# Integrating Categorical Features in End-to-End ASR

###### Abstract

All-neural, end-to-end ASR systems gained rapid interest from the speech
recognition community. Such systems convert speech input to text units using a
single trainable neural network model. E2E models require large amounts of
paired speech text data that is expensive to obtain. The amount of data
available varies across different languages and dialects. It is critical to
make use of all these data so that both low resource languages and high
resource languages can be improved. When we want to deploy an ASR system for a
new application domain, the amount of domain specific training data is very
limited. To be able to leverage data from existing domains is important for
ASR accuracy in the new domain. In this paper, we treat all these aspects as
categorical information in an ASR system, and propose a simple yet effective
way to integrate categorical features into E2E model. We perform detailed
analysis on various training strategies, and find that building a joint model
that includes categorical features can be more accurate than multiple
independently trained models.

Index Terms—  Multilingual E2E ASR, Multi-domain ASR, Categorical features.

##  1 Introduction

In recent years, all-neural, end-to-end (E2E) models that directly convert
speech into text through a sequence model have become popular. Instead of
separately optimized components, an E2E model is a single trainable neural
network. It removes the HMM assumptions and enables end-to-end optimization.
Architectures like Connectionist Temporal Classification (CTC) [1], attention
based sequence models such as Listen, Attend and Spell (LAS) [2], transformer
[3, 4], and Recurrent Neural Network Transducer (RNN-T) [5] have obtained
impressive results and sometimes surpass conventional systems [6, 7, 8].

Though E2E models are theoretically strong, they require large amounts of
paired speech text data which is usually expensive to obtain. The amount of
paired speech text data also varies across different languages and locales.
Locale-specific ASR systems can be less accurate in under-represented locales
simply because there is insufficient transcribed data. When developing an ASR
system for a new application domain, there is typically little domain specific
transcribed data. Thus the model quality suffers. In this study, we treat the
different languages, dialects, domains as categorical information to the ASR
system. In this paper, we propose a simple method to inject the categorical
information into the E2E model, which allows the pooling as much data as
possible to train the E2E model. Not only are we able to train better models
for the less represented languages and domains, but the performance on the
primary language and domain is also improved. We also find this joint model
performs better than an individually fine-tuned model. This is desirable since
we have less models to maintain and deploy.

The multilingual E2E model has been studied previously. In [9], language
information is added as a token in the beginning or the end of the output
sequence. In [10, 11, 12], the language information is inserted into the model
directly either as an embedding or one-hot vector. In [13], separate decoders
are used for different groups of languages. The main difference in our work is
we expand the idea into multiple categorical features, not only including
language and dialect, but domain and potentially other types of categorical
features like device types and contexts. We propose a simple method to combine
multiple categorical features and compare different ways to inject the
resulting combination into the model. Another contribution is we perform
extensive experiments and analysis of strategies in multilingual and multi-
domain E2E training. We use an LAS model in our study, although the method
should be applicable to other types of E2E models like RNN-T or transformer.

##  2 Base LAS Model

Given a sequence of speech frames
$\textbf{x}=\left\\{x_{1},...,x_{L}\right\\}$ with length $L$, and output
token sequence $\textbf{y}=\left\\{y_{1},...,y_{U}\right\\}$ with length $U$,
the E2E model computes the probability

$P(\textbf{y}|\textbf{x})=\prod_{i=1}^{U}P(y_{i}|\textbf{x},y_{1},y_{2},...,y_{i-1})$
(1)

An encoder converts x to intermediate outputs
$\textbf{h}=\left\\{h_{1},...,h_{T}\right\\}$ through a Recurrent Neural
Network (RNN), typically an LSTM. One important aspect for ASR is there are
many more speech frames than the number of output tokens in y, usually there
is a reduction factor $N$, thus $T=\frac{L}{N}$ is the length of encoder
output.

$h_{j}=\mathrm{EncoderRNN}(x_{j},h_{j-1})$ (2)

The decoder is also an RNN. It takes encoder outputs h (a.k.a. memory), and
previous output token $y_{i-1}$, generates the current decoder state $s_{i}$:

$s_{i}=\mathrm{DecoderRNN}(y_{i-1},s_{i-1},c_{i})$ (3)

which is then passed through a generation network, typically a feedforward
network with softmax output, to produce the next output token $y_{i}$:

$y_{i}=\mathrm{Generate}(s_{i},c_{i})$ (4)

$c_{i}$ is the context vector at decoder step $i$ that summarizes information
from the encoder:

$c_{i}=\sum_{j=1}^{T}\beta_{i,j}h_{j}$ (5)

where $\beta_{i,j}$ is attention weight at output step $i$ on $j$-th encoder
output.

##  3 Injection of Categorical Features

The categorical information like language, dialect, domain is sentence based.
One way to inject a categorical feature $f_{k}$ into the model is by using an
embedding:

$e_{k}=E_{k}(f_{k})$ (6)

for the $k$-th categorical feature. We can combine $M$ categorical features
into a single feature vector:

$e=\sum_{k=1}^{M}V_{k}e_{k}+b_{k}$ (7)

where $V_{k}$ is a weight matrix, and $b_{k}$ is a bias vector for $k$-th
categorical feature. All embeddings and weights are trained as part of the
whole E2E model.

###  3.1 Encoder

There are various places the categorical feature vector $e$ can be inserted
into the model [10, 11, 12]. We can append it to the input feature in the
encoder:

$\textbf{x}=\left\\{[x_{1},e],[x_{2},e],...,[x_{L},e]\right\\}$ (8)

###  3.2 Decoder

The categorical feature vector $e$ can also be inserted into the decoder by
concatenating it with the context vector $c_{i}$. Specifically, Eq. 3 becomes

$s_{i}=\mathrm{DecoderRNN}(y_{i-1},s_{i-1},[c_{i},e])$ (9)

###  3.3 Encoder and decoder

The categorical feature vector $e$ can be inserted into both the encoder and
decoder. For increased flexibility, we apply different weight matrices
$V_{k,enc}$, $V_{k,dec}$, and bias vectors $b_{k,enc}$, $b_{k,dec}$ in Eq. 7
for encoder and decoder respectively. In the experiment section, we will
present results of each method.

##  4 Experiments

###  4.1 Data

We use Chinese data in all our experiments. The data includes following four
language/dialects: Mandarin, Cantonese, Taiwanese, and Shanghainese. 111We use
the terms language and dialect loosely and interchangeably here. For Mandarin
and Shanghainese, Simplified Chinese characters are used; for Cantonese and
Taiwanese, Traditional Chinese characters are used. Each dialect has various
number of domains: assistant (ast), message (msg), search (srch), map, in-home
smart speaker (home), in-car smart speaker (car). Mandarin has all the
domains, while Shanghainese has only message domain. The amount of training
data available for each dialect and domain is listed in Table 1. Each domain
in a dialect has a test set. The amount of data for each test set ranges from
10 to 40 hours. We only perform domain dependent modeling experiments in
Mandarin because other dialects do not have enough domain specific data.

Table 1: Amount of training data across dialects and Mandarin domains Dialect | Hours | text
---|---|---
Mandarin | 18k | Simplified Chinese
assistant (ast) | 7k |
message (msg) | 4k |
home | 2k |
search (srch) | 500 |
car | 400 |
Cantonese | 7k | Traditional Chinese
Taiwanese | 3k | Traditional Chinese
Shanghainese | 100 | Simplified Chinese

###  4.2 The E2E model

The baseline E2E model is LAS. The encoder is a 5-layer bi-directional LSTM,
1200 cells in each direction, with 600-dim projections. The 80-dim log mel-
filter bank feature is the input to the encoder. A 4-head, 1200-dim attention
is used. The decoder uses a 2-layer unidirectional LSTM, each has 800 cells.
All the training texts are merged and processed with 19k BPE tokens derived
from the training data. The model has 178m parameters.

The dialect and domain features are modeled with separate 80-dim embedding
tables, the transformed dimension is 20 and 160 for injecting into encoder and
decoder respectively. The value is chosen so the total amount of increased
parameters is around 200K regardless of where the categorical features are
injected. This amounts to only 0.1% parameter increase over the baseline
model.

The E2E model is trained with block-momentum SGD [14], 32 V100 GPUs, 10000
frames per minibatch per node, L2 normalization on gradient, SpecAugment [15]
on the encoder input, with label smoothing [16] weight 0.05 and schedule
sampling [17] weight 0.1. The cross entropy training is followed by one epoch
of Minimum Word Error Rate training (MWER, [18, 19]). The weight on the cross
entropy loss during MWER is 0.05. The initial learning rate is 0.025 and
decayed by factor 0.8 when no improvement observed on the validation set. We
use beam size 8 during beam search and length penalty [20] 0.1.

###  4.3 Different experiment setups

We will present results from a few independently trained, jointly trained, and
fine-tuned models. Table 2 explains the different setups in the study. For
fine-tuning after joint training, the setup denoted with suffix $d$ (dialect)
or $t$ (targeted domain) means fine-tuned to the dialect and fine-tuned to the
targeted domain in the dialect, respectively.

Table 2: Different experiment setups in the study Setup | Description
---|---
S0 | dialect independently trained
S1 | dialect and domain independently trained
S2 | jointly trained
S3 | jointly trained, categorical feature in encoder
S4 | jointly trained, categorical feature in decoder
S5 | jointly trained, cat. feature in encoder & decoder
S*d | fine-tune a jointly trained model to dialect
S*t | fine-tune a jointly trained model to targeted domain

###  4.4 Joint trained models

We could simply pool all the data together and train a single model. This is a
baseline (setup S2) for comparing the effectiveness of injecting categorical
features into the model. Please note that all the results for setup S2-S5 are
obtained using a single shared model for all dialects and domains. The jointly
trained model results are presented in Table 3.

Table 3: The CER (Character Error Rate) of independently and jointly trained models on different dialects and domains. Setup | Ast | Car | Home | Map | Msg | Srch
---|---|---|---|---|---|---
Mandarin
S0 | 5.44 | 5.91 | 2.92 | 7.35 | 6.11 | 10.36
S1 | 5.87 | 14.85 | 4.25 | 8.24 | 7.22 | 10.16
S2 | 5.99 | 6.25 | 3.19 | 7.61 | 6.80 | 11.0
S3 | 5.27 | 5.66 | 2.57 | 6.88 | 6.04 | 9.78
S4 | 5.34 | 5.75 | 2.47 | 7.07 | 5.77 | 9.95
S5 | 5.23 | 5.62 | 2.57 | 6.90 | 5.91 | 9.68
Cantonese
S0 | 6.16 | 5.07 | 2.96 | 9.47 | 5.21 | 10.62
S2 | 6.66 | 5.68 | 3.04 | 10.48 | 5.64 | 11.60
S3 | 5.60 | 5.00 | 2.66 | 9.23 | 5.14 | 9.20
S4 | 5.72 | 4.99 | 2.63 | 9.18 | 5.01 | 9.65
S5 | 5.63 | 4.85 | 2.63 | 8.68 | 5.19 | 9.19
Taiwanese
S0 | 5.89 | 5.64 | 4.79 | 7.28 | 5.91 | 12.97
S2 | 10.12 | 9.38 | 7.43 | 10.11 | 6.86 | 17.38
S3 | 4.15 | 4.68 | 3.44 | 5.56 | 4.34 | 9.26
S4 | 4.44 | 5.04 | 3.47 | 6.09 | 4.52 | 10.08
S5 | 4.35 | 4.57 | 3.47 | 5.58 | 4.31 | 9.35
Shanghainese
S0 | - | - | - | - | 53.11 | -
S2 | - | - | - | - | 20.03 | -
S3 | - | - | - | - | 15.83 | -
S4 | - | - | - | - | 16.48 | -
S5 | - | - | - | - | 14.63 | -
Table 4: The CER of fine-tuned models on different dialects and domains, along with non-fine-tuned results. Setup | Ast | Car | Home | Map | Msg | Srch
---|---|---|---|---|---|---
Mandarin
S2 | 5.99 | 6.25 | 3.19 | 7.61 | 6.80 | 11.0
S2d | 5.61 | 6.14 | 2.92 | 7.38 | 6.45 | 10.62
S2t | 5.51 | 6.07 | 2.80 | 7.21 | 6.17 | 10.16
S5 | 5.23 | 5.62 | 2.57 | 6.90 | 5.91 | 9.68
S5d | 5.16 | 5.59 | 2.47 | 6.96 | 5.90 | 9.70
S5t | 5.16 | 5.55 | 2.48 | 6.86 | 5.85 | 9.63
Cantonese
S2 | 6.66 | 5.68 | 3.04 | 10.48 | 5.64 | 11.60
S2d | 5.70 | 4.89 | 2.75 | 8.95 | 4.76 | 9.65
S5 | 5.63 | 4.85 | 2.63 | 8.68 | 5.19 | 9.19
S5d | 5.59 | 4.77 | 2.64 | 8.53 | 4.63 | 9.05
Taiwanese
S2 | 10.12 | 9.38 | 7.43 | 10.11 | 6.86 | 17.38
S2d | 4.28 | 4.66 | 3.61 | 5.56 | 4.38 | 9.65
S5 | 4.35 | 4.57 | 3.47 | 5.58 | 4.31 | 9.35
S5d | 4.20 | 4.28 | 3.40 | 5.25 | 4.19 | 8.88
Shanghainese
S2 | - | - | - | - | 20.03 | -
S2d | - | - | - | - | 14.60 | -
S5 | - | - | - | - | 14.63 | -
S5d | - | - | - | - | 14.15 | -

###  4.5 Fine-tune model to dialect and domain

After the jointly trained model is finished, we can fine-tune this model to
each dialect and domain. The fine-tuning process is straightforward: beginning
with the best jointly trained model, we continue training with dialect or
domain specific data until convergence. In the end we will have one model for
each dialect or domain. From Table 3, we see that a single model injected with
categorical features perform well across dialects and domains (setup S3-S5). A
natural followup question is, what if we can fine-tune the base model and
deploy a dialect/domain specific model, will a single model still be the best?
Overall, we perform this fine-tuning process for setup S2 and S5 in Table 4.

Table 5: Average CER for each setup and dialect Setup | Mandarin | Cantonese | Taiwanese | Shanghainese
---|---|---|---|---
S0 | 6.35 | 6.58 | 7.08 | 53.11
S1 | 8.43 | - | - | -
S2 | 6.81 | 7.18 | 10.21 | 20.03
S3 | 6.03 | 6.14 | 5.24 | 15.83
S4 | 6.06 | 6.20 | 5.61 | 16.48
S5 | 5.98 | 6.03 | 5.27 | 14.63
S2d | 6.52 | 6.12 | 5.36 | 14.60
S2t | 6.32 | - | - | -
S5d | 5.96 | 5.87 | 5.03 | 14.15
S5t | 5.92 | - | - | -

##  5 Analysis

In this section, we present detailed analysis on experimental results. For
easier comparison, we calculate the unweighted mean CER across all tasks in
Table 5.

Simply pooling all data together (S2) does not perform better than
individually trained dialect dependent models (S0), except for extremely low
resource dialects like Shanghainese (compare S0 and S2 in Table 5 and Table
3).

Fine-tuning the S2 model with dialect dependent data greatly helps accuracy.
S2d models are better than S0 models on lower resource dialects now (Table 5).
However, it still cannot match the dialect dependent model on the high
resource dialect (compare S0 and S2d for Mandarin in Table 5). Perhaps because
the modeling capacity is redirected from the main dialect to other dialects.

Domain dependent models (S1) do not work better than dialect dependent models
(S0) except on the search task (compare Mandarin S1 and S0 in Table 3). This
is probably because there are similar utterances in various domains. Sharing
data across the domains makes the model more robust. However, if a model sees
data from all domains and is later fine-tuned to a specific domain, there is
still an accuracy benefit. The domain adapted model has a small advantage over
the dialect adapted model (compare Mandarin S2t and S2d in Table 4). The
average relative CERR (Character Error Rate Reduction) is 3%.

Incorporating categorical features into the E2E model gives significant
accuracy boost (compare S3, S4, and S5 with S2 in Table 5). The relative CERR
is larger on low resource dialects (comparing S5 with S2, 48% and 27% on
Taiwanese and Shanghainese respectively), and smaller on high resource
dialects (12% and 16% on Mandarin and Cantonese respectively). Similar to
[12], we also find inserting the feature into encoder (S3) is better than
inserting into decoder (S4). However, we also observe inserting into both the
encoder and decoder (S5) gives small but consistent gains over inserting the
feature into the encoder only (S3). Note that in all cases, the model size is
only increased by 0.1% over the baseline E2E model used in S0, S1, and S2.

It is also important to note that the S3/S4/S5 setups use one model for all
the dialects. This has a huge development and deployment advantage over the
dialect specific model setups S0 and S2d. In our study, S5 also outperforms S0
and S2d by 28% and 3% respectively (averaged over all dialects).

We see further accuracy gains from fine-tuning the S5 model to individual
dialects. Comparing S5d with S5 in Table 5, we find no gain on Mandarin, but
still 3-4% relative CERR for the other dialects. Fine-tuning on the individual
domains gives insignificant additional gain (compare Mandarin S5t with S5d in
Table 5).

Overall, if only one model is used for all dialects studied here, S5 achieves
12-48% relative CERR over S2. If each dialect has its own model, S5d achieves
3-9% relative CERR over S2d.

##  6 Conclusion

Dialect, language, domain etc categorical information is important knowledge
for improving ASR. In this study, we propose a method to incorporate multiple
categorical features into an E2E model. We find that injecting the combined
feature into both encoder and decoder performs the best. We train a single
model with categorical features for 4 Chinese dialects and 6 domains. This
model (S5) performs better than dialect independently trained models (S0) and
dialect adapted models (S2d) by 28% and 3% respectively. Further gains are
achieved by fine-tuning to language/domain. The model S5d achieves 3-9%
relative CERR over baseline dialect adapted model (S2d). In the future, we
plan to extend this categorical feature into more languages and other types of
categorical information.

##  7 Acknowledgments

We thank Donald McAllaster, Ernest Pusateri, John Bridle, Russ Webb, and
Woojay Jeon for helpful feedback.

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School of Physics, Sun Yat-sen University, Guangzhou 510275, China Ikerbasque,
Basque Foundation for Science, 48013 Bilbao, Spain

# Extending the spin excitation lifetime of a magnetic molecule on a
proximitized superconductor

Katerina Vaxevani  CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain
Jingcheng Li  CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain  Stefano
Trivini  CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain  Jon Ortuzar
CIC nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain  Danilo Longo  CIC
nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain  Dongfei Wang  CIC
nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain  Jose Ignacio Pascual  CIC
nanoGUNE-BRTA, 20018 Donostia-San Sebastián, Spain<EMAIL_ADDRESS>
###### Abstract

Magnetic molecules deposited on surfaces are a promising platform to
individually address and manipulate spins. Long spin excitation lifetimes are
necessary to utilize them in quantum information processing and data storage.
Normally, coupling of the molecular spin with the conduction electrons of
metallic surfaces causes fast relaxation of spin excitations into the ground
state. However, the presence of superconducting paring effects in the
substrate can protect the excited spin from decaying. In this work, we show
that a proximity-induced superconducting gold film can sustain spin
excitations of a FeTPP-Cl molecule for more than 80 $\mathrm{ns}$. This long
value was determined by studying inelastic spin excitations of the S=5/2
multiplet of FeTPP-Cl on Au films over V(100) using scanning tunneling
spectroscopy. The spin lifetime decreases with increasing film thickness, in
apparent connection with the gradual gap-closing of a pair of de Gennes-Saint
James resonances found inside the superconducting gap. Our results elucidate
the use of proximitized gold electrodes for addressing quantum spins on
surfaces, envisioning new routes for tuning the value of their spin lifetime.

Magnetic molecules have been under the spotlight for new quantum applications,
such as quantum information processing, sensing and data storage.1 Magnetic
molecules can be tailored to behave as quantum bits (qubits), given that they
exhibit long coherence (T2) and spin-relaxation times (T1) 2, 3. The former is
one major prerequisite for engineering efficient molecular qubits 4, 5, 6 as
it describes the lifetime of their superposition state, while the latter gives
the upper limit to T2. Incorporating molecular spins on solid-state platforms
is the next step towards creating electrically addressable quantum devices.
However, the interaction with metallic electrodes opens fast decaying channels
that damp the spin dynamics. Thus, there is a need of finding metallic
substrates for magnetic molecules that do not alter their spin dynamics while
allowing electrical access.

Previous measurements on single transition metal atoms on surfaces reported
spin excitation lifetimes up to a few hundreds picoseconds 7, 8, 9, 10.
Inserting a Cu2N decoupling layer over the metallic surface can enlarge spin-
relaxation lifetime to nanosecond time scales 11. Another method to decouple
spins from the electronic bath is to use a superconducting substrate. The
energy gap around the Fermi level (EF) can efficiently protect the spin
excitations from decaying through generation of electron-hole pairs. For
example, spin excitation lifetimes reaching $\approx$10 $\mathrm{ns}$ have
been observed in a Fe-based porphyrin over a lead substrate 12. Unfortunately,
many elemental superconductors strongly hybridize with molecular species,
quenching their spin state, or simply are difficult to integrate into large
scale devices.

Here, we took advantage of the proximity effect to induce a superconducting
gap on a gold thin film 13, 14, 15, 16 that extended the excitation lifetime
of a tetraphenylporphyrin iron(III) chloride (FeTPP-Cl) for more than 80
$\mathrm{ns}$. High quality gold films were epitaxially grown on top of the
oxygen reconstructed 1x5-V(100) surface. We used a scanning tunneling
microscope (STM) at 1.2 $\mathrm{K}$ to perform Inelastic Electron Tunneling
Spectroscopy (IETS) on FeTPP-Cl molecules adsorbed on the Au/V(100) surface
and revealed the existence of such very long spin excitation lifetimes.
Moreover, we found that increasing the thickness of the gold layer resulted in
a reduction of the excited state lifetime, which coincided with the gradual
shift down of the proximity-induced in-gap resonances. By approaching the STM
tip to the molecules, we modified the magnetic coupling with the substrate to
a stronger regime, where Yu-Shiba-Rusinov (YSR)17, 18, 19 states appear inside
the gap20.

Figure 1:  (a) STM image of the oxygen reconstructed 5$\times$1-V(100)
surface, where oxygen atoms occupy bridge positions along every fifth V-atom
row (as shown in inset); I= 1 $\mathrm{nA}$, V=700 $\mathrm{mV}$; inset: I= 3
$\mathrm{nA}$, V= 3 $\mathrm{mV}$. (b) STM image after depositing 0.5ML (I=
100 $\mathrm{pA}$, V= -300 $\mathrm{mV}$; inset: I= 100 $\mathrm{pA}$, V= 5
$\mathrm{mV}$) and (c) 9ML of Au on V(100)-O(5$\times$1) (I= 100
$\mathrm{pA}$, V= 1 $\mathrm{V}$; inset: I= 400 $\mathrm{pA}$, V= 50
$\mathrm{mV}$). (d) STS spectra (using a superconducting V-covered tip) on
different number of Au layers on V(100)-O(5$\times$1). Inset: evolution of the
dGSJ intra-gap states compared to the amount of grown Au layers.

Vanadium is a type-II superconductor with a critical temperature of
$T_{c}=5.4$\mathrm{K}$$. Vanadium single crystals contain impurities embedded
in the bulk, namely oxygen, carbon and nitrogen 21, 22. In particular, the
presence of oxygen creates a reconstructed V(100)-O(5×1) surface 23, 24, 25,
26 persisting even after very high temperature annealing (Figure 1a). Scanning
Tunneling Spectroscopy (STS) measurements were performed to study the
magnitude of the superconducting gap. To maximize the energy resolution, the
tip was indented in the V sample to become superconducting 27. Differential
conductance (dI/dV) spectra on the V(100)-O(5×1) surface revealed two clear
dI/dV peaks at V=$\pm$1.5 $\mathrm{mV}$ (blue plot in Figure 1d),
corresponding to tunneling between coherence peaks of tip and sample at V =
$\pm(\Delta_{t}+\Delta_{s}$), and in agreement with a gap value for bulk
vanadium of $2\Delta_{s}\approx 1.5~{}$\mathrm{meV}$$ 28.

Figure 2:  (a): STM image of the 4-fold FeTPP-Cl (orange circle), 2-fold
FeTPP-Cl (blue circle) and 2-fold FeTPP (green circle) on Au/V(100) (16x16
$\mathrm{nm}$, I=20 $\mathrm{pA}$, V=200 $\mathrm{mV}$) , (b): STS spectra of
the different molecular species on Au/V(100) (I=200 $\mathrm{pA}$, V=5
$\mathrm{mV}$)

Molecular adsorption on bare V(100) 29 is challenging due to the high
reactivity of the surface, which can distort molecular structure and its
functionality. Therefore, we covered the vanadium surface with gold films, a
metal typically employed for hosting molecular assemblies. We grew multiple
gold layers on the V(100)-O(5$\times$1) surface and studied the formation of
superconducting pairing correlations through the proximity effect 15, 30. In
Figure 1b,c, STM images reveal the epitaxial growth of gold on the
V(100)-O(5$\times$1) (herein referred to as V(100)) surface after annealing
the substrate to 550∘C (see methods). Atomic resolution images of the gold
lattice reveal the high quality of the films, with (100) surface orientation
and lattice constant $x=y\approx 3$\AA$$.

STS measurements on the gold films show that they maintain the superconducting
character of the underlying V(100) crystal with a proximity-induced gap of
width $2\Delta_{s}\approx 1.5~{}$\mathrm{meV}$$. For all film thicknesses
explored in Figure 1d, spectra show characteristic shoulders (black arrows in
Figure 1d) close to $\pm(\Delta_{s}+\Delta_{t})$, the convoluted gap of the
vanadium bulk and tip. This is expected for proximitized films thinner than
the superconducting coherence length of vanadium 31, 13. In addition, a pair
of sharp spectral resonances appear inside the proximity gap. These
resonances, first described by de Gennes-Saint James 32, are intra-gap
quasiparticle excitation peaks resulting from interfering pathways between the
metal-vacuum surface and Andreev Reflections at the metal-superconductor
interface 31, 33. The de Gennes-Saint James resonances (dGSJ) shift down in
energy with increasing film thickness, from 0.69 $\mathrm{meV}$ (4 ML) to 0.2
$\mathrm{meV}$ (20 ML) (see Supporting Information34).

Next, we deposited FeTPP-Cl molecules on the Au/V(100) system. As previously
reported 35, 36, deposition of FeTPP-Cl molecules on metallic substrates at
room temperature usually results in coexistence of chlorinated and
dechlorinated FeTPP species (Figure 2a). The presence of the chlorine atom in
STM topographic images appears as a protrusion in the center of the molecule,
whereas the dechlorinated FeTPP molecules show a depression. Furthermore, as
shown in Figure 2a, FeTPP-Cl appears with two distinctive adsorption
geometries, referred to as 4-fold and 2-fold structures, due to the different
apparent positions of the phenyl rings. The 4-fold species lie in a stronger
interaction regime with the surface that will be described elsewhere. In
contrast with previous results on Pb(111) and Au(111) 37, 38, 39, 40, 41,
dechlorinated molecules on this substrate do not exhibit neither YSR in-gap
states nor inelastic spin excitations outside the gap (Figure 2b), indicating
that they may lie in a different coupling regime.

In this letter, we focus on the 2-fold FeTPP-Cl molecules. Characteristic
dI/dV curves recorded on the molecular center show excitation peaks outside
the superconducting gap, at $\approx\pm 2.6~{}$\mathrm{mV}$$ and $\approx\pm
3.8~{}$\mathrm{mV}$$ (Figure 3a). These peaks have been previously attributed
to inelastic excitations of the $S=5/2$ molecular spin multiplet12, 42. Using
the phenomenological hamiltonian $H=DS^{2}_{z}$ to describe the effect of a
ligand field, a positive magnetic uniaxial anisotropy $D$ found for these
molecules splits the degenerate Fe multiplet into three spin states,
$S_{z}=\pm\ket{1/2},\pm\ket{3/2},\pm\ket{5/2}$ 4. The inelastic signal appears
as replica of the dGSJ peaks in the spectra and the energy separation between
them (red arrows in Figure 3a) corresponds to the excitation energies. That
is, 2$D$ from the ground state $S_{z}=\pm\ket{1/2}$ to the first excited state
$S_{z}=\pm\ket{3/2}$, and 4$D$ subsequently to the second excited state,
$S_{z}=\pm\ket{5/2}$ (Figure 3c). Therefore, from these measurements we obtain
that the axial magnetic anisotropy for FeTPP-Cl amounts to
$D=0.65~{}$\mathrm{meV}$$. Due to the spin selection rule $\Delta S_{z}=\pm
1$, the occupation of the second excited state can only be achieved from the
first excited state 9, 12. The observation of a peak at 4$D$ thus indicates
that the first excited state reaches a finite population in a stationary state
with the tunneling current 42, 12. Such step-wise excitation of higher lying
spin states is referred to as spin-pumping 9.

Figure 3:  (a) Single STS spectra taken on a 2-fold FeTPP-Cl molecule (blue)
and on the substrate (grey) (I=150 $\mathrm{pA}$, V=6 $\mathrm{mV}$). (b) 2D
intensity plot of a series of distance-dependent dI/dV spectra for 4 ML Au
thickness. (c) Zero field splitting excitations for a total spin of
$S_{z}=5/2$ , (d) Top (bottom) panel: Relative amplitude $A_{r1}$ ($A_{r2}$)
of the first (second) excitation resonance as a function of $I_{BCS}$, the
current of the BCS peaks. Error bars indicate the error propagation of the
relative amplitude averaged over positive and negative side of the spectra.
Top: Fit (red line) for determining the lifetime of the first excited state
$\pm\ket{3/2}$ with thickness of 4ML ($P=0.423\pm
0.001,\tau_{1}=80~{}$\mathrm{ns}$\pm 20~{}$\mathrm{ns}$$ ), Bottom: Fit (red
line) for determining the lifetime of the second excited state $\pm\ket{5/2}$
with thickness of 4ML, with fixed $\tau_{1}$ ($P=0.304\pm
0.014;\tau_{2\rightarrow 1}=1.8~{}$\mathrm{ns}$\pm 0.8~{}$\mathrm{ns}$$)

We study the spin excitation dynamics of 2-fold molecules first on a 4
monolayer (ML) thick Au film on V(100), with characteristic spectra like the
one shown in Figure 3a. Interestingly, the excitation into the
$S_{z}=\pm\ket{5/2}$ state appears for tunneling currents as small as 20
$\mathrm{pA}$, suggesting a particularly long lifetime for the first excited
state ($S_{z}=\pm\ket{3/2}$). The lifetime of the excited states, $\tau_{1}$,
can be extracted from the behaviour of the IETS peaks with current, using a
set of rate equations
$\frac{dN_{i}}{dt}=\sum\limits_{j}(R_{ji}N_{j}-R_{ij}N_{i})$ connecting states
$N_{i}$ and $N_{j}$ with excitation/de-excitation rates $R_{ij}$ and $R_{ji}$
12.

For the first excited state, the de-excitation rate $R_{ji}$ includes a
spontaneous decay constant, $\lambda_{1}$, and a current-induced de-excitation
factor $f$ (see Supporting Information 34). The former gives the lifetime of
the first excited state ($\lambda_{1}=1/\tau_{1}$) and defines the threshold
to a stationary non-equilibrium state. In this regime, only the inelastic
current drives transitions between the ground state and the first excited
state, which dynamically acquires a finite population. This opens a new
conduction channel for the second excited state.

To determine $\tau_{1}$, we acquired multiple spectra similar to the one shown
in Figure 3a with increasing set-point current. A stacked plot of distance-
dependent dI/dV spectra is shown in Figure 3b, where we observe an increase in
the intensity of the excitation peaks as the tip approaches the molecule. The
ratio $A_{r1}$ between the amplitude of the first excitation peak, $A_{1}$,
and that of the coherence peaks, $A_{BCS}$, is plotted in Figure 3d (top
panel) as a function of $I_{BCS}$, the current at the coherence peaks. The
inelastic amplitude first increases with the tunneling rate and then
stabilizes in a plateau characteristic of a stationary state. Fitting these
data with rate equations from Heinrich et al. 12 yields a value of
$\tau_{1}\approx 80~{}$\mathrm{ns}$$ for FeTPP-Cl on 4ML of Au on V(100) (see
fitting procedures in the Supporting Information 34). Such large lifetime is
attributed to the protection of the excited state by the superconducting gap,
which forbids spin relaxation via creation of electron-hole excitations
because $2D<2\Delta_{s}$.

Interestingly, the value of $\tau_{1}$ obtained for FeTPP-Cl on Au/V(100) is 8
times larger than the related molecule Fe-OEP-Cl on Pb(111) 12, where the de-
excitation is protected by an even larger superconducting gap. As previously
shown 43, 44, another decaying mechanism could take place through the direct
emission of phonons, with energy $\omega\hbar\approx 2D$, to the phononic bath
of the substrate. Thus, a possible origin for the larger lifetime on this
substrate could be the lower phonon density of states at the Fermi level of
vanadium and gold compared to lead 45, 46, 47, as well as the lower electron-
phonon coupling present in Au 48, 49. From the stacked spectra in Figure 3b,
we can also obtain an estimation of the lifetime $\tau_{2\rightarrow 1}$ of
the second excited state $S_{z}=\pm\ket{5/2}$. In the bottom panel of Figure
3d, we plot the relative amplitude of the second excitation peak, $A_{r2}$,
with respect to $I_{BCS}$. Fitting the data with a set of rate equations (red
line) yields a value of $\tau_{2\rightarrow 1}\lesssim 2~{}$\mathrm{ns}$$ (see
Supporting Information 34). Electrons populating the second excited state have
now sufficient energy ($4D>2\Delta_{s}$) to directly decay into the substrate
by electron-hole pair excitations, lowering the lifetime of the highest
excited state. Nevertheless, this value is still relative large, and
comparable to magnetic atoms on insulating films 9.

Figure 4:  (a) 2D intensity plots of a series of distance-dependent dI/dV
spectra for 4 ML, 9ML and 14ML Au thickness on V(100). (b) Single STS spectra
taken on a FeTPP-Cl molecule on 4ML (blue), 9ML (orange) and 14ML (green) Au
thicknesses on V(100). (I=200 $\mathrm{pA}$, V=6 $\mathrm{mV}$). (c): Fit for
determining the lifetime of the first excited state $\pm\ket{3/2}$ with
thickness of 9ML ($P=0.460\pm 0.003,\tau_{1}=39~{}$\mathrm{ns}$\pm
10~{}$\mathrm{ns}$$)

To test the influence of the intra-gap bound states on the lifetimes of the
excited states, we compared FeTPP-Cl spin excitation dynamics in samples with
different Au thicknesses. In Figure 4a, two dimensional intensity plots of a
series of distance-dependent dI/dV spectra for 4, 9 and 14 ML Au thickness are
shown. The plots show the shift of the dGSJ resonances to lower energies as a
function of the Au thickness, similar to Figure 1b.

We follow the same fitting procedure for determining the excited state
lifetime of FeTPP-Cl on every film thickness. For 9 ML, the fit yields a value
of $\tau_{1}=39~{}$\mathrm{ns}$\pm 10~{}$\mathrm{ns}$$ and $\tau_{2\rightarrow
1}=1.1~{}$\mathrm{ns}$\pm 2.2~{}$\mathrm{ns}$$ for the lifetime of the first
and second excited state, respectively (Figure 4c and Figure S2). On the 14 ML
film, we could hardly observe faint second excitation peaks (Figure 4b) by
approaching the tip to the closest possible position ($I=200~{}$\mathrm{pA}$$)
before picking up the molecule. This determined an upper limit for the spin
excitation of $\tau_{1}<1~{}$\mathrm{ns}$$.

The reduction in excitation lifetime is in agreement with the gradual shift of
the dGSJ resonances in the proximitized Au film. From Figure 1d, we obtain
that the bound state values decrease from $\sim 0.69$\mathrm{meV}$$ (4 ML) to
$\sim 0.65$\mathrm{meV}$$ (9 ML), and finally to $\sim 0.45$\mathrm{meV}$$ (14
ML). In contrast, the magnetic anisotropy, as obtained from the position of
the spectral peaks, remains $D\approx 0.65~{}$\mathrm{meV}$$ for the 4 and 9
ML of Au on V(100), while increases to $D\approx 0.8~{}$\mathrm{meV}$$ for the
14ML film. Variations in $D$ have been previously observed in different
magnetic systems on metallic substrates and attributed to either structural
changes 12, 50, 51 or variations in the Kondo coupling with the substrate 52.
Comparing the spectra of FeTPP-Cl on the different gold thicknesses in Figure
4b, we note that the dGSJ peaks show a clear asymmetry for the 4 ML sample,
that decreases for 9 ML, and vanishes for the 14 ML case. Such spectral
imbalance reflects a particle-hole asymmetry in the quasi-particle excitations
of the superconductor probably due to the presence of a finite coupling with
the molecule. The absence of peak asymmetry for the 14 ML reveals a
significant smaller Kondo coupling with the substrate, which can explain a
renormalized magnetic anisotropy to a larger value 53, 54.

Figure 5:  (a) 2D intensity plot of a series of distance-dependent dI/dV
spectra for a switching FeTPP-Cl molecule. (b) STM images taken before (top)
and after (bottom) the change of the interaction regime. Insets: line profiles
taken across the molecule as indicated by the blue dotted line. (c) Single
dI/dV spectra before (top) and after (bottom) the change of the interaction
regime. Insets: Cartoon model representing the tip-induced effect far from
(top) and close to (bottom) the molecule.

The weak adsorption regime of this molecular species could be irreversibly
modified by approaching the tip beyond a specific distance. In this case, we
observed an abrupt change in the dI/dV signal (Figure 5a). The two
characteristic spin excitation peaks disappear, while two pairs of YSR states
arise within the superconducting gap (Figure 5c, bottom spectra). The
emergence of YSR states indicates the increase of the exchange coupling
strength, $J$, of the molecular spin with the Cooper pairs of the
superconducting condensate 20. Such a change in the interaction regime,
previously observed by Heinrich et al. 55, is understood as a slight variation
of the molecular geometry induced by the tip in close proximity to the
molecule. Attractive forces exerted to the Cl atom, weaken the Cl-Fe bond and
Fe is allowed to relax in the molecular plane as shown in the cartoon of
Figure 5c. In order to verify that this change of coupling regime is not due
to the detachment of the Cl ligand, or any other irreversible molecular
distortion, we checked the STM images before and after the tip approach
(Figure 5b). Additionally, a broad peak emerges in the new regime outside the
superconducting gap at $eV\approx 1.7~{}$\mathrm{mV}$$. This new molecular
configuration has been associated with a different oxidation state, with
$S=2$, stabilized by the hybridization of the Fe ion with the surface 56.

In summary, in this work we have shown that proximity-induced superconducting
gold thin films can enhance the spin excitation lifetime of magnetic
molecules. We explored the spin excitation lifetimes of an S=5/2 iron(III)
porphyrin-chloride molecule on Au films grown on V(100) by implementing IETS
with an STM. Our results found spin excitation lifetimes of $\approx
80$\mathrm{ns}$$ for the excitation of the S${}_{z}=\pm$3/2 multiplet, which
is protected from decaying to an electron-hole pair excitation by the absolute
proximity-induced gap of the substrate. The excitation lifetime in this
surface platform is even larger than the one found for related species on
Pb(111) 12. This is attributed to the lower density of phononic states in the
substrate, suggesting that direct phonon emission is a lifetime limiting
process. However, we also determined that the lifetime is affected by a pair
of in-gap de Gennes-Saint James resonances in the film, which separate from
the gap edge and shift inwards towards zero energy, thus opening alternative
(coherent) channels for decaying. Overall, the Au/V(100) platform offers the
advantage of employing a noble metal, mild in molecular adsorption and
reactions, for studies of long spin dynamics. Additionally, the presence of
coherent sub-gap states in the proximitized metal film suggests new potential
methods for addressing spin states and excitations of magnetic molecules.

##  1 Methods

All experiments were carried out on a commercial ultra-high vacuum scanning
tunneling microscope of SPECS with a Joule-Thomson cooling stage reaching a
base temperature of $1.2~{}$\mathrm{K}$$. For the acquired STS spectra, an
external lock-in was used with a modulation frequency of $938~{}$\mathrm{Hz}$$
and a amplitude of $V_{rms}=20-50~{}$\mathrm{\SIUnitSymbolMicro V}$$.

The vanadium (100) crystal used in this project was repeatedly sputtered with
Ar+ at 1.5$\mathrm{kV}$ in UHV conditions ($P=5\times 10^{-9}$\mathrm{mbar}$$)
and annealed at high temperatures ($\sim 1000^{\circ}$C) in an attempt to
remove the residual impurities as suggested by Kralj et al. 24. Gold thin
films were deposited on V(100) with an e-beam evaporator, while maintaining
the crystal at 550∘C. Afterwards, the samples were post-annealed for 10
minutes at 600 ∘C. The calibration of the deposition rate was made by
evaporating 0.5 monolayers and subsequently checking the Au coverage by STM.

The tip was prepared by indenting up to 20$\mathrm{nm}$ into the substrate. A
superconducting tip results in a substantial increase of the energy
resolution, since tunneling of electrons takes place between the two sharp DOS
of tip and sample 27. Sublimation of FeTPP-Cl molecules from a Knudsen cell at
297∘C resulted in a mixture of FeTPP-Cl and FeTPP species on the surface,
shown in Figure 2.

Deconvolution of acquired dI/dV spectra for different Au thicknesses on
V(100), as well as fit for the energies of the intra-gap states based on de
Gennes and Saint-James 32 model are provided. A brief description of the rate
equations leading to the fitting function for $A_{r1}$ and $A_{r2}$ and the
fit for extracting the lifetime of the second excited state of the sample with
9ML of Au are presented. Finally, a magnetic field dependent measurement is
shown.

The authors thank Sebastian Bergeret for stimulating and helpful discussions,
and Christian Ast for information regarding the preparation of the V(100)
surface. We also gratefully acknowledge financial support from the Red
guipuzcoana de Ciencia, Tecnología e Innovación through program NEXT01, the
Agencia Estatal de Investigación (AEI) (project No. FIS2017-83780-C1 and the
Maria de Maeztu Units of Excellence Programme MDM-2016-0618), the European
Regional Development Fund, and the European Union (EU) H2020 program through
the FET Open project SPRING (grant agreement No. 863098). J.O. thanks the
Basque Departamento de Educación through the PhD scholarship no.
PRE_2019_2_0218.

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