036\AA{}$)[19] films grown
by molecular beam epitaxy. Ideally, the lack of octahedral rotations in BTO
will suppress the octahedral rotations in the BBO layers at the BTO/BBO
heterointerface and the field effect arising from the ferroelectric
polarization can potentially lead to non-volatile electrostatic doping of the
BBO layers.[20]

Surprisingly, while a large 10% lattice mismatch exists between BBO
(pseudocubic(pc) apc=4.35 Å)[6] and SrTiO3 (STO) (a=3.905 Å), BBO films have
been successfully grown on single-crystal STO substrates using pulsed laser
deposition and molecular beam epitaxy [21, 22, 23, 10, 24]. An interfacial
layer is observed between the BBO and the substrate with the thickness of the
transitional layer, $t_{int}$, on the order of 1-2 nm (2-4 BBO unit cells
(ucs)). As the film thickness increases past $t_{int}$, BBO layers nucleate
with bulk-like lattice parameters. Understanding the structure and composition
of the interface layer is critical for understanding electron interactions
with the substrate, and for designing strategies for synthesizing BBO films
with thicknesses on the order of 1 unit cell in short-period superlattices to
realize the exotic states predicted by first-principles theory.[12]
Transmission electron microscope measurements have been reported for BBO films
on STO with varying structures. Bouwmeester et. al. propose an interface
structure comprising of a rocksalt AO (where A may be Ba or Sr) bilayer on the
STO substrate prior to the nucleation of the BBO layer. Strain relaxation is
proposed to occur in the second AO layer.[13] Jin et. al. propose an
interfacial structure comprising of a double BiO layer with a $\delta$-Bi2O3
(BO)-like phase with fluorite structure. [24] However, the authors point out
that the interface thickness and crystallinity is dependent on the Ga ion
milling procedure used to prepare the samples for the TEM measurements.

In this work, we investigate the structural properties of m BTO/n BBO
heterostructures on (001)-oriented STO substrates by molecular beam epitaxy.
The BBO thickness, n, is constrained to be on the order of the reconstructed
interface layer between 2-4 unit cells (uc) with the BTO thickness, m, is
fixed at 4 ucs. Schematics of the structures studied are shown in Figure 1(c)
and (d) for n=4 and 2, respectively. The interface structure is determined
using synchrotron X-ray diffraction which permits a non-destructive
determination of the atomic structure and composition of the buried
interfaces. For a single 4 uc BTO buffer/ 4 uc BBO /4 uc BTO trilayer on STO
([4/4/4]x1), Bi-Ti intermixing between the BBO layer and the capping layer
leads to strain relaxation. As the number of BTO/BBO bilayer increases in [4
BTO/4 BBO]x5 ([4/4]x5) superlattices (SLs), both BBO and BTO relax to their
bulk values as evidenced by in-situ reflection high energy diffraction (RHEED)
measurements and X-ray reciprocal space maps. On reducing the BBO thickness to
2 uc in [4 BTO/ 2 BBO]x5 ([4/2]x5), two BBO domains are observed. The first
domain is fully relaxed, while the second domain is compressively strained to
the BTO layer with a strong tetragonal distortion. Piezoforce microscopy (PFM)
measurements indicate that the BTO layers retain their ferroelectric
properties. While Raman spectroscopy measurements indicate a suppression of
the breathing mode associated with the CDW and the electronic gap in undoped
BBO, the films remain insulating.

##  II Experimental Details

###  II.1 Synthesis

BTO/BBO/BTO trilayers and [4/4]x5 and [4/2]x5 superlattices were grown by
molecular beam epitaxy on (001)-oriented single-crystal SrTiO3 substrates. The
BBO thickness was varied from 2-4 unit cells and the BTO thickness was fixed
at 4 unit cells. High-purity Bi, Ba, and Ti were evaporated from effusion
cells. The fluxes were calibrated before the film deposition using a quartz
crystal monitor. To account for Bi desorption at the growth temperature, the
Bi:Ba ratio was fixed at 2:1 based on optimizing the crystallinity and
stoichiometry of 40 uc thick BBO films. The BBO and BTO films were deposited
at 650 C in 6.5$\times$ 10-6 Torr Oxygen plasma. After growth, the films were
cooled to room temperature in the oxygen plasma. The SLs were capped with 4 uc
BTO. The film crystallinity during the growth was monitored by reflection high
energy electron diffraction.

###  II.2 Structural Measurements

Crystal truncation rods (CTRs)[25] and reciprocal space maps (RSMs) were
measured at the 33ID beamline at the Advanced Photon Source at Argonne
National Laboratory to determine the structural properties of the films. The
measurements were performed at room temperature with an incident photon energy
of 13.5 KeV. The CTRs were fit using the GenX genetic fitting algorithm [26,
27, 28] to determine the structures of the epitaxial fractions of the films.
Raman spectroscopy measurements were performed at room temperature using a
Horiba Confocal Raman Microscope with a 532 nm laser.

Figure 2:  RHEED pattern of [4 BaTiO3/4 BaBiO3]5/4 BaTiO3 heterostructure on
(001)-oriented STiO3 after growth of (a) the first 4 ucs of BaTiO3 (b)the
first 2 ucs of BaBiO3 (c) 4 layer of BaBiO3. (d) Final RHEED image at the end
of the growth of the superlattice and the 4 uc BaTiO3 capping layer.

##  III Results and Discussion

###  III.1 RHEED Results

RHEED images taken during the growth of [4/4]x5 superlattice are shown in
Figure 2. Figure 2(a) show the RHEED images after the growth of the first 4 uc
of BTO on STO. The film crystallinity is evident by the sharpness of the RHEED
streaks. During the deposition of BBO on the BTO buffer layer, the RHEED
pattern evolves from sharp streaks after 2 unit cells (Figure 2(b)) to
diffraction spots superimposed on the RHEED streaks ((Figure 2(c))) after 4
ucs. The transition is indicative of roughening of the surface as the
thickness is increased. The final RHEED image after completion of the growth
of the[4/4]x5 SL is shown in Figure 2(d). The in-plane lattice constant
determined from the spacing of the RHEED diffraction pattern alternates
between $\sim$ 3.98 $\pm 0.02$Å during the deposition of the BTO layers to
$\sim$ 4.35 $\pm 0.01$ Å for the BBO layers, indicating structural relaxation
of the BBO and BTO layers in the superlattice structure relative to the STO
substrate.

Figure 3: (a)Schematic of 4 BTO/4 BBO/ 4 BTO trilayer structure grown on
(001)-oriented SrTiO3 (b) Reciprocal space map around the STO (0 1 1) Bragg
peak showing the crystal truncation rod along K=1 and the relaxed diffraction
peak (indicated by dashed line) along K=0.98. (c) Representative CTRs measured
(blue circles) along the STO ( 0 0 L) and (1 1 L) directions and calculated
intensities (red) for the best fit model of the coherently strained fraction
of the trilayer. (d) Measured composition profile for the coherently strained
component of the film and (e) layer-resolved out-of-plane lattice parameters
determined from the fits in (c). The dashed lines indicate the bulk lattice
parameters of STO, BTO and BBO.

###  III.2 Analysis of [4 BTO/4 BBO/4 BTO] Trilayer

Synchrotron X-ray CTRs were measured along the 00L, 10L, 11L, and 20L
directions for the nominal 4 BBO/4 BTO/ 4 BTO trilayer sample. A schematic of
the sample is shown in 3(a). The CTRs with in-plane lattice vectors fixed to
reciprocal lattice units (r.l.u.) defined by the bulk STO substrate (1
r.l.u.=$1/3.905\AA{}$) measure the crystalline fraction of the film coherently
strained to the substrate. Thus, fractions of the film that are relaxed and/or
incoherently strained do not contribute to the intensities along the CTRs. The
reciprocal space map around the STO (1,0,1) Bragg peak is shown in Figure
3(b). The intensities corresponding to the coherently strained fraction of the
film lie along H=1 STO rlu. A broad diffuse peak corresponding to the relaxed
fraction is observed centered along H=0.98 STO rlu corresponding to a 3.98 Å
in-plane lattice. The in-plane lattice constant is consistent with the RHEED-
determined lattice constant of the surface layer, thus, we conclude that the
fractions of the surface layers are relaxed, relative to the STO substrate.

Figure 3(c) shows representative CTRs measured for the 4 BBO/4 BTO/ 4 BTO
sample and intensities calculated for the best-fit structural model. The
initial model for fitting the CTR data comprised of fully strained BTO and BBO
layers with the nominal thicknesses and stoichiometry does not match the
periodicity of the measured intensities. However, allowing the B-site (Ti, Bi)
occupation to vary and non-unity layer occupations of the surface layers
yields a good fit to the measured data. Figure 3(d) and (e) shows the layer-
resolved Ti and Bi fractional occupations and the lattice spacings,
respectively, determined by the differences in the z-positions of the A-site
(Ba) along the growth direction. The coherently strained fraction in each
layer decreases from layer 5 to layer 10 where BBO and the top BTO layer
should be nominally located. The Bi content at the B-site is less than 20%,
indicating possible incorporation of Ti from the BTO cap layer in the BBO
film. The average composition in the nominal BBO layer (layer 5-8) is
Ba(Ti0.8Bi0.2)O3. The lattice constant increases in the 1st BTO layer from 4 Å
to 4.2 Å in the nominal Ba(Ti0.8Bi0.2)O3 layer.

###  III.3 Structure of [4 BTO/4 BBO]N superlattice

Figure 4: (a) Reciprocal map around the STO (0 1 1) Bragg peak for a
[4BTO/4BBO]5 superlattice The relaxed BBO and BTO diffraction peaks are
indicated by the vertical black and white dashed lines, respectively. (b)
Comparison of the (1 0 $L$) crystal truncation rods for the [4/4/4] trilayer
and [4/4]5 superlattice (c) Measured (blue circles) and calculated (red line)
X-ray reflectivity intensities and (d) converged model structure for the
[4BTO/4BBO]5 superlattice.

Next, we investigate the structure of a [4/4]x5 SL capped with 4 uc BTO. The
increase by a factor of 5 of the BTO/BBO bilayer thickness should result in a
decrease in the film peak width along the L direction and an increase in the
film Bragg peak intensity for the off-specular CTRs. However, we find that the
CTRs along the off-specular directions are identical to the trilayer sample,
as shown in Figure 4(a) indicating that only the initial layers are coherently
strained to the STO substrate. The reciprocal space map for the sample is
shown in 4(b). The narrow peak centered at (1,0,0.98) corresponds to
intensities from the coherently strained fraction of the film. The STO
substrate Bragg peak is located at (1,0,1). Two broad film peaks are located
at (0.890,0,0.901) corresponding to relaxed BBO with apc=4.38 Å and cpc=4.34 Å
and (0.960,0,0.955) corresponding to relaxed tetragonal BTO with a=4.06 Å and
c=4.09 Å. The expanded volume of the BTO layer relative to bulk, suggests Bi
interdiffusion into the BTO layer.

X-ray reflectivity measurements validate the nominal layer sequence. Figure 3
(c) shows the measured reflectivity for the [4/4]x5 and the calculated
reflectivity for the best-fit model comprising of the nominal layer sequence.
The fitted thicknesses for the BBO and BTO layers are 16.5 Å and 17.6 Å, in
agreement with the nominal values. The layer roughness determined from the
fits are on the order of 1-2 unit cells. Thus, we conclude, based on the X-ray
and RHEED data, that the BTO/BBO lattice grows with the individual layers
relaxed relative to the STO substrate.

###  III.4 Structural analysis of [4 BTO/2 BBO]5 superlattice

To understand the effect of the BBO thickness on the the strain state of the
system, we investigate the structural properties of a [4/2]x5 SL. Figure 5(a)
shows the reciprocal space map for the [4/2]x5 SL sample around the substrate
(1, 0, 1) Bragg peak. The BTO peak is located at (0.981, 0 0.944) STO rlu and
is relaxed relative to the STO substrate. The lattice constants for the BTO
layers are a=3.982 Å and c=4.135 Å. A 2nd peak at (0.896,0,0.903) corresponds
to relaxed BBO with a=4.358 $\pm$0.01 Å and c = 4.325 $\pm$0.01 Å. The lattice
parameter is comparable to pseudocubic lattice constant of the BBO bulk
monoclinic phase,$a_{pc}=$4.35 Å.[29] The slight increase may be attributed to
Bi vacancies[11] or cubic BBO[10]. In contrast to the [4/4]x5 SL, a weak
diffraction peak is observed for the [4/2]x5 SL at (0.957, 0, 0.765) STO rlu
with lattice constants a= 4.0386 Å and c= 5.1121 Å . This peak is associated
with BBO compressively strained to BTO. The calculated volume of the strained
BBO is 83.374 $\AA{}^{3}$ in close agreement with the bulk value of 82.59
$\AA{}^{3}$.[29]

Figure 5: (a) Reciprocal space map around (101) Bragg peak for [4 BTO/ 2 BBO/
4 BTO]x5 superlattice on STO.

The X-ray diffraction measurements confirm the growth of relaxed crystalline
BBO/BTO bilayers with 2-4 uc thick BBO layers thicknesses. To determine if the
structural breathing distortion associated with the CDW is suppressed in the
ultrathin BBO layers, we compare Raman spectroscopy measurements for a ”bulk”
40 uc BBO film and the [4/4]x5 SL in Figure 6. An A1g Raman-active mode is
observed for bulk BBO at 570 cm-1, which is attributed to the breathing phonon
mode.[30, 31] The mode is observed for the 40 uc BBO film on STO as shown in
Figure 6. Additional peaks below and above 570 cm-1 are related to the second-
order Raman-active modes in the bulk cubic STO substrate[32, 33]. In contrast
to the 40 uc BBO sample, the A1g Raman active mode is strongly suppressed in
the [4/4]x5 SL as shown in Figure 6. A similar suppression has been reported
in hole-doped cubic superconducting BaKxBi1-xO3[31] where the CDW is
suppressed and metallicity emerges.

The absence of the A1g Raman peak in BBO films grown on STO with thicknesses
below a critical thickness of 11 unit cells was previously attributed to a
dimensionality induced monoclinic to cubic ($Pm\bar{3}m$) transition and the
suppression of the CDW.[10] However, the formation of an interfacial layer
between BBO and STO[24] and Bi off-stoichiometry may explain the absence.[11]
In our current work, we observe a clear structural peak related to
stoichiometric BBO in the [4/4]x5 (Figure 4) superlattices without the
observed A1g peak. However, the slightly larger lattice constants and lattice
volume compared to bulk BBO may be associated with Bi-deficient Ba1-xBixOy
films.[11] Our superlattices are insulating and exhibit a strong ferroelectric
response.

Figure 6: Raman spectra of [4 BTO/4 BBO]x5 /4 BTO heterostructure and 40 uc of
BaBiO3 grown on (001)-oriented STO.

###  III.5 PFM measurements

Finally, we confirm the ferroelectric properties of the samples by piezoforce
microscopy. Figure 7 shows the amplitude and phase contrast measured after
writing with $\pm$8 V bias and reading with 0.5 VAC driving voltage. Up and
down ferroelectric domains are clearly visible. The PFM loops show clear
ferroelectric hysteresis and ferroelectric switching at 4 V indicating that
the BTO retains its ferroelectric properties in the BTO/BBO heterostructures.
The ferroelectric field effect potentially provides an effective route to
accumulate excess holes and electrons in the interfacial BBO layers without
disorder related to chemical doping. [34] In the symmetric [BTO/BBO/BTO]
heterostructures, the separation of the BBO hole-rich and electron-rich
interfaces must be above a critical thickness to induce an insulator-to-metal
transition. Theoretical investigations of electron and hole gases formed at
polar LaLuO3/SrBiO3 interfaces estimate a critical thickness on the order of 4
unit cells.[14] Thus, tuning of the BBO thickness and/or asymmetric
ferroelectric/BBO heterostructures may be necessary to induce two-dimensional
electron and hole gases in the ultrathin BBO layers.

Figure 7:  Piezoforce microscopy measurements of [4 BTO/ 4 BBO]x5 on STO (a)
PFM amplitude and (b) Phase as a function of applied bias. (c)Amplitude and
(d) phase contrast measured after writing domains with a +/-8 V bias.

##  IV Conclusion

In conclusion, we have investigated the structural properties of BTO/[m BBO/ 4
BTO]xN heterostructures grown by molecular beam epitaxy on (001)-oriented STO
substrates. The nominal lattice mismatch between the BBO and STO substrate is
12%. Relaxation is observed after deposition of the 1st bilayer by in-situ
RHEED and ex-situ reciprocal space maps. While the stoichiometry is preserved
for 2 uc BBO on the 4 uc BTO buffer on STO, Bi/Ti intermixing leads to
coherent epitaxy in the 1st bilayer when the BBO thickness is increased to 4
unit cells. For [2 BBO/ 4 BTO]x5 SLs, the BBO is compressively strained to the
BTO leading to tetragonal BBO layers with a c/a ratio of 1.25. For [4 BBO / 4
BTO] x5 SL with increased thicknesses of the BBO, the increase in strain
energy leads to relaxation of the BBO layers to the monoclinic bulk phase with
apc = cpc = 4.38 Å. The breathing mode distortions are suppressed in the
relaxed confined BBO layers for thicknesses up to 6 unit cells.While a
tetragonal distortion is observed from the [2BBO/4 BTO] heterostructure, no
metallicity is currently observed and doping strategies via the field effect
and/or chemical substitution may be required to induce metallicity and/or the
proposed topologically protected phase in BBO heterostructures.[1]

##  V Acknowledgements

Use of the Advanced Photon Source was supported by the US Department of
Energy, Office of Science, Office of Basic Energy Sciences, under Contract No.
DE-AC02-06CH11357. This work was performed in part at the Analytical
Instrumentation Facility (AIF) at North Carolina State University, which is
supported by the State of North Carolina and the National Science Foundation
(award number ECCS-2025064). This work made use of instrumentation at AIF
acquired with support from the National Science Foundation (DMR-1726294). The
AIF is a member of the North Carolina Research Triangle Nanotechnology Network
(RTNN), a site in the National Nanotechnology Coordinated Infrastructure
(NNCI).

##  VI Data Availability Statement

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

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