11institutetext: Fraunhofer IESE, Kaiserslautern 67663, Germany
11email: {rodrigo.falcao<EMAIL_ADDRESS>

# Towards a decentralized data privacy protocol for self-sovereignty in the
digital world††thanks: This work has been funded by the German Federal
Ministry of Education and Research (BMBF) (grant numbers 16KIS1507 and
16KIS1510).

Rodrigo Falcão 11 0000-0003-1222-0046 Arghavan Hosseinzadeh 11
0009-0001-8699-9972

###### Abstract

A typical user interacts with many digital services nowadays, providing these
services with their data. As of now, the management of privacy preferences is
service-centric: Users must manage their privacy preferences according to the
rules of each service provider, meaning that every provider offers its unique
mechanisms for users to control their privacy settings. However, managing
privacy preferences holistically (i.e., across multiple digital services) is
just impractical. In this vision paper, we propose a paradigm shift towards an
enriched user-centric approach for cross-service privacy preferences
management: the realization of a decentralized data privacy protocol.

###### Keywords:

personal data privacy protocol.

##  1 Motivation

Not long ago, users navigated through Internet-based services (e.g., websites)
leaving behind an unnoticed trail of personal data, browsing habits, and
online interactions. Tracking technologies such as cookies, the development of
data analysis techniques, and the rise of tech giants such as Google and
Facebook (whose online presence became pervasive) have given rise to a massive
concentration of data, which has supported targeted advertising for diverse
purposes, sometimes raising ethical concerns [1]. These concerns led to the
emergence of several data protection initiatives around the globe, resulting
in regulations such as the GDPR [6] and the Data Governance Act [7], which aim
to facilitate data exchange while increasing trust and ensuring data
protection. One of the most tangible consequences a user experiences occurs
when they visit a website using cookie technology: On first access, they are
asked to accept or reject cookies.

While users have been given some sort of freedom to choose which types of data
are used by different services and for what purposes, and have also been
entitled to change their preferences and revoke permissions for data usage, it
is still hard for them maintain sovereignty over their choices. Gradually,
their data and their choices regarding data usage are spread across the
dozens, hundreds, or even thousands of digital services they interact with. In
the long run, it is easy to lose track of where data is stored and used, by
whom, and for what purpose. Taking back control of the usage of their data
becomes a near-impossible endeavor. Even if each digital service were shipped
with a comprehensive and easy-to-use privacy preferences management tool,
users would still have to remember all the services that use their data, visit
them, and, one after another, review their privacy preferences if they want
to. In other words, from the end user’s perspective, privacy preferences
management solutions are distributed across virtually all digital services
they interact with. For this very reason, they cannot be effective. To make
matters worse, there is a lack of standardization in the field.

In this vision paper, we propose a paradigm shift in how we approach the issue
of privacy preferences management. The current paradigm focuses on the
interaction between a user and a digital service. Usable privacy management
tools are a necessary but insufficient solution. We envision a future where a
fully user-centric approach takes a holistic view of all digital services,
allowing users to manage their preferences in one place, without any
particular service provider monopolizing this space. This is where the
decentralized data privacy protocol comes into play. It can be implemented by
any party and offers benefits to both end users and service providers. It also
opens up opportunities for the development of new privacy-enhancing
technologies on top of it. The remainder of this paper is structured as
follows: In Section 2, we review recent related work; Section 3 outlines the
protocol concept; Section 4 explores the benefits and opportunities; and
Section 5 concludes the paper, outlining our next steps.

##  2 Related work

The most recent advancements in research with respect to preserving user
privacy focus on privacy policy languages and user-friendly settings for
privacy preferences. Gharib [9] argues that most data subjects blindly accept
the notices, not because they do not value their privacy, but because most
privacy policies and terms of services are long, complex, and hard to
understand, so the author introduces a model for informed consent. The model
involves a Matching Component that compares the privacy preferences of the
user that is included within their Personal Privacy Profile (PPPo) and the
privacy policies that are published by the service providers and automates the
process of giving consent. A dynamic contextual notice is provided to the user
when the user preferences and the policies do not match. Accordingly, the user
can make an informed decision concerning the consent request. Gharib also
proposes an ontology that can be used for realizing preferences and policies.
However, where to store the PPPos seems to be out of the scope of this work.

Dehling et al. [2] introduce Privacy Cockpits, which serve as central
dashboards for users to navigate and manage their personal data. This solution
aims to ease the enforcement of regulations such as the GDPR, although the
focus of their work is on protecting the data used across various services
within specific digital ecosystems.

In 2020, the European Data Protection Supervisor introduced the Personal
Information Management Systems (PIMS) concept [5]. The PIMS concept offers a
new approach in which individuals are the “holders” of their own personal
information. PIMS aims to empower users to take charge of their digital
identity and the use of their personal information across various services and
platforms. In recent years, several initiatives and projects have claimed PIMS
features. Among these, the Solid protocol [10] stands out. It proposes a set
of conventions and tools for building a decentralized platform for social Web
applications. In order to address the challenge of obtaining consent for
processing personal data, Florea and Esteves [8] introduced a policy layer
into the Solid ecosystem. They integrated the usage of the ODRL Policy
Language [11], the ODRL profile for Access Control (OAC) [3], and the Data
Privacy Vocabulary (DPV) [12] to allow Solid users to express their privacy
preferences. By integrating such a policy layer into the Solid ecosystem, the
matching process regarding users’ preferences and requests for data can be
automated. However, the focus of the Solid protocol remains on data management
mechanisms that allow users to store their data such as contacts and photos in
Personal Online Datastores (PODs) and control access of applications to this
data. We therefore still see an ongoing need for a protocol specifically
designed for privacy preferences management.

##  3 A paradigm shift

We propose a paradigm shift by adjusting the context of the problem. Users
need adequate means to exercise their data sovereignty. Tools can implement
diverse models to provide such means; however, regardless of whether we
consider the implementation of the “notice and consent model”, the “informed
consent model”, or “data protection cockpits”, to name but a few strategies,
solutions address the data sovereignty challenge in the context of the
interaction between the user and a given digital service (or ecosystem).
Consider now the exercise of data sovereignty in the context of not only one
digital service, but all of them. If we have this goal in mind, current
strategies – though valuable and necessary – fall short. It is not enough that
each digital service provides its own means for users to manage their
preferences; instead, each individual should be able to manage their data
preferences across all digital services that use their data. A new centralized
digital service could fill this gap; however, to be effective, it would
require the providers of digital services to adhere to it, and users would
still have to rely on a centralized service offered by yet another service
provider.

Due to these reasons, we argue that a more adequate solution should be
positioned at a higher level of abstraction and be developed as an open
protocol that anyone can implement. We envision a decentralized protocol for
users and services to manage data privacy preferences. A protocol can be
defined as a set of syntactic and semantic rules that standardize
communication between two or more entities. Using a defined protocol, users
could tell the digital services where they (the users) want to store and
manage their privacy preferences. We call this place the user’s Personal
Privacy Preferences Place (P4). Users can decide who will implement their P4,
where, and how. P4 instances could be hosted by a user’s trusted third-party
company or even be self-hosted, for example. Figure 1 illustrates an example
scenario where two users, Alice and Bob, use different sets of digital
services. Alice manages her privacy preferences through a P4 instance hosted
and operated by a trusted company, while Bob manages his using a self-hosted
P4 instance. The digital services can interoperate with both P4 instances
because they (the digital services and the P4 instances) implement their roles
in the protocol.

Figure 1: Overview of the decentralized data privacy protocol (ddpp).

### Shaping the requirements

The goal of the protocol is to improve the usability and self-sovereignty of
privacy preferences management from the point of view of end users in the
context of numerous digital services. To achieve this goal, the protocol must
fulfill certain quality and functional requirements. From a quality
perspective, the list includes (but is not limited to) openness (the protocol
shall have an open specification in order to enable operational independence,
meaning that anyone could implement its elements), adaptability (the
implementation of the protocol shall not prevent service providers from
specifying the privacy preferences as they want, meaning that service
providers should not be obliged to change the way they define privacy
preferences), and confidentiality (the personal privacy preferences place
shall not store nor exchange private user data, but only users’ privacy
preferences data). Concerning the functional aspects, we highlight three
fundamental constructs: the data structure (the protocol shall specify a
privacy preferences meta-model whose instances express privacy preferences
using generic elements), the behavior (the protocol shall specify the
interaction flows between the participants, namely the user, their P4, and the
digital service), and the interfaces (syntactic and semantic description of
each interface that the participating systems – P4 instances and digital
services – must implement to enable the desired behavior).

### On the interaction flows

The protocol must support at least two key flows: handshake and update. Using
the handshake flow, the user informs their digital service about their P4
instance. After the user sets their initial privacy preferences and after the
authorization process, the digital service can communicate with the user’s P4
instance to exchange privacy preferences data. Using the update flow, every
change that the user makes in the privacy preferences on their P4 should be
reflected in the affected digital services, and every change made in a digital
service should be reflected in the user’s P4.

##  4 Benefits and opportunities

For users, the envisioned approach is an additional step towards enabling data
sovereignty as the implementation of the protocol takes the exclusive control
of privacy management means from the service providers and gives it to the
actual data subjects, i.e., the users. From the point of view of the service
provider, and given that we are already living in a regulated society
concerning data privacy, non-compliance poses a significant financial risk.
Therefore, adherence to an open standard would help service providers transfer
at least part of the risk beyond the boundaries of their companies.
Furthermore, adopting an open privacy management standard would increase
transparency and help build trust in the service providers who adopt the
protocol.

This idea can be boosted by the adoption of self-sovereign identities (SSI),
which have gained increasing traction through initiatives such as the eIDAS
regulation [4]. The location of the user’s privacy preferences could be tied
to their identities. When a user provides their identity to an arbitrary
digital service, the service would directly know the user’s P4 instance and,
based on the protocol, privacy preferences would be stored on the user’s P4.

Customized and optimized P4 instances can give users extended privacy
management capabilities in comparison to those offered by their digital
services. For example, while a certain digital service may only allow for
either consenting or denying access to certain data for a given purpose, P4
instances can provide users with the ability to set dynamic rules or
constraints on their preferences (e.g., revoke consent for data X for the
purpose Y in all digital services located in Z 30 days after consent was
granted). The development, customization, and operation of P4 instances opens
up new business opportunities for companies.

Furthermore, following the same specification language and a standard
ontology, we can facilitate the matching process between privacy policies and
user’s preferences and further automate it.

##  5 Conclusion and outlook

So far, it has been hard for users to maintain sovereignty over their privacy
preferences because privacy preferences management is not centered on the
users but scattered across numerous digital services. In this paper, we
sketched our vision of a decentralized data privacy protocol. The
implementation of this protocol will allow users to manage their privacy
preferences effortlessly. It primarily enables communication between web
services and P4 instances but is also available for any digital service to
implement and utilize. Research plays a key role in the fulfillment of this
vision. From our point of view, the next steps include a review of extensible
data privacy meta-models, the design of the protocol flow, the design of a
reference architecture for P4, and prototyping of a reference implementation.

## References

  * [1] Daoud, M.K., Al-Qeed, D.M., Al-Gasawneh, J.A., Ziani, A.: Examining the ethical implications of data privacy and targeted advertising in digital marketing: Consumer perceptions. In: SNAMS-2023. pp. 1–6. IEEE (2023)
  * [2] Dehling, F., Ludborzs, S., Weßner, A., Falcão, R.: Konzepte für gebrauchstaugliche Datenschutzfunktionen in digitalen Ökosystemen. Datenschutz und Datensicherheit-DuD 48(2), 95–102 (2024)
  * [3] Esteves, B., Pandit, H.J., Rodríguez-Doncel, V.: ODRL Access Control Profile. https://besteves4.github.io/odrl-access-control-profile/oac.html (2021), accessed on 2024-02-15
  * [4] European Commission: eIDAS Regulation. https://digital-strategy.ec.europa.eu/en/policies/eidas-regulation (2023), accessed on 2024-02-22
  * [5] European Data Protection Supervisor: Techdispatch 3/2020: Personal information management systems (2021), https://data.europa.eu/doi/10.2804/096824, accessed on 2024-02-12
  * [6] European Parliament and Council of the European Union: Regulation (eu) 2016/679 of the european parliament and of the council of 27 april 2016 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing directive 95/46/ec (general data protection regulation). https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32016R0679 (2016), accessed on 2024-02-15
  * [7] European Union: Data governance act (2022). https://eur-lex.europa.eu/eli/reg/2022/868/oj (2022), accessed on 2024-02-12
  * [8] Florea, M., Esteves, B.: Is Automated Consent in Solid GDPR-Compliant? An Approach for Obtaining Valid Consent with the Solid Protocol. Information 14(12), 631 (2023)
  * [9] Gharib, M.: Toward an architecture to improve privacy and informational self-determination through informed consent. Information & Computer Security 30(4), 549–561 (2022)
  * [10] Sambra, A.V., Mansour, E., Hawke, S., Zereba, M., Greco, N., Ghanem, A., Zagidulin, D., Aboulnaga, A., Berners-Lee, T.: Solid: a platform for decentralized social applications based on linked data. MIT CSAIL & Qatar Computing Research Institute, Tech. Rep. (2016)
  * [11] World Wide Web Consortium: ODRL Version 2.0. https://www.w3.org/ns/odrl/2/ (2021), accessed on 2024-02-15
  * [12] World Wide Web Consortium: Data Privacy Vocabulary (DPV). https://w3c.github.io/dpv/dpv/ (2023), accessed on 2024-02-15


# Spin-Orbit Proximity Effect in Bi/Co Multilayer: The Role of Interface
Scattering

Arthur Casa Nova Nonnig  Instituto de Física, Universidade Federal do Rio
Grande do Sul, 90501-970 Porto Alegre, RS, Brazil  Alexandre da Cas Viegas
Instituto de Física, Universidade Federal do Rio Grande do Sul, 90501-970
Porto Alegre, RS, Brazil  Fabiano Mesquita da Rosa  Instituto de Física,
Universidade Federal do Rio Grande do Sul, 90501-970 Porto Alegre, RS, Brazil
Paulo Pureur  Instituto de Física, Universidade Federal do Rio Grande do Sul,
90501-970 Porto Alegre, RS, Brazil  Milton Andre Tumelero
<EMAIL_ADDRESS>Instituto de Física, Universidade Federal do Rio Grande
do Sul, 90501-970 Porto Alegre, RS, Brazil

###### Abstract

The Spin-Orbit Proximity Effect is the raise of Spin-Orbit Coupling at a layer
near to the interface with a strong spin-orbit material. It has been seen in
several system such as graphene and ferromagnetic layers. The control of the
Spin-Orbit Coupling can be a pathway to discover novel and exotic phases in
superconductor and semimetallic systems. Here, we study the magnetoelectrical
transport, i.e., magnetoresistance and anomalous Hall effect, in
Cobalt/Bismuth multilayers looking for traces of spin-orbit proximity effect
and evaluate the origin of such effect. Our results point for an increase of
Spontaneous Magnetic Anisotropy of Resistivity and Anomalous Hall Resistivity
at very low thicknesses of Cobalt. The analysis of the Anomalous Hall
Resisitivity indicate that the Bismuth layers change the scattering mechanism
of Hall effect to the extrinsic skew-scattering type, indicating that the
spin-orbit proximity effect could be related to the elastic scattering of
cobalt free carriers by bismuth sites at the interface.

Keywords

Spin-Orbit Proximity Effect, Ferromagnetism, Bismuth Multilayers.

##  I Introduction

The interplay between Spin-Orbit Coupling (SOC) and Ferromagnetism (FM) has
been shown to be responsible by several novel and emergent phenomena in
physics, most of them discovered in the last decades [1, 2]. Such discoveries,
such as Skyrmions [3, 4], Quantum Anomalous Hall Effect [5, 6], Spin-Orbit
Torque [7, 8, 9] and Triplet Magnetic Josephson Junctions [10, 11] became even
more outstanding because of its promising applications in information
technology [1]. Most of this emergent physics occurs, or is enhanced, at the
interfaces between FM and strong Spin-Orbit Materials (SOM) [2]. From the
technological perspective, one of the main objectives is to increase or
control the SOC in semiconductor and ferromagnetic systems in order to improve
the materials applicability. Some current attempt are based in ferroelectric
tuning of Rashba SOC [12, 13] and Proximity Induced SOC [14, 15]. Although the
Ferroelectricity can help to control the SOC in semiconductors, it can hardly
be used for metallic FM system.

The proximity induced SOC or Spin-Orbit Proximity Effect (SOPE) occurs in few
atomic layers of a low spin-orbit coupling (SOC) metal near its interface with
a material characterized by strong SOC. It was observed when interfacing
Graphene with strong SOC materials [15, 16] or by doping Graphene with strong
SOC impurities [17]. In graphene-based heterostructures, the effect
essentially results from the hybridization of the $\pi$ orbital in graphene
with the d-band of metallic layers at interfaces [18, 15, 17, 16, 19].
Hybridization of the $\pi$ orbital with localized wave-functions of point
defects is the basis for SOPE induced by impurities [14]. Such hybridization
processes remove the spin degeneracy without destroying the Dirac cones [17].
Also interesting is the fact that he Rashba SOC in graphene could also be
enhanced by codoping. In this process, the presence of p- and n- dopants could
lead to the presence of an electrostatic potential that breaks the inversion
symmetry [20].

In the case of SOM/FM bilayers, the inverse effect, known as the magnetic
proximity effect, has been observed, in which the SOM presents magnetic
properties [21, 22]. The case of proximity enhancement of SOC in the FM
layers, it was reported by Zhang, et al [23]. A 10-fold increment of SOC in
CoFeAl (CFA) layers at CFA/Pt bilayer samples was observed by measuring the
Anomalous Hall Effect (AHE). However, the origin the SOPE remains unclear in
FM material. Zhang, et al, [24] suggested the possibility of magneto-
scattering of the charge carries to play as a source for the enhacement of SOC
in CFA/Pt bilayer. It seems clear that the mechanism responsible for SOPE,
whether governed by hybridization or scattering processes, should be first
fully understood in order to allow its application in spintronics devices
quantum computing, etc.

Here we study the SOPE in ultrathin Cobalt and Bismuth multilayers. We used Bi
as a source of SOC at the Bi/Co interfaces and measured SOC sensitive effects
such as Spontaneous Magnetic Anisotropy of the Resistivity (SAR) and Anomalous
Hall Effect (AHE) in order to map the SOC at the Cobalt Layers. SAR describes
the resistivity anisotropy resulting from the relative orientation of the
electrical current and the magnetization. This effect is also called as
anisotropic magnetoresistance (AMR) since it is measured in the presence of
small fields applied either parallel or perpendicular to the current. SAR
furnishes a direct measure of the SOC intensity [25]. The anomalous Hall
resistivity, otherwise, scales with magnetization, thus being intrinsically
dependent on the spin-orbit interaction. The Bismuth was chosen due to it
strong SOC and low conductivity. Our findings shown evidences of a enhancement
of SOC at the Co layers close to the interface with bismuth. Our results
suggested that the origin of the observed SOC increment is related to spin-
dependent scattering of conduction electrons of Co by the Bismuth atoms at the
interfaces.

##  II Methods

The samples were prepared by Magnetron Sputtering using independent targets of
Bismuth and Cobalt (both 99.99$\%$). Power sources with 10W (DC) and 45W (RF)
were employed for Bi and Co sputtering, respectively. The Vacuum chamber base
pressure was $8x10^{-8}torr$, the deposition pressure was $1x10^{-3}torr$,
maintained by 200 $cm^{3}/mim$ (sccm) of ultrapure argon gas (99.9999 $\%$)
flux. The substrate was a 100 nm $SiO_{2}$ over a silicon (100) wafer. The
sample thicknesses were confirmed by Rutherford Backscattering and the crystal
structure was checked by X-Ray Diffraction, showing polycrystalline pattern
for both Bismuth and Cobalt (in HCP crystal structure). All the samples were
covered by a 2 nm Titanium capping layer to prevent degradation. Samples with
the following structure were prepared $[Co(t)Bi(3)]_{x10}$ with t = 0.5, 0.75,
1.0, 2.0 nm. The Magnetoresistance and Hall effect were measured using a
standard Hall Bar geometry, with six electrical contacts. Current was applied
at the extremities of the samples. Two inner contacts were used for detecting
the longitudinal resistivity signal, while two other, placed in opposite edges
of the sample, were used for measuring the Hall voltage. For the
magnetoresistance experiments, in-plane and perpendicular-to-plane magnetic
field orientations were applied. Fields up to 1.5 kOe were used for the
magnetoresistance measurements, while fields up to 40 kOe were employed for
the Hall effect experiments. Temperatures were varied in the range 3 K to 300
K. The magnetotransport experiments were performed using an equipment based on
a CMag9 cryocoller manufactured by Cryomagnetics Inc.. Auxiliary magnetization
measurements were also carried out in the low field range. For these
experiments, a VSM EV9 magnetometer manufactured by Microsense was used.

##  III Results

Figure 1: In panel (a) are shown the normalized (at room temperatura)
electrical resistivity vs. temperature for the studied Co/Bi Multilayer. Also
shown are measurements for the reference samples Bi(30nm) and Co(20nm). In (b)
The Magnetization vs. Magnetic Field, the Hystereses curve for the
multilayered samples measured at 300 K whith the field laying at the samples
plane.

_Electrical and magnetic characterization_. Figure 1a shows the normalized
electrical resistance of the studied Co/Bi multilayers as a function of the
temperature. Results for the references samples, Bi(30 nm) and Co(20 nm) are
also presented. The Co reference sample displays the typical metallic behavior
with Residual Resistance Ratio (RRR) of about 1.2, which is low compared to
values reported in refs. [26, 27], but expected due to very low thicknesses of
the layers. The Bismuth otherwise shows a Negative Temperature Coefficient
(NTC) which is related to the polycrystalline nature of the layers. It is
worthwhile to mention that the absolute value of Bi(30nm) sample resistivity
is two orders of magnitude higher than that for Co(20nm). The electrical
behavior of the multilayers cannot be simply described by a parallel or series
association of resistors representing the individual layers. In films with
small Cobalt thickness, such as 0.5 and 0.75 nm, the layers are not
necessarily continuous, but form large flat clusters, which imposes a serial-
like electrical behavior to the heterostructure. For thicker Co layers, such
as 1 and 2 nm, the transport is likely to flow mostly within the Co layers in
a parallel-type association with the Bi acting as spacer. As displayed in
Figure 1a, a change in the resistivity vs. temperature behavior, from Positive
Temperature Coefficient (PTC) to NTC is observed at the Bi/Co content ration
gradually increases.

The Figure 1b shows the magnetic behavior of the samples in the M x H curve.
The saturation magnetization confirm that the magnetic moment of Cobalt layers
does not change significantly due to stacking with Bismuth layers. In the same
figure, one also observes a systematic increase of coercivity by intercalating
Cobalt with Bismuth. The coercive field $H_{c}$ sistematically increases with
the thickness of the Bi layers. This behavior could be related to the increase
of the spin-orbit coupling.

Figure 2: In (a) the magnetoresistance curve of the samples
$[Co(2)Bi(3)]_{x10}$ in longitudinal configuration (MRL) is shown in black,
while the transversal configuration (MRT) is shown in red. (b)
Magnetoresistance for the samples $[Co(2)Bi(3)]_{x10}$ measured at the quoted
temperatures. (c) The SAR ratio vs. temperature and (d) the SAR ratio vs.
Cobalt thickness measured at 30 K and 300 K. The contínuous black and red
lines in this panel are guide for the eyes. The dashed and dotted lines are
explained in the text.

_Magntotransport characterization_. Now we proceed to analyse the results of
magnetotransport of the Co/Bi multilayers. The magnetoresistance of the sample
$[Co(2)Bi(3)]_{x10}$) is depicted in the Figure 2a. These measurements were
done at 30 K, under two distinct field configuration, namely, transversal
(MRT) and longitudinal (MRL), in the first, both magnetic field and electrical
current lays horizontally in the sample plane, but are perpendicular to each
other. In the case of longitudinal, the field and current are parallel to each
other. The opposite sign of magnetoresitance in the configuration MRT and MRL
are signature of the (SAR) [28, 29] in ferromagnetic materials. This effect
comes from the Cobalt layers only. The arrows in the Figure 2a indicate the
magnetization and current relative orientations. The MRL and MRT values could
depends on the samples magnetic anisotropy and do not are necessarily equals
[30].

Figure 2b shows the SAR curves for the samples $[Co(2)Bi(3)]_{x10}$ obtained
at different temperatures. Notice that there is almost no change in the AMR
ratios by varying the temperature. The decrease of the temperature,
nevertheless, increase in the coercive field, as seen from the peak
separation. The same increase in coercivity is observed in the other samples
with Bismuth intercalation, but not in the pure cobalt samples.

The SAR ratio is given by [29]

$\Delta\rho/\rho_{(0)}=\gamma(\alpha-1)$ (1)

where $\rho_{0}$(0) is the resistivity at zero field, $\gamma$ is a parameter
depending on the spin-orbit coupling and
$\alpha=\rho_{\uparrow}/\rho_{\downarrow}$ is the ratio between the
resistivities for the two spin-dependent current channels. $\Delta\rho$ could
be experimentally determined as $\Delta\rho=MRL-MRT$, where both longitudinal
and transverse magnetoresistances are obtained at the technical saturation
field. Either $\gamma$ and $\alpha$ are not expected to depend much on the
temperature. Thus, the results in Figure 2b are in agreement with expectations
from the Campbell-Fert [29] model for SAR.

The Figure 2c presents the SAR (or AMR) Ratio vs. Temperature for the samples
$[Co(t)Bi(3)]_{x10}$ with t = 0.75, 1 and 2 nm. As discussed above, the SAR
ratio barely depends on the temperature, except for the sample
$[Co(1)Bi(3)]_{x10}$ in which this ratio decreases weakly, but consistently,
upon heating. This behavior is possibly due to a mixing of the spin-dependent
currents, leading to a decrease in the effective value for alpha in Eq(1). A
similar effect was also observed in magnetic Platinum layers (due to the
magnetic proximity effect) [22]. Figure 2d shows the SAR ratio for the studied
multilayers versus the cobalt thickness. The highest SAR ratio was found for
the sample $[Co(1)Bi(3)]$. The peak profile shown by the red and black lines
(for 30 and 300 K, respectively) may be interpreted as originated by two
factors. The first one is the bismuth shunt at very low thicknesses of Co
[31], which fully drives the electrical current through the Bismuth layers,
nullifying the SAR ratio at the lowest Co thickness. Such effect is
represented by the dotted line in the Figure 2d. The peak of SAR in 2d
suggests the occurrence of proximity effect due to the Bismuth layers, which
increases locally (near to the interface) the SOC and consequently the SAR
ratio. In the limit of large contents of Co in the multilayer, the relative
effect of the proximity effect should become less pronounced leading to a
decrease in the SAR ratio. The expected variation of SAR due to the Spin-Orbit
Proximity Effect (SOPE) as a function of the Co thickness is displayed by the
dashed line in Figure 2d, for temperatures of 30 K and 300 K. Then, the
combination of the shunt effect and SOPE lead to the round maximum observed in
SAR data of Figure 2d. Notice that the dotted and dashed lines are only a
qualitative description of the effect pointed above, and were not obtained
using any model, they are only eye-guides. Similar results were observed by
Honda, et al, [32], in Bi-Co thin films alloys.

Figure 3: IN (a) Transverse Hall resistivity for the sample
$[Co(2)Bi(3)]_{x10}$ at different temperatures vs. external magnetic field.
(b) The Anomalous Hall Resistivity vs. Cobalt Thickness in the multilayer, at
distinct temperatures. (c) The Anomalous Hall Resistivity vs. Temperature and
(d) the Anomalous Hall Resistivity vs. the longitudinal resistivity for the
multilayers.

_Anomalous Hall effect characterization_. Hall effect results for the studied
samples are show in the Figure 3. The Figure 3a displays the total Hall
Resistivity ($\rho_{xy}$) for the sample $[Co(0.75)Bi(3)]_{x10}$ at different
temperatures. The results show clearly the presence of an anomalous
contribution, which scales with the magnetization, superimposed to the
ordinary effect that scales with the applied field, as given by the usual
expression.

$\rho_{xy}=R_{0}H+R_{S}.M$ (2)

where $R_{0}$ and $R_{S}$ are the ordinary and anomalous Hall coefficients,
respectively. The anomalous Hall resistivity, $\rho_{AHE}$, is obtained by
extrapolating the high-field linear behavior of $\rho_{xy}$ to zero field. The
so determined $\rho_{AHE}$ are shown in Figure 3b for the studied
heterostructures at three different temperatures. Interestingly enough,
$\rho_{AHE}$ shows the same peak profile as obtained in the SAR analysis.

It is clear in Figure 3b that $\rho_{AHE}$ is dependent on the temperature.
This is due to the fact that $R_{S}$ varies a power law of the longitudinal
resistivity for Co. The qualitative description of the data is quite the same
as discussed previously for SAR. At small thicknesses there is a shunt of the
Bismuth layer and the $\rho_{AHE}$ is strongly reduced. Increasing the Co
content, SOPE causes a sharp increase in $\rho_{AHE}$, that goes through a
maximum at about 1 nm Co, then decreases slowly with further augmentation of
the Co thickness. As for SAR, the effect of the proximity induced SOC near the
interface becomes less relevant in the response of the whole multilayer when
the Co thickness reaches a certain threshold. At the highest Co content, the
Hall resistivity typical of bulk cobalt is recovered and a saturation is
observed. This behavior is also shown by the data collected in ref[27] and
depicted in 3b, in star symbols. These data are for the Hall resistivity of
thin Co films with variable thickness. The observed increase of $\rho_{AHE}$
by decreasing film thickness was interpreted as effect of SOPE at the surface
of Co[27]. The $\rho_{AHE}$ values found in Ref.[27] are smaller than the one
seen in our multilayers. This fact could be attributed to the stronger SOC
induced by the Bi layers, as compared to that due to surface. Moreover, the
shunt effect does not occur in the single layers of Co studied in ref ref[27].

Figure 4: Schematic of the spin-dependent scattering near to the interface
induced be the strong Bismuth spin-orbit and leading the the SOPE.

Measurements of $\rho_{AHE}$ as a function of temperature for the studied
multilayers are shown in Figure 3c, whereas Figure 3d depicts the
$\rho_{AHE}vs.\rho_{xx}$ plot. We point out, however, that was not possible
single out the longitudinal resistivity due to the Cobalt layer of each
heterostructure. Then, we used the $\rho_{xx}$ for the Co (20nm) reference
sample for all the multilayers. The straight lines that relates $\rho_{AHE}$
and $\rho_{xx}$ data in Figure 3d are consistent with a description based on
the skew-scattering mechanism for the AHE observed in our multilayers [33].

_Discussion about the AHE and SAR data_. The prevalence of this extrinsic type
of scattering, i.e., the Skew Scattering, suggests that the Bi atoms at the
interface are the main responsible by the enhancement of $\rho_{AHE}$ in the
multilayers. Notice that the dominant AHE mechanism in bulk cobalt is the
intrinsic one [34, 33], where a quadratic relation between $\rho_{AHE}$ and
$\rho_{xx}$ is expected [27, 35]. Then, our data indicate that the SOPE
observed in the SAR and AHE in the multilayers is related to a spin-dependent
scattering of charge carriers in cobalt by the strong SOC bismuth atoms at the
interfaces. Such spin-dependent scattering occurs only near to interface,
given the range of the SOPE. To enlighten the discussion above, a simple
scheme of the spin-dependent scattering close to the interface is presented at
the Figure 4. In this picture, the region of the Co layer affected by SOPE is
indicated.

In previous report, Zhang Y.Q., et al, [23] showed that the SOPE can be
estimated as a combination of both, Skew Scatting and Side Jump contribution
to Spin-Momentum scattering. Here our analysis indicate that Skew Scattering
seems to be the dominant mechanism on this Bi/Co heterostructures. Sanches
J.C.R., et al. [36] showed that the introduction o Bi can lead to a high
enhancement in the Inverse Spin Hall Effect signal on Ag/NiFe heterostructure.
Our results can also shed some light in this debate about the spin-to-charge
conversion in the Ag/Bi bilayer [36, 37, 38], once such system should also
present SOPE due to the presence of Bi layer.

Another important discussion is the impact of the structure and morphology of
the multilayers in the SAR and AHE results. Zhang Y. Q., et al. [23] pointed
that the interdiffusion of atoms at the interfaces and the roughness can
slight decrease the Hall angle, and so, the Anomalous Hall Resistivity. Here,
we do not expect flat and uniform layers for Co thickness smaller than 1 nm,
however, the presence of impurities should reduce the RRR ratio of the
samples, with imply in almost no dependence of $\rho_{AHE}$ on the
temperature. Which is the opposite what occurs in the results (see Figure 3b)
presented here. So we the presence of small portion of Bi interdiffusion on
the Co should be of small importance to the description of our results.

In conclusion, by performing detailed measurements of the spontaneous
anisotropy of the resistivity and the anomalous Hall effect Bi/Co multilayers
we have found evidences of Spin-Orbit Proximity Effect (SOPE) occurring at Co
ferromagnet thin layers near its interface with the Bi layers. Our findings
indicate that the enhancement of spin-orbit coupling close to the interface
between layers is related to the spin-dependent scattering of carrier in the
Co layer by the strong spin-orbit coupling of Bi atoms.

###### Acknowledgements.

We would like to acknowledge the funding agencies CAPES, CNPQ and FAPERGS by
the support. We thanks the grants CNPQ/UNIVERSAL 438171/2018-7, CNPQ/PQ
312938/2020-9, CNPQ/PQ 310171/2017-2 and PRONEX 16/0490-0. We also would like
to thank the support of the Laboratory of Nanoconformation (LCN) and
Laboratory of Ionic Implantation (LII) at UFRGS for XRD and RBS facilities. ….

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