# Can Telematics Improve Driving Style?
The Use of Behavioural Data in Motor Insurance

Alberto Cevolini
Dept of Political and Social Sciences
University of Bologna
Elena Morotti
Dept of Political and Social Sciences
University of Bologna
Elena Esposito
Dept of Political and Social Sciences, University of Bologna
Faculty of Sociology, Bielefeld University and
Lorenzo Romanelli
Swiss Re Europe S.A., Rappresentanza per l’Italia Riccardo Tisseur
Swiss Re Europe S.A., Rappresentanza per l’Italia Cristiano Misani
Swiss Re Europe S.A., Rappresentanza per l’Italia

(July 2023)

###### Abstract

The use of behavioural data in insurance is loaded with promises and
unresolved issues. This paper explores the related opportunities and
challenges analysing the use of telematics data in third-party liability motor
insurance. Behavioural data are used not only to refine the risk profile of
policyholders, but also to implement innovative coaching strategies, feeding
back to the drivers the aggregated information obtained from the data. The
purpose is to encourage an improvement in their driving style. Our research
explores the effectiveness of coaching on the basis of an empirical
investigation of the dataset of a company selling telematics motor insurance
policies. The results of our quantitative analysis show that this
effectiveness crucially depends on the propensity of policyholders to engage
with the telematics app. We observe engagement as an additional kind of
behaviour, producing second-order behavioural data that can also be recorded
and strategically used by insurance companies. The conclusions discuss
potential advantages and risks connected with this extended interpretation of
behavioural data.

_K_ eywords Behavioural data $\cdot$ Usage-Based Insurance $\cdot$ Engagement
$\cdot$ Coaching

##  1 Introduction

One of the main problems for insurance is that policyholders’ behaviour is
unobservable. Since the early 2000s, however, insurance companies selling
third-party liability motor insurance policies have invested heavily in the
use of telematics data to track drivers’ behaviour. The data collected should
make it possible to assess policyholders’ risk profile and adjust their policy
premiums accordingly. The insurance industry terms this opportunity ’usage-
based-insurance’ (UBI).

Business experience over the last two decades shows a significant evolution in
the use of behavioural data. Insurance companies not only use it to refine the
risk profile of policyholders, but also feed the aggregated information they
obtain from behavioural data back to the drivers. The aim is to promote
greater awareness by policyholders of their driving style and to encourage a
change in their driving behaviour in the case their driving habits show
criticalities that increase risk exposure. In this respect, insurance
companies speak of coaching (Donaldson, 2020; Tanninen, Lehtonen & Ruckenstein
2021; Cevolini, 2022). The possibility of providing feedback introduces a
profound change in the tasks and objectives of insurance practices. Indeed,
since its origins, insurance has been a reactive institution that intervenes
to compensate for a damage after it has occurred. With practices such as
coaching, on the other hand, insurance would intervene before damage occurs,
either to reduce its likelihood or to mitigate its effects —a challenge that
would entail a far-reaching re-organisation of insurance business, moving from
established actuarial practices to innovative forms of data mining and
counselling (Ericson, Doyle & Barry, 2003; Cultu, Ganjani, Larrea & Müssig,
2022). The insurer would become a sort of ‘advisor’ selling preventive
services (Picard, 2018).

The effectiveness of coaching, however, is yet to be proven and depends on a
crucial factor: the propensity of policyholders to take in and use the
information fed back by the insurance company in order to motivate them to
change their behaviour. This depends, in turn, on the willingness of users to
consult the tools that convey this information, which are usually digital
apps. Based on a rapidly developing strand of research (Lupton, 2013;
Asimakopoulos, Asimakopoulos & Spillers, 2017; Bucher, 2020), we suggest to
term this kind of activity engagement.

Our research assumes that engagement is also a behaviour, which like driving
behaviour is (or can be) tracked by digital devices. If by ‘behaviour’ we do
not only mean ‘the use of the car’ but also ‘the use of the app’, then
insurance companies have to deal with two different types of behavioural
data—behavioural data on driving attitudes, and behavioural data on users’
interaction with the app.

Our hypothesis is that the effectiveness of current experiments depends on the
integration of these two distinct types of behavioural data. However, this
integration raises a number of new questions: How should engagement be
properly defined? How should it be measured? Is there any empirical evidence
of a connection between engagement and driving behaviour improvement? And how
does this connection change over time?

To answer these questions, we investigated the dataset of an insurance company
selling telematics motor insurance policies. Before presenting our empirical
research, we first outline its historical and conceptual context. In section
2, we describe the emergence of the idea of insurance as a loss prevention
institution, and the evolution of usage-based auto insurance policies over the
past two decades. In section 3, we illustrate our research hypothesis about
the crucial role of engagement for effective coaching practices. In section 4,
we provide a brief overview of relevant research. In sections 5 and 6, we
describe the dataset we worked on, the methodology we followed, and our main
findings. Finally, in section 7, we draw some conclusions and suggest possible
directions for future research.

##  2 The evolution of usage-based auto insurance policies

In the mid-1990s, the motor insurance industry began to question the insurance
model that merely compensates policyholders’ claims. Starting from the
assumption that the vast majority of road accidents are caused by human
miscalculations (of driving capability, road conditions, or driving control
under certain road and weather conditions), the possibility of insurance
companies acting as loss prevention companies began to be discussed. The aim
was “stopping claims before they happen” (Ericson, Doyle & Barry, 2003, p.
271).

Underpinning this project was the conviction that insurance could not simply
be a risk spreading mechanism. Spreading risks basically means that
policyholders transfer their risks to the insurance company, which distributes
them over the pool. The result is a risk mitigation for the customers who feel
relieved from the financial consequences of possible future damages. A
consequence, however, can also be that policyholders are less incentivized to
take precautionary measures, producing the thorny problem of moral hazard
(Heimer, 1985; Stone, 2002).

To counter-act this attitude, it was suggested to try “to make people more
individually accountable for risks” (Baker & Simon, 2002, p. 1). The basic
idea was to move from “spreading risks” to “embracing risks”: even if
policyholders pay for coverage, they should be aware that they retain, at
least in part, both a moral and financial responsibility for the consequences
of their behaviour (Baker & Simon, 2002, p. 3).

In the case of auto insurance, this meant that drivers should engage in
preventive actions. But prevention first requires an awareness of the risks to
be avoided in order for bad driving habits to be removed (Ericson, Doyle &
Barry, 2003, p. 278). What remained unclear, however, was how the insurance
industry could tackle the problem of bad driving. This is where digital
devices used as monitoring devices to produce behavioural data come into play.

The first form of UBI tested in the early 2000s was the so-called pay-as-you-
drive (PAYD) insurance policy (Litman, 2005). The novelty of this policy was
that its pricing system was based on the mileage driven by the policyholders
during the policy term. The underlying idea was that mileage is a crucial risk
factor statistically related to claim probability. The assumption was that
people with low mileage are low-risk motorists and should pay less, whereas
people with high mileage are high-risk motorists and should pay more.

The PAYD-pricing system was later questioned as it does not take into account
the fact that higher mileage can also mean higher driving experience producing
better driving skills. Increasing mileage can be connected with a ‘learning
effect’ (Guillen, Nielsen, Ayuso & Pérez-Marín, 2019) that, in turn, might
decrease the risk of road accidents. Between young licensed drivers and claim
probability, on the other hand, there is a similar statistically significant
relationship.

UBI has later evolved into pay-how-you-drive (PHYD) insurance policies, based
on the idea that driving style is causally related to the risk of road
accidents and should also be taken into consideration when setting the policy
premium. PHYD insurance policies keep measuring mileage, but they also track
drivers’ behaviour to assess their actual driving style. This driving style
then affects the policy premium.

Drivers’ behaviour is tracked by means of telemetry packages. PHYD insurance
policies usually require the installation of a black box in the car with
policyholder’s consent. This black box generates a huge amount of behavioural
data that allows the company to monitor the policyholders’ driving style—how
they steer, how and how often they brake, whether they exceed the speed limit,
whether they drive predominantly during the day or at night, and so on. The
aggregation of these features makes it possible to assess the individual risk
profile and can be used to adjust the policy premium accordingly. This
information can also be the basis for coaching services that aim to prevent
claims before they occurr (Guillen & Cevolini, 2022).

The crucial condition to implement coaching strategies is feedback. In most
advanced telematics insurance solutions, drivers who take out a PHYD insurance
policy are supposed to download an app on their smartphone. This app notifies
policyholders of the overall score they achieved depending on how good or bad
they drove. The same app also communicates the scores achieved in the main
features (maneuvers) that the company uses to define the individual driving
profile (Discovery, 2020; Romanelli & Albers, 2021). Finally, the app shows
every single trip travelled by the insured and indicates exactly if and what
criticalities were encountered (e.g., where the insured exceeded the speed
limit or made a u-turn).

By means of this feedback, information literally circulates, that is, it runs
circularly. Drivers disclose information about their driving behaviour to the
insurance company. The insurance company, in turn, discloses information
concerning risk assessment and risk profile to the drivers. Telematics
insurance policies, thus, do not simply turn information asymmetry upside
down, as many scholars argue (Siegelman, 2014; Lasry, 2015). They rather
trigger a circular relationship where behaviour produces information, and
information is fed back to change behaviour. What is really going on in PHYD
insurance policies is a kind of feedback loop.

##  3 Engagement as a precondition for coaching

The feedback loop can achieve a coaching effect only in the case policyholders
are engaged. By ‘engagement’ we mean the user interaction with the app, that
is, the active dealing of policyholders with the information fed back by the
insurance company via different functionalities of the app (Asimakopoulos,
Asimakopoulos & Spillers, 2017; Bucher, 2020). Without such engagement it is
impossible to say whether an improvement in driving behaviour is the result of
coaching or simply a matter of chance.

For this reason, the usual ‘usage-based-insurance’ (UBI) formulation should be
clarified. The success of proactive strategies implemented by insurance
companies is, in fact, based on two different types of behaviour: not only on
the driving behaviour of policyholders but also on their interaction with the
app, i.e., on their being engaged. The use of the app is itself a behaviour
tracked by telematics apps, as well as driving behaviour. Insurance companies
selling PHYD insurance policies collect a lot of data about both behaviours -—
use of the car and use of the app -— and this is, in our opinion, a crucial
novelty.

Behavioural data are considered a “remarkable advance” in automobile insurance
(Guillen, Nielsen, Ayuso & Pérez-Marín, 2019, p. 662). Previously, the
insurance industry could only use variables related to fixed characteristics
of the policyholder and the vehicle, many of which, such as age and gender,
are not causally related to the risk of getting into a crash. They are
therefore proxy variables.

Behavioural variables, instead, are causally related to the risk of road
accidents and promise to enable personalised tarification, which may be
considered a fairer policy premium setting system (Meyers & Van Hoyweghen,
2017; Cevolini & Esposito, 2022). Moreover, as we have seen, behavioural data
processing can be carried out to implement coaching strategies and possibly
improve policyholders’ driving behaviour. Behavioural data processing, thus,
impacts on policyholders (who know that their behaviour is monitored), on
insurance companies (which can improve their predicting capacity by combining
behavioural and non-behavioural variables), and on the relationship between
policyholders and insurance companies (triggering feedback loops).

But what happens in practice? Is behavioural data-based motor insurance
actually working, and how? The usual abstract assumption is that coaching
works because policyholders who receive feedback improve their driving
attitude and become better drivers (Soleymanian, Weinberg & Zhu, 2019, p. 22).
This assumption, yet, leaves open many questions which should be investigated
more thoroughly. They concern, particularly, the interplay between feedback
and improvement in driving behaviour, since the information fed back can be
effective and produce a coaching effect only if the driver is engaged. In the
next section, we briefly describe relevant research on the effectiveness of
monitoring in motor insurance. We then introduce our empirical research.

##  4 Previous research

Even though the idea of improving traffic safety by changing safety-related
driving behaviour is not new, a recent overview on studies investigating the
impact of telematics on road safety points out that there is still little
research on this impact in terms of before/after feedback provision to the
drivers (Ziakopoulos, Petraki, Kontaxi & Yannis, 2022).

More than twenty years ago, Wouters and Bos (2000, p. 644ff.) already put
forward the hypothesis that drivers who know that they are being monitored
might be encouraged to change their behaviour, especially if they receive
feedback as a result of this monitoring. In their empirical research on a
business fleet, Wouters and Bos assessed the effect of this ‘behavioural
feedback’ based on JDR (journey data recorder) by comparing an experimental
group with a control group of vehicles for a period of 12 months. A
statistically significant accident reduction could be detected only for some
of the fleet sets, but the overall accident rate in the experimental group was
reduced by 20$\%$ after the intervention. However, both monitoring and
behavioural feedback were not linked to an insurance policy and lacked the
reinforcement that insurance policies usually provide in addition to feedback,
namely, financial incentives.

A decade later, Farmer, Kirley and McCartt (2010) tested the effects of in-
vehicle monitoring on the driving behaviour of teenagers, whose crash rates,
as well-known, is consistently higher than any other age group. Feedback, in
this case, was notified to their parents on a dedicated website. After 24
weeks monitoring on 85 recently licensed drivers in a suburban Washington DC
area, it turned out that there were no statistically relevant changes in
driving behaviour and that parents themselves made few visits to the website
to check the driving behaviour of their children. Also in this case, feedback
was not associated to an insurance policy.

Ten years ago, Bolderdijk, Knockaert, Steg and Verhoef (2011) carried out a
field experiment on the effects of a PAYD insurance policy on young drivers’
speeding behaviour. The basic reasoning was that young drivers are
overrepresented in road accidents statistics because they tend to drive at
higher speed, and speed is one of the most important behavioural determinant
of crash risk. The goal of their research was to test if the provision of
financial rewards for keeping the speed limit could encourage young drivers to
modify their driving behaviour. Participants could check their performance by
logging in to a website which provided a detailed feedback on speed
violations, mileage and night-time driving, and showed by default the
prospective overall discount they could earn. The incentive group (ca. 150
participants) showed a modest but significant reduction in speeding, strongly
associated to financial incentives (when financial incentives were removed,
speeding increased again).

The research that comes closest to the problems we investigate in this article
is that of Soleymanian, Weinberg and Zhu (2019). Based on the dataset provided
by a major US insurance company offering a PHYD policy, Soleymanian and
colleagues were able to observe more than 100,000 customers over a 32-months
time period. Their main research question was whether there is a statistically
significant improvement in driving behaviour of UBI customers compared to
usual customers. Their research showed that UBI customers improved their
driving score by ca. 9$\%$ (from 62.05 in week 1 to 67.87 in week 26), that
this improvement was higher in early weeks and for young drivers, and that it
did not depend solely on feedback but also on financial incentives. 15$\%$ of
UBI customers dropped out in weeks 11 and 12. The consequence was a
significant decline in hard braking, that can be interpreted as the outcome of
self-selection: PHYD policies retain best costumers and let bad customers
leave.

Soleymanian, Weinberg and Zhu’s research (2019) is very important. However, it
does not investigate many issues that are crucial for us. For example, if the
purpose of coaching strategies is the improvement of policyholders’ driving
behaviour, how should an improvement be properly defined? And how should it be
measured by insurance companies that have access to behavioural data? Since
improvement should be the result of coaching, how should a coaching process be
defined? Are there short-term and long-term coaching effects? Other crucial
questions for us are how engagement can be defined and measured, whether there
is a connection between engagement and driving behaviour improvement, and how
this connection changes over time. In our empirical research we deal with
these questions.

##  5 Dataset and methodology

The data we worked on were taken from PHYD insurance policies based on mobile
telematics. In this case, the smartphone replaces the usual black box. This
replacement has advantages and disadvantages. The main disadvantage is that
telematics data produced by a smartphone are less accurate than the telematics
data produced by a black box and require more pre-processing. The main
advantage is that the smartphone detects phone distraction, which today is one
of the main causes of road accidents and a crucial feature to be integrated
into the score evaluation process.

Moreover, the smartphone is usually regarded as an excellent platform for
providing users with feedback (Wahlstrom, Skog & Handel, 2015). In the app we
analysed, customers can easily check their driving performance. Immediately
after each driving session, the trip score is shown, and all significant
critical events are localized on the trip map. Past trips remain visible and
searchable in the app. On the app homepage, a weekly score for the current
week is updated. The weekly overall can be used by insurance companies to
adjust the monthly premium (also reported on the homepage), or to reward
policyholders with financial incentives (e.g., cashback, vouchers, discount).

In mobile telematics, raw data from GPS, accelerometer, and gyroscope, as well
as geolocation information by the map provider, are collected and then
processed to describe each driving session in terms of speeding, phone usage,
contextual data, and maneuvers. The data we considered for this paper concern
new customers onboarded in a 9-month period from March 2022 in a West European
region. The observation period was 35 weeks. We investigated coaching effects
in a pool of 498 customers.

###  5.1  Data Preprocessing

We accessed trip scores and trip metadata of all customers. In the weekly
summary, the automatically defined week always starts on Monday, disregarding
the exact onboarding day of each individual. For this reason, we considered
Monday-starting weeks and associated the week indexes $i=0,1,\dots$ to each
trip, where $i=0$ corresponds to the onboarding week for each user, ‘aligning’
the users according to their own timing.

Coherently, for each user $k\in{1,...,498}$, we have computed the weekly score
$s_{i}^{(k)}$ at each i-th week, as the mean of the trip scores of that week.
Each $s_{i}^{(k)}$ takes values from 0 (bad) to 1 (excellent). The value of
the score corresponds to the assessment of the quality of driving of the user
according to the current utilization of behavioural data. The better the
driver, the higher the score. The total number of weekly scores is 4419. This
feature is described in the histogram in Figure 1 and in the first row of
Table 1. The median score is 0.6065 and half of the values are between 0.4343
and 0.7690.

Table 1: Descriptive statistics of aggregated weekly data. Feature | Minimum | Q1 | Q2 | Q3 | Maximum
---|---|---|---|---|---
Weekly Score | 0.0120 | 0.4343 | 0.6065 | 0.7690 | 1
Weekly Duration (secs) | 0 | 0 | 12 | 186 | 4813
Number of weekly App Sessions | 0 | 0 | 1 | 3 | 54
Figure 1: Histogram of all the weekly scores.

The factors that go into the score, however, are not the only type of
behavioural data that are collected by telematics devices. Our app also
records the users’ app usage by collecting data about browsing sessions. Each
session is defined as a continuous time frame where the app is in the
foreground on the smartphone. For each session, we have insights describing
which of the possible app pages the user is looking at. We used these data to
measure users’ engagement.

To this purpose, conceptual decisions are required. One can use the number of
sessions, or the time spent on the app. The number of sessions itself can be
per day or per week. The time spent on the app, in turn, can be computed per
session or aggregated. We opted for time spent on the app aggregated over the
week. The original dataset provided 21283 app sessions of varying durations,
up to 16 minutes. For each user, we first aggregated each session duration on
a daily scale, then on a weekly scale, to match the processing workflow
previously described for scoring. We denoted such aggregated values as
$d_{i}^{(k)}$. Figure 2, summarizing the behaviour of our users, shows that
almost all policyholders look at the app mainly in the very first weeks of the
program, and they spend few minutes weekly interacting with the app.

Figure 2: Top: Visualization of the number of active users on the telematics
application (i.e., with at least one app session during the week) and inactive
users (with no app sessions), as a function of the week index. Bottom:
Histogram of the computed weekly durations (in seconds).

###  5.2 Approaches for Data Analysis

The first step of our analysis focused on improvement in driving behaviour. In
the available literature, the notion of improvement has not yet been clearly
defined. Weidner, Transchel and Weidner (2017, p. 214) claim that neither in
science nor in practice there is a “standardised method to achieve a clear
‘score’ of driving behaviour”. Soleymanian, Weinberg and Zhu (2019) aggregate
scores as mean values over weeks for the entire pool of policyholders and
compare them among weeks. Should any increase of the overall score be
considered an improvement, or are there more refined ways of defining it?

To analyse improvement in driving behaviour, we designed two different
workflows. The first one, described in section 5.2.1, explores for each user
if there is an improvement of the initial driving style in any week of the
period under consideration. The second one, discussed in section 5.2.2,
instead observes the trend for the entire period.

In both cases, we split the users into four classes according to the quartile
values of $s_{0}^{(k)}$. The classes, labeled as “very-low”, “medium-low”,
“medium-high” and “very-high”, represent different initial scenarios for our
analysis of coaching. In order to reliably measure improvement, we reasoned,
it is implausible to include all drivers in an undifferentiated group, because
the margins for improvement are of course very different for bad drivers with
various critical issues, which can be addressed, than for drivers who already
drive excellently, for whom there is little or no room for improvement.
However accurate and effective it may be, coaching will have little effect on
good drivers (those we include in the "medium-high" and "very-high" groups),
while we can expect it to make a difference in the driving style of "very-low"
and "medium-low" groups. Our analysis of improvement, therefore,
differentially explores the improvement effects in the four groups of drivers
with different skill levels. A precise description of merit-based classes can
be found in Table 2.

Table 2: Statistical characterization of the four merit-based classes, used to divide the policyholders according to their initial driving score.  | Classes based on $s_{0}$
---|---
| very low | medium-low | medium-high | very high
Range for $s_{0}$ | [0, 0.4060] | (0.4060, 0.6041] | (0.6041, 0.7713] | (0.7713, 1]
Median | 0.2915 | 0.4993 | 0.6853 | 0.8417
Number of users | 124 | 125 | 124 | 125

In the following sections, we present the two approaches we used to
investigate coaching effects, based on two very different metrics to quantify
the improvement of driving scores.

####  5.2.1 Coaching effects over single weeks

In our first set-up we considered data points corresponding to the
$s_{i}^{(k)}$ for i > 0\. To study users’ behaviour after their initial week,
we simply considered the difference:

$\delta_{i}^{(k)}=s_{i}^{(k)}-s_{0}^{(k)},\quad\forall i=1,2,...$ (1)

for each user k-th. In this case, we could independently study 3921 data
points that reflected changes in the driving styles of our pool. If we
consider any (sufficiently high) increase in the score of a user as an
improvement, $\delta_{i}^{(k)}>0.05$ signals an improvement in the driving
style for the k-user in the i-th week. We associate the corresponding data
point to the “Positive” class of improvement. On the contrary, we cast the
data points with $\delta_{i}^{(k)}<-0.05$ into the “Negative” class, whereas
values $\delta_{i}^{(k)}\in[-0.05,+0.05]$ correspond to a stable behavior
(“Null” class). We set the stability range corresponding to the 5$\%$-wide
interval of $\delta$, which takes values from -1 to +1.

From a methodological perspective, we remark that the definition of
$\delta_{i}$ could also be based on the ratio $s_{i}^{(k)}/s_{0}^{(k)}$
instead of on the difference $s_{i}^{(k)}-s_{0}^{(k)}$. In that case, the
three classes “Positive,” “Negative,” and “Null” would be defined around 1 by
setting as stability range the thresholds based on the 5% central interval.

In our analysis, we initially took both measures into account and then opted
for the difference because, based on the dataset at our disposal, this
approach allowed us to better discriminate between the three classes
“Positive,” “Negative,” and “Null”. In our investigation of coaching effects
over single weeks, we associated each $\delta_{i}^{(k)}$ to the cumulative
duration $D_{i}^{(k)}$ of the usage of the app during three weeks. We
quantified the users’ app usage by summing the weekly durations (in seconds)
over the current i-th week and the two previous ones, as:

$D_{i}^{(k)}=d_{i-2}^{(k)}+d_{i-1}^{(k)}+d_{i}^{(k)},\quad\forall i>1,\forall
k.$ (2)

####  5.2.2 Coaching effects over the entire period

The previous approach enabled us to take into account only temporary coaching
effects, as the changes in each driver’s score do not correlate with the
passing of time. Since we are interested in long-lasting improvements as well,
we also analyzed the evolution of the score with respect to the week indices i
for each user. We implemented linear regression models:

$s=s(i):=\beta_{0}+\beta_{1}i$ (3)

for each policyholder separately. An example of linear regression is reported
in Figure 3, for one (anonymous) user: on the horizontal axis, we read the
index i of the week since the user’s enrollment into the PHYD program, whereas
the [0, 1] vertical range is relative to the driving scores $s$. A positive
slope coefficient $\beta_{1}$ denotes (on average) continuously improving
driving performances over all tracked weeks. As before, we denote as
“Negative”, “Null” or “Positive” the improvements associated respectively to
$\beta_{1}<-0.005$, $-0.005\leq\beta_{1}\leq 0.005$, and $\beta_{1}>0.005$.

Figure 3: Example of simple linear regression (blue line) computed on the
weekly scores (in red) as function of the week index i, for a user with 25
tracked weeks.

Unfortunately, not all users have many associated weekly scores. This is a
crucial issue for this setting, since the reliability of the regression
procedure relies on the statistical analysis of a reasonably big amount of
data. As the data-driven recognition of patterns and relationships computed on
very few samples would be mathematically not representative, we removed from
our dataset the users with less than 8 scored weeks within the program. For
this reason, we calculated regression coefficients for 257 users.

The engagement factor was computed as the sum of all weekly $d_{i}^{(k)}$
seconds over the weeks of each k-th user. In order to avoid penalizing
policyholders who enrolled later, we normalized that sum over the user’s
specific number of weeks $N^{(k)}$, hence:

$D^{(k)}={1\over N^{(k)}}\sum_{i=1}^{N^{(k)}}d_{i}^{(k)}$ (4)

for each k-th user.

##  6 Results and discussions

We can now outline the main results achieved based on our dataset. They are
not representative of the reference universe, i.e., of the telematics motor
insurance worldwide, but offer interesting cues to analyze and understand some
real dynamics of the telematics motor insurance market. We first focus on
improvement. In a second step, we analyse engagement.

###  6.1 Improvement

In our opinion, a useful definition of improvement should consider two main
issues: (i) how to measure it and (ii) what variation must be detected in
order to speak of improvement and, consequently, of coaching.

Focusing on the first issue, we point out that even slightly different
measures (i.e., difference or ratio) lead to very different interpretations of
single week-improvement.

Figure 4: Scatterplots of data points given by $s_{0}^{(k)}$ initial scores,
on the horizontal axis, and metrics for improvement quantification, on the
vertical directions. On the top, the values of $\delta_{i}^{(k)}$ are given by
difference as in Equation 1; on the bottom, by ratio.

In the scatterplots of Figure 4, we look at our data points in terms of
initial scores $s_{0}^{(k)}$ (on the horizontal axis) and $\delta_{i}^{(k)}$
values (on the vertical axis). In the first plot, the improvement values are
computed as in Equation 1, in the second plot through the ratio between
scores. In both plots, the three improvement-based classes are highlighted
with different data point colors and the corresponding cardinality of each
class is reported in Table 3. The two measures of single week improvement lead
to important differences: 35% of data points (1390 out of 3921) remark a
positive improvement when it is measured with difference, but the percentage
decreases to 29% (1158 out of 3921) if we adopt the ratio-based approach. In
any case, our data indicate an improving effect in the single week for about
one third of the users.

Table 3: Countings of data points in each merit-based class, according to two different definitions of the improving metric for coaching analysis. | Difference | Ratio
---|---|---
| Negative | Null | Positive |  Negative | Null | Positive
very low | 114 | 182 | 475 | 119 | 173 | 476
medium-low | 306 | 215 | 541 | 265 | 320 | 477
medium-high | 471 | 222 | 313 | 371 | 438 | 197
very high | 759 | 262 | 64 | 527 | 550 | 8
Totals | 1650 | 881 | 1390 | 1282 | 1481 | 1158

If we understand improvement, instead, not as the result of single-week
factors but as a positive change in driving behavior over time, we measure the
improvement with the slope parameter $\beta_{1}$ of the regression model in
Equation 3. In this case, the $\beta_{1}$ values computed for the 257 users
are reported in the histogram of Figure 5, and the cardinalities of the
relative improvement-based groups are reported in the last column of Table 4.
Most of the policyholders have regression slopes very close to zero or even
negative, and only 25% of the policyholders (65 out of 257) significantly
enhanced their driving style. This means that observing the entire pool, no
effective long-term coaching effect can be detected.

Figure 5: Histogram of the computed slope coefficients $\beta_{1}$ of Equation 3, for the selected subset of policyholders. Table 4: Number of data points for each merit-based class and improvement-based group. | very low | medium-low | medium-high | very high | Totals
---|---|---|---|---|---
Negative | 20 | 16 | 24 | 16 | 76
Null | 28 | 32 | 31 | 25 | 116
Positive | 16 | 13 | 17 | 19 | 65
Totals | 64 | 61 | 72 | 60 | 257

On the other hand, these results show that small increases in the score of
policyholders associated with the “medium-high” and “very-high” merit-based
classes tend to be underestimated (and vice-versa, small decreases tend to be
over-estimated). This is particularly evident in Figure 4 showing improvements
mainly in “very-low” and “medium-low” classes (left side of scatterplot).

Figure 6: Boxplots of the $\delta_{i}^{(k)}$ values of Equation 1

The division of policyholders into the four merit-based classes introduced in
section 5.2 allows us to describe our heterogeneous pool more accurately,
taking into account the initial level of driving ability. We can then better
interpret the real complexity and variety of the results. In Figure 6, we
separately report through boxplots the $\delta_{i}^{(k)}$ values (computed
with differences, as in Equation 1) for the merit-based classes. For "very-
low" and "medium-low" classes, the positive median values (represented with
horizontal lines inside the orange and red boxes) show an improvement in the
driving style of policyholders. Moreover, for the “very-low” class, the entire
orange box lies over the zero line, denoting that in 75$\%$ of cases there was
an increase in the score.

###  6.2 Engagement

In the last step of our analysis, we faced the conceptual challenges
concerning the idea of engagement. The very definition of engagement is
actually problematic. When is a driver really engaged? How can we measure
engagement? Is there a correlation between engagement and improvement in
driving behaviour? To the best of our knowledge, in the literature no one has
yet addressed these questions based on an insurance company PHYD dataset.

Since by ‘engagement’ we mean the active dealing of policyholders with the
information fed back by the insurance company, in our research we measured the
duration of each user’s interaction with the telematics app according to the
definitions given in Equations 2 and 4. We have computed the average
engagement (in seconds) splitting the data in twelve subgroups, given by all
possible combinations among the four merit-based class and the three
improvement-based groups. The results of the two approaches referring
respectively to single weeks and the entire period are reported in Figures 7
and 8.

Figure 7: Average of the engagement metric defined in Equation 2, for the
merit-based and the improvement-based classes in single weeks. Figure 8:
Average of the engagement metric defined in Equation 4, for the merit-based
and the improvement-based classes over the entire period.

In both cases, we observed a correlation between engagement and improvement.
The users of the "very-high" class (blue bars) are the most engaged with the
telematics app, independently from their improvement status in single weeks.
In Figure 8, the group of best drivers shows very strong engagement over the
entire period, well above the other groups. In Figure 7, we also observed that
in the "very-low" and "medium-low" classes (orange and red bars) the customers
manifesting positive coaching effects in single weeks are the most engaged
ones, whereas less engaged customers do not improve their driving scores. In
Figure 8, however, only the “very-low” class (orange bars) confirms this
trend, not the “medium-low” one (red bars). These findings are coherent with
our expectation to find improvement effects mostly in the classes of drivers
with lower initial scores.

Overall, these results show that there is an interplay between engagement and
improvement, but this connection is not strongly evident in all cases. We
suppose that the weak interplay is due to the poor engagement characterizing
our dataset. Figure 2, in fact, shows that the number of users looking at the
app is very low if compared to the number of users enrolled in the telematics
program, and the interest in checking feedbacks and scores rapidly decreases
over time. Moreover, users do not have long sessions with the app, which can
suggest that they do not properly read all informative pages.

##  7 Conclusions

Our investigation of the dataset of an insurance company offering a PHYD
policy showed that the relationship between coaching, improvement of driving
behaviour, and engagement is trickier than usually believed. This also depends
on the product (the app) and its capability of implementation of coaching
strategies. In our research, we faced conceptual and methodological problems
especially regarding the two main pre-conditions of coaching, that is,
improvement of driving style and user engagement. Here, we draw some general
conclusions about the role of behavioural data in proactive insurance.

Behavioural data promise to change both the traditional insurance business
model and the interaction between insurers and policyholders. In the case of
motor insurance, behavioural data are expected to provide a solution to the
classical problem of moral hazard. The underlying paradox is that
policyholders are less incentivised to take precautionary measures because
they are insured (Arrow, 1971; Stiglitz, 1983). Moral hazard is ‘moral’
precisely because it refers to behaviour, and behaviour is usually under
policyholder’s control.

In proactive insurance, the argument goes, if individual behaviour could be
observed and either rewarded or penalised depending on exposure to dangers,
this could affect the propensity of policyholders to control their behaviour
and the problem of moral hazard could be, if not removed, at least mitigated.
PHYD insurance policies, for example, might mitigate moral hazard because
policyholders know that their behaviour is monitored, they receive information
on their driving attitude and can learn to drive more carefully. In addition,
they might be encouraged to drive better because in this case they receive
financial incentives (Stevenson, Harris, Wijnands & Mortimer, 2021).

Telematics of course does not control moral hazard by directly steering
individual behaviour. The only control that might take place is a kind of
self-control, that can be based on the awareness of being tracked or on the
mere possibility of earning financial incentives. We cannot exclude that it
also depends on some kind of motivation to improve behaviour. In UBI, however,
this motivation is not a self-evident precondition (Cevolini, 2022). This is
why engagement plays such a crucial role. Our research shows that improvement
effects are higher in policyholders that actively engage with the app.

Our findings, however, also show that this engagement cannot be taken for
granted. Many policyholders do not look at the app at all, and the ones who do
it tend to have short and superficial sessions. The usage of any app is time-
consuming and can be annoying over time. This finding is confirmed by research
in behavioural data-based health insurance, that is, in the so called pay-as-
you-live (PAYL) insurance policies. Such insurance policies also use self-
tracking devices, and also in this case there is a feedback loop between
insurance company and policyholders who should be encouraged to change their
behaviour and move towards a healthier lifestyle (Lupton, 2016; Ruckenstein &
Pantzar, 2017). Also in PAYL “the impetus for change” (Gorm & Shklovski, 2019,
p. 2517) depends on the awareness of policyholders, which is connected with
their usage of the app. Empirical research, however, shows that the customers
of PAYL insurance policies are prone to a rather episodic use of their
tracking devices, or do not use them at all (Gorm & Shklovski, 2019; Tanninen,
Lehtonen & Ruckenstein, 2022).

If the goal of PHYD insurance policies is to improve driving style,
policyholders must first be motivated to engage with the app in order to be
motivated to change their behaviour. Is there anything insurance companies can
do to increase the level of engagement? Effective engagement can depend on the
app usability, but also on short messages and notifications proposing
challenges to achieve in order to improve driving behaviour, earn points, and
be rewarded. Insurance companies could expand the functionality of the app and
make the interaction with it more appealing.

But the interaction with the app is itself a kind of behaviour producing
second-order behavioural data that can be recorded and used strategically.
Insurance companies, therefore, could also implement second-order coaching
strategies with the goal of improving engagement, besides the first-order
strategies aiming at improving driving behaviour.

In principle, the level of engagement could be taken into account in the
scoring process as well. Including engagement into the score, however, is not
without risks. One could reward the most engaged users with points they earn
when they interact with the telematics app. But users who knew that their
score also depends on this interaction could be inclined to game the system,
learning to improve their score rather than learning to improve their driving
behaviour.

Indeed, information fed back to the drivers can affect how people behave, but
also how people deal with their behaviour. For example, a father who is late
in driving his daughter to school might turn off his mobile phone and turn it
back on when he drives calmly from school to work. The interaction with the
app becomes strategic, if not even opportunistic. Sure, a single event does
not affect a long exposure, and by means of crossing data the lack of trip can
be detected. On the other hand, a systematic misuse can be associated to
fraud. Regardless of these two extreme cases, it would be fine to reward users
who stay tuned, but a reward based on the level of engagement with the app
would work only if it were not disclosed. However, can insurance companies not
disclose how they calculate the score?

These difficulties can be interpreted as flaws of behavioural insurance
policies, but also as confirmation of the crucial role of engagement, which
could give rise to innovative approaches. In mundane everyday life, instead of
optimizing their driving style, users are rather prone to optimize their
interaction with the tracking device. Instead of keeping their driving
behaviour under control, users keep their tracking behaviour under control.
This could explain why long-term engagement is so difficult to achieve, and
could be the starting point for insurance companies to improve their UBI
business model.

The issues we raised for motor insurance could be investigated in health
insurance as well. Also in that sector there are ongoing experimentations with
insurance policies based on behavioural data, with striking overlaps with
motor insurance both in terminology and in the structure of the relationship
with the customers. Our hypothesis is that this is due to the truly disruptive
innovation underlying UBI policies: the potential use of behavioural data in
the extended sense we propose in our research, including engagement as a
specific form of behaviour.

### Funding.

This work was supported by the European Research Council (ERC) under Advanced
Research Project PREDICT no. 833749.

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# Inducing or suppressing the anisotropy in multilayers based on CoFeB

R. L. Seeger<EMAIL_ADDRESS>SPEC, CEA, CNRS, Université Paris-
Saclay, 91191 Gif-sur-Yvette, France  F. Millo  Université Paris-Saclay, CNRS,
Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France  A.
Mouhoub  Université Paris-Saclay, CNRS, Centre de Nanosciences et de
Nanotechnologies, 91120 Palaiseau, France  G. de Loubens  SPEC, CEA, CNRS,
Université Paris-Saclay, 91191 Gif-sur-Yvette, France  A. Solignac  SPEC, CEA,
CNRS, Université Paris-Saclay, 91191 Gif-sur-Yvette, France  T. Devolder
Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies,
91120 Palaiseau, France

###### Abstract

Controlling the uniaxial magnetic anisotropy is of practical interest to a
wide variety of applications. We study Co40Fe40B20 single films grown on
various crystalline orientations of LiNbO3 substrates and on oxidized silicon.
We identify the annealing conditions that are appropriate to induce or
suppress uniaxial anisotropy. Anisotropy fields can be increased by annealing
up to 11 mT when using substrates with anisotropic surfaces. They can be
decreased to below 1 mT when using isotropic surfaces. In the first case, the
observed increase of the anisotropy originates from the biaxial strain in the
film caused by the anisotropic thermal contraction of the substrate when back
at room temperature after strain relaxation during annealing. In the second
case, anisotropy is progressively removed by applying successive orthogonal
fields that are assumed to progressively suppress any chemical ordering within
the magnetic film. The method can be applied to CoFeB/Ru/CoFeB synthetic
antiferromagnets but the tuning of the anisotropy comes with a decrease of the
interlayer exchange coupling and a drastic change of the exchange stiffness.

††preprint: AIP/123-QED

##  I  Introduction

The control of the anisotropy of a given magnetic material is very often
required in the applications of magnetism Hirohata  _et al._ (2020). The
amorphous metallic CoFeB films are widely used in spintronics, both when very
soft properties are desired such as in flux guides Smith  _et al._ (1991), or
in contrast when a well defined uniaxial anisotropy is wanted as in the free
layers of magnetoresistive field sensors Hirohata  _et al._ (2020). Depending
on the targeted applications, a very same material platform can even be
sometimes used with opposite requirements for anisotropy. This is the case of
artificial multiferroics composed of ferromagnetic films and piezoelectric
layers. When meant for instance for energy harvesting, they require a well
defined anisotropy Roy  _et al._ (2011) while when meant for racetrack
applications isotropic properties are welcomeLei  _et al._ (2013). Tailoring
the uniaxial anisotropy –both inducing and suppressing– is thus an important
challenge of technological interest.

Various knobs can be employed to tune the magnetic anisotropy. Interface
engineering can be used in ultrathin filmsO’Handley (1999); Chappert  _et al._
(1998). In bulk materials one can either rely (i) on some sort of chemical
ordering van de Riet  _et al._ (1997) or, (ii) on the induction of anisotropic
strain in magnetostrictive materials Mathews and Prestigiacomo (2023).

In the first case, one use generally saturates the magnetization using a
strong magnetic field, and then provide thermal energy (hence atomic mobility)
to let the structure of the material evolve towards a new state compatible
with the desired magnetization orientation Chikazumi (2009). In metallic glass
like CoFeB, the anisotropy is related to some degree of alignment of the Boron
atoms within the material and this can be effectively tuned and reoriented by
in-field annealing van de Riet  _et al._ (1997). For the same reason, magnetic
anisotropy can already be induced during deposition if done under an applied
field West (1964).

The second case applies to magnetostrictive materials only. There, if an
appropriate choice of the substrate influences the growth (e.g. epitaxy or
strain relaxation) the resulting anisotropic strain leads to magnetic
anisotropy Mathews and Prestigiacomo (2023). This elastic coupling between the
magnetic film and the substrate is systematically desired in SAW-FMR devices
Weiler  _et al._ (2011); Kuszewski  _et al._ (2018); Rovillain  _et al._
(2022) and magneto-acoustics Küß  _et al._ (2022) when one harnesses the
interaction between a surface acoustic wave (SAW) hosted by a piezoelectric
substrate and the ferromagnetic resonance (FMR) of the magnetic film. Note
that this situation fundamentally entails a dilemma when isotropic properties
(meaning often stress-free layers) are desired in addition to a tight elastic
coupling between film and substrate. This dilemma is significant in SAW-FMR of
synthetic antiferromagnets (SAFs) since in this case a vanishing anisotropy is
required for resonant coupling between the SAWs and the spin wavesVerba  _et
al._ (2019). Unfortunately it is difficult to obtain quasi-isotropic SAFs, one
typically is left with uniaxial anisotropy fields $\mu_{0}H_{\textrm{k}}$ that
remain above a couple of mT Hindmarch  _et al._ (2008); Rushforth  _et al._
(2008); González-Guerrero  _et al._ (2007); Chang  _et al._ (2021).

In this paper, we study how to tailor (increase or suppress) the magnetic
anisotropy of magnetostrictive layers grown on piezoelectric substrates. We
develop our method on Co40Fe40B20 single layer films on LiNbO3 single crystals
that are very adequate for rf acoustical waves. We show that our method is
applicable to SAFs. The paper is organized as follows. We initially quantify
the uniaxial anisotropy in CoFeB and show how to control it through
appropriate annealing and substrate choice. The surface orientation of LiNbO3
strongly impacts how the annealing alters the anisotropy of the magnetic
material. A well designed procedure can lead to quasi-isotropic CoFeB layers,
and can be extend to CoFeB/Ru/CoFeB SAFs. However, spin wave spectroscopy
experiments show that the tailoring of the anisotropy of the SAF comes
together with an evolution of the exchange stiffness and of the interlayer
exchange coupling.

Figure 1: Schematic illustration of the samples consisting of a single CoFeB
layer (a) and a CoFeB/Ru/CoFeB SAF (b). All thicknesses are given in nm. (c)
Studied substrates. The red arrows indicate the direction of the ferroelectric
order parameter (i.e., crystalline direction Z${}_{\textrm{LiNbO}_{3}}^{+}$)
around which a bulk substrate would exhibit rotational symmetry.

##  II  Experiments

Figure 2: Schematics of the experiment and representative results for a CoFeB
single film on a Y128-cut substrate in the as-grown state. (a) VNA-FMR is
conducted in an in-plane orientated applied field of fixed magnitude
$\mu_{0}H_{\textrm{ap}}$ = 11.6 mT and variable orientation $\theta\in[0,360]$
deg. with respect to the long axis of the sample. (b) Example of VNA-FMR loss
spectrum $||S_{21}(H_{\textrm{ap}})||-||S_{21}(H=0)||$ and definition of the
resonance frequency $f_{\textrm{res}}$. (c) Symbols: experimental
$\theta$-dependence of $f_{\textrm{res}}$. Line: fit within the macrospin
model with uniaxial anisotropy field $H_{\textrm{k}}$ and magnetization as
free parameters. Insets: experimental hysteresis loops obtained along the
easy- (red curve, $\theta\cong$ 90°) and hard-axis (black curve, $\theta\cong$
180°).

###  II.1 Films

Fig. 1 depicts our material systems. The magnetic stacks are : Ta(6,
buffer)/CoFeB(34)/Ru(0.4)/Ta(3, cap) (short name: single CoFeB) and Ta(6,
buffer)/CoFeB(17)/Ru(0.7)/CoFeB(17)/Ru(0.4)/Ta(3, cap) (short name:
CoFeB/Ru/CoFeB) SAF. All thicknesses are given in nm. The CoFeB layer was
deposited from a Co40Fe40B20 (at. %) target. The deposition is done at room
temperature by dc-magnetron sputtering at pressure of argon of $5\times
10^{-3}$ mbar and base pressure below $10^{-7}$ mbar. No intentional magnetic
field is applied during growth. The thickness of the Ru(0.7) spacer of the SAF
is chosen to maximize the interlayer exchange coupling Mouhoub  _et al._
(2022).

###  II.2 Substrates

The depositions were done on several substrates ranging from naturally
oxidized silicon wafers (to be referred as Si/SiO${}_{\textrm{x}}$) to LiNbO3
single crystals of various surface orientation (Z-, Y- and Y128-cut) Kushibiki
_et al._ (2002). Since the properties of the magnetic materials can be
impacted by the stress induced by the underlying substrateBartasyte  _et al._
(2012), we cast the substrates in two categories. The first category gathers
the substrates whose surface expands in a quasi-isotropic manner upon
annealing. For the second category the thermal expansion is anisotropic at the
surface, as illustrated in Fig. 1(c).

###  II.3 Post-growth annealing conditions

In order to unravel the respective roles of substrate induced applied stress,
applied field, and Boron diffusion onto the annealing-induced evolution of the
magnetic properties, we have annealed our material systems using 4 different
procedures:

  * •

without any applied magnetic field.

  * •

with a 70 mT applied in a given direction in a 1 step manner. We will see that
the field direction (i.e., along or orthogonal to the initial anisotropy axis)
shall not influence the final result.

  * •

With a 70 mT field applied in 2 successive steps: the sample is first annealed
with a field oriented at some randomly chosen in-plane direction, then at
along an orthogonal direction.

  * •

In a 30 mT field rotating at 5 rpm in the sample plane.

The annealing temperature $T$ ranges from 100 to 200 °C, above which
systematic crystallization is expected for our Boron content You  _et al._
(2008); Conca  _et al._ (2014); Devolder  _et al._ (2018); Sriram  _et al._
(2022). The annealing time is set to 4 min on a hot plate for (i), (ii) and
(iii). The annealing in rotating field (iv) is done in vacuum for 10 h. In all
cases the field is applied while ramping up and down the temperature and is
strong enough to saturate the magnetization.

###  II.4 Magnetic characterizations

The magnetic characterization of samples was performed by vibrating sample
magnetometry (VSM) and Vector Network Analyzer ferromagnetic resonance Bilzer
_et al._ (2007) (VNA-FMR). An in-plane applied field $\mu_{0}H_{\textrm{ap}}$
was used, and its direction $\theta$ [see Fig. 2(a)] was varied to access to
the sample’s magnetic anisotropy. The resonance spectra (FMR absorption
signal) are obtained by measuring the field dependence of the VNA transmission
parameter $||S_{21}(H_{\textrm{ap}})||-||S_{21}(H=0)||$, as plotted in Fig.
2(b). The resonance frequencies (FMR for the single CoFeB or acoustical and
optical resonances of the SAF) $f_{\textrm{res}}$ are defined from the maxima
of absorption.

The $\theta$-dependence of the FMR of single CoFeB films were analyzed in the
macrospin approximation using numerical energy minimization and subsequent
application the Smit-Beljers equationSmit and Beljers (1995). A fitting
procedure allowed to extract independently the values of the uniaxial
anisotropy field $H_{\textrm{k}}$, the orientation of the easy axis and the
saturation magnetization $M_{\textrm{s}}$. Fig. 2(c) illustrates this
procedure when applied to a single CoFeB film grown on a Y128-cut substrate in
the as-grown state. The orientation of the easy axis and the uniaxial
character of the anisotropy are systematically consistent with the hysteresis
loops.

The $\theta$ and $H$ dependence of the acoustical $f_{\textrm{acou}}$ and
optical $f_{\textrm{opt}}$ resonances of the SAF were analyzed in the full
micromagnetic framework Vansteenkiste  _et al._ (2014) following the method
described in ref. Mouhoub  _et al._ , 2022. There, it was shown that the
competition between the interlayer coupling $J$ and the intralayer exchange
stiffness $A_{\textrm{ex}}$ results in the existence of a gradient of the
magnetization orientation in the growth direction. This gradient renders the
curvature of the $f_{\textrm{opt}}(\theta)$ near $H=0$ very sensitive to the
ratio of $A_{\textrm{ex}}$ and $J$, that can thus be deduced reliably. A
fitting procedure of $f_{\textrm{acou}}(\theta)$ can then be used to extract
the anisotropy fields, assumed to be exactly the same for the two magnetic
layers of the SAF.

##  III  Evolution of the magnetic anisotropy upon annealing

###  III.1 Results

Figure 3: (a) Anisotropy field $H_{\textrm{k}}$ dependence with the annealing
temperature $T$ as measured for single CoFeB grown on Y-cut LiNbO3, as an
example of effect of annealing on a substrate with anisotropic surface. (b)
Representative $H_{\textrm{k}}$-dependence for samples subjected to various
annealing procedures with $T$ = 200 °C , as measured for single CoFeB grown on
Z-cut LiNbO3, a substrate with quasi-isotropic surface. Insets in (a) and (b)
are representative $\theta$-dependence of $f_{\textrm{res}}$ before and after
annealing. The line is a fit to the experimental data.

The main features of the evolution of the magnetic anisotropy upon annealing
are illustrated in Fig. 3 and compiled in Table 1. An annealing temperature
above 100°C appeared necessary to observe an evolution of the magnetic
properties. The atomic mobility within the CoFeB films is likely insufficient
below this temperature. For larger annealing temperatures, the magnetic
anisotropy evolves in very different ways depending if the substrate has an
isotropic or an anisotropic surface, and also on the field applied.

When working on substrates with anisotropic surfaces (Y-cut and Y128-cut
LiNbO3), the annealing increases substantially the anisotropy, see Fig. 3(a).
The inset compares for instance the angular dependence of the FMR of a CoFeB
film on a Y-cut LiNbO3 substrate before and after a 200 °C field-free
annealing. Annealing increases the anisotropy field $\mu_{0}H_{\textrm{k}}$
from 3.05 mT to 9.00 mT. This comes with a reorientation of the hard axis
towards the X${}_{\textrm{LiNbO}_{3}}$ (i.e., $\theta$ = 0 deg. in our
convention). The Y128-cut samples follow a similar trend but with a lower
increase of the anisotropy. As soon as the anisotropy increases, the hard axis
also reorients towards X${}_{\textrm{LiNbO}_{3}}$ axis and the easy axis
towards the in-plane projection of the Z${}_{\textrm{LiNbO}_{3}}$ axis. When
working on these substrates with anisotropic surfaces, the magnetic field
applied (or not) during the annealing has a minor influence on the evolution
of the magnetic anisotropy.

Conversely, the anisotropy can be reduced for the films grown on the
substrates with quasi-isotropic surfaces: Z-cut LiNbO3 and oxidized silicon.
The inset in Fig. 3(b) shows for instance angular dependence of the FMR before
and after a 2 steps annealing procedure in the case of a Z-cut LiNbO3
substrate. This 2-step annealing lowers the anisotropy down to 0.6 mT.
Notably, the rate of decrease of the anisotropy depends strongly on the field
sequence used during annealing, and the hard axis systematically ends
perpendicular to the field applied during the last annealing step.

###  III.2 Physical origins of the evolution of anisotropy

The previous results can be discussed by considering two thermodynamic
phenomena: (i) the interplay between magneto-elasticity and anisotropic strain
and, (ii) the chemical ordering within the magnetic material. We recall that
for the annealing temperatures studied here, no crystallization of the CoFeB
layer is expected. Let us first discuss the magneto-elastic scenario.

Table 1: Summary of the material parameters in single CoFeB subjected to
different thermal treatments. "Variable" means that the value of the
anisotropy field and its orientation depend on the sample position within the
deposition machine – the evolution of $H_{k}$ is however taken for a
consistent sample position.
Sub. | Thermal |  $\mu_{0}H_{k}$ (mT) | Hard axis |  $\mu_{0}M_{s}$ (T)
---|---|---|---|---
| treatment | $\pm 5\%$ |  | $\pm 0.01$
Substrates with quasi-isotropic surface: |
SiOx | as grown | 3.0 | variable | 1.70
| 200∘C, H=0 | 3.1 | variable | 1.72
| 200∘C, rotH | 1.5 | variable | 1.71
| 200∘C 2-step H | 0.9 |  $\perp$ to last field | 1.76
Z | as grown | 2.2 | variable | 1.70
| 200∘C, H=0 | 2.8 | variable | 1.71
| 200∘C, rotH | 2.4 | variable | 1.82
| 200∘C 2-step H | 0.6 |  $\perp$ to last field | 1.70
Substrates with anisotropic surface: |
Y128 | as grown | 3.1 | variable | 1.77
| 200∘C, H=0 | 4.3 |  $\parallel$ X${}_{\textrm{LiNbO}_{3}}$ | 1.87
Y | as grown | 3.0 | variable | 1.70
| 200∘C, H=0 | 9.0 |  $\parallel$ X${}_{\textrm{LiNbO}_{3}}$ | 2.00
| 200∘C, rotH | 6.4 |  $\parallel$ X${}_{\textrm{LiNbO}_{3}}$ | 2.00
| 200∘C 2-stepH | 11.4 |  $\parallel$ X${}_{\textrm{LiNbO}_{3}}$ | 2.00

####  III.2.1 Magneto-elastic scenario

When annealing above $T_{\textrm{a}}>$ 100°C, the atoms within the CoFeB film
acquire some mobility, as observed in other soft magnetic materials van de
Riet  _et al._ (1997). Being amorphous, the glassy CoFeB film slowly flows,
such that after a sufficient delay it reaches a relaxed (stress-free) state at
the annealing temperature. Cooling (defining $RT-T_{\textrm{a}}=\delta T<0$)
to room temperature (RT) quenches suddenly any atomic mobility, while
triggering a thermal contraction. Since the CoFeB film is clamped by the much
thicker substrate, the in-plane strain $\epsilon$ of the substrate is imposed
to the magnetic film. The natural contraction of an hypothetically free-
standing CoFeB film would be isotropic (its thermal expansion coefficient
$\beta$ is isotropic). That of the LiNbO3 substrate is not: the thermal
expansion coefficient in the X${}_{\textrm{LiNbO}_{3}}$ direction is stronger
than in the other direction of the substrate plane Bartasyte  _et al._ (2012).
As a result the stress $\bar{\bar{\epsilon}}$ within the CoFeB at RT is
biaxial and more compressive in the X${}_{\textrm{LiNbO}_{3}}$ direction.
Defining $x$ and $y$ as the two directions of the surface of the substrate
with $x\parallel$ X${}_{\textrm{LiNbO}_{3}}$ [see Fig. 1(c)], we have:

$\epsilon_{xx}=\beta_{x}\delta
T<0\textrm{~{}and~{}}\epsilon_{yy}=\beta_{y}\delta T<0$ (1)

Whatever the substrate cut, the largest deformation is always along
X${}_{\textrm{LiNbO}_{3}}$, see ref. Bartasyte  _et al._ , 2012. We have
$\beta_{x}>\beta_{y}$ for both the Y-cut case and the Y128-cut case. As the
CoFeB has essentially a free surface, its stress is purely biaxial, such that
there is no shear strain (i.e., $\epsilon_{xy}=0$).

This biaxial strain generates a magnetic anisotropy of CoFeB. Indeed for an
in-plane magnetized film, the magneto-elastic energy is
$E_{\textrm{me}}=B_{1}(m_{x}^{2}\epsilon_{xx}+m_{y}^{2}\epsilon_{yy})+B_{2}m_{x}m_{y}\epsilon_{xy}$,
where $B_{1}$ and $B_{2}$ are the usual magneto-elastic coefficients. In
amorphous materials, they reduce to $-\frac{3}{2}\lambda E_{\textrm{Young}}$
which amounts to $-7.6$ MJ/m3 with the magnetostriction coefficient
$\lambda=27~{}\textrm{ppm}$ for Co40Fe40B20 from ref. Masciocchi  _et al._ ,
2021 and the Young’s modulus $E_{\textrm{Young}}=187$ GPa, from ref. Peng  _et
al._ , 2016. Note that $\lambda>0$, meaning a tensile strain lowers the
energy. The CoFeB film being more compressed in the X-direction than in other
directions, X${}_{\textrm{LiNbO}_{3}}$ will become the hard axis. Using the
conservation of the magnetization norm and $\epsilon_{xy}=0$, we can rewrite
this energy in the form of an effective uniaxial anisotropy:

$E_{me}=B_{1}m_{x}^{2}(\epsilon_{xx}-\epsilon_{yy})$ (2)

with a magneto-elastic effective anisotropy field of:

$\mu_{0}H_{k}^{\textrm{mel}}=\frac{2B_{1}}{M_{s}}(\beta_{x}-\beta_{y})\delta
T$ (3)

that is predicted to be linear with the annealing temperature, which bears
some similarity with the experimental results [see Fig. 3(a)] above
$T_{\textrm{a}}$=100°C.

Table 2: Thermal expansion coefficients in the two directions of the surface
plane, in units of $10^{-5}/^{\circ}$C.
Surface |  $\beta$ in first direction |  $\beta$ along a perp direction
---|---|---
Y-cut | along X${}_{\textrm{LiNbO}_{3}}$: $\beta_{1}=1.5$ | along X${}_{\textrm{LiNbO}_{3}}$: $\beta_{3}=0.7$
Y128-cut | along X${}_{\textrm{LiNbO}_{3}}$: $\beta_{1}=1.5$ | $\beta_{1}\sin^{2}(128)+\beta_{3}\cos^{2}(128)=1.2$
Z-cut | along X${}_{\textrm{LiNbO}_{3}}$: $\beta_{1}=1.5$ | along X${}_{\textrm{LiNbO}_{3}}$: $\beta_{1}=1.5$
Si[001] | along [100]: 0.468 | along [010]: 0.468

Using the data of Table 2 with $\delta T=-180$ K, Eq. 3 predicts
$\mu_{0}H_{k}^{\textrm{mel}}=5.5\textrm{~{}mT}$ for the Y128-cut case and
$\mu_{0}H_{k}^{\textrm{mel}}=13.7\textrm{~{}mT}$ for the Y-cut case, with hard
axes along X${}_{\textrm{LiNbO}_{3}}$ in both cases. This magneto-elastic
contribution dominates any other contribution to the uniaxial anisotropy,
including the one present in the as-grown state and those possibly related to
the magnetic field applied during the annealing. This correlates with our
finding on the minor influence of the field applied during the annealing of
Y-cut and Y128 samples Note that the predicted values of the anisotropy field
$H_{k}^{\textrm{mel}}$ are slightly marger than our experimental findings.
This may indicate that the stress release is incomplete during the annealing,
or that the magnetostriction coefficient of the literature Masciocchi  _et
al._ (2021) is over estimated.

Another conclusion of our study concerns the evolution of the magnetization
$M_{\textrm{s}}$ upon annealing (Table 1). There is little evolution for the
Si/SiO${}_{\textrm{x}}$ case, but a substantial increase otherwise. For our
nominal Boron concentration, bulk crystallisation or stress-induced bulk
crystallization are not supposed to occur at our annealing temperatures
Trexler and Thadhani (2010) and can therefore not be invoked for the observed
increase of the magnetization. However, some compression-induced diffusion of
the Boron atoms out of the magnetic films may start to occur, thereby reducing
the Boron concentration. The corresponding densification is generally
associated with an increase of the magnetization Kim  _et al._ (2022). We
indeed observe that the increase of the magnetization after the 200°C
annealings seems to correlate with the amount of compression (see Tables 1 and
2).

This anisotropic strain-induced scenario is effective only for the substrates
with anisotropic thermal expansion like Y-cut and Y128-cut LiNbO3. Another
scenario must thus be invoked for the Z-cut of LiNbO3 and the oxidized silicon
cases.

####  III.2.2 Chemical order scenario

In many magnetic alloys, it is routinely observed that annealing in a magnetic
field induces a preferred direction of magnetization O’Handley (1999);
Chikazumi (2009). A plausible model often invoked to explain this mechanism is
the migration of atoms on a local scale in such a way as to favor
magnetization in a given direction. At annealing temperatures leading to some
atomic mobility, some atom pairs orient themselves relative to the direction
of magnetization set by the field, so as to decrease their magnetic anisotropy
energy. Cooling to a temperature where atomic diffusion gets quenched, the
anisotropy axis remains along the direction it has acquired during annealing.
Metalloids like Boron play an important role in this process thanks to their
high mobility and chemical interaction with transition metals van de Riet  _et
al._ (1997). In metallic glass like CoFeB the applied field drives an
anisotropic distribution of atoms pairs among Co, Fe and B, and this mechanism
is active at the time scales used for annealing for the temperatures
considered here van de Riet  _et al._ (1997). This process is generally used
to induce anisotropy, using a fixed field orientation and a long annealing.

However it is important to figure out that the material evolution is a
thermodynamical process: during our first annealing step, the field-induced
(energy-minimization-driven) chemical ordering process competes with a
temperature-induced (random, entropy-driven) disordering trend. This
competition leads to a slow formation of a uniaxial anisotropy. During the
subsequent annealing step, the magnetic field orientation is different. As a
result, the entropy-driven and energy-driven thermodynamical forces both tend
to destroy the previously favored chemical order, and therefore they concur to
reduce the anisotropy. Because of this coincidence of the two thermodynamical
forces at play, this destruction of the previously set anisotropy is a fast
process. The building-up of any uniaxial anisotropy along a new field
direction is a much slower process. In practice, it is not seen at the time
scales used in our annealings.

This explains how one can progressively reduce the anisotropy by applying
successive orthogonal fields during annealing when there is no magneto-elastic
contribution at play. Each annealing step with a new field direction
statistically breaks pair alignments which results in a progressive
randomization of the chemical ordering within the magnetic film and, thus, a
decrease of the anisotropy. The effect of annealing under a rotating field is
qualitatively similar as a two-step annealing, but their relative efficiency
depends on the characteristic time-scales of atomic diffusion versus the field
rotation period.

To summarize the discussion so far, the findings presented in Fig. 3 indicate
that, with regards to the substrate, different contributions to the uniaxial
anisotropy of CoFeB may arise. For surface substrates with anisotropic thermal
expansion (Y-cut and Y128-cut LiNbO3), the anisotropy is controlled by
anisotropic strain, while for quasi-isotropic surface substrates
(Si/SiO${}_{\textrm{x}}$ and Z-cut LiNbO3), the anisotropy is controlled by
the chemical ordering favored or broken by the sequence of applied magnetic
fields.

##  IV  Applicability to synthetic antiferromagnets

Figure 4: Effect of annealing in a rotating field for CoFeB/Ru/CoFeB SAFs
grown on Si/SiOx. (a) $\theta$-dependence of $f_{\textrm{res}}$ before and
after annealing. Symbols are experimental data. The lines show the calculated
dependencies from micromagnetic simulations Vansteenkiste  _et al._ (2014)
using magnetic parameters fitted from the broadband VNA-FMR characterization
of the acoustical and optical modes shown in (b) in the as-grown state and in
(c) after annealing. Insets show color maps of the distance $\chi$ between the
experimental and simulated spin wave frequencies used to determine
$A_{\textrm{ex}}$ and $J$.

It is important to investigate whether the conclusions previously established
for single CoFeB films can be extended to multilayers. In particular, let us
see if one can obtain isotropic CoFeB/Ru/CoFeB synthetic antiferromagnets
(SAF) when grown on quasi-isotropic substrates. Fig. 4 shows the results for a
SAF grown on Si/SiO${}_{\textrm{x}}$ in the as-grown state and after annealing
in a rotating field. The two lowest order spin wave modes can be detected, the
acoustical ($f_{\textrm{acou}}$) and the optical ($f_{\text{opt}}$) modes. The
value of $f_{\text{acou}}$ at low field is known to be very sensitive on the
anisotropy fieldDevolder and Ito (2012). The $\theta$-dependence of
$f_{\textrm{acou}}$ [Fig.4(a)] clearly indicates that the annealing procedure
defined for the single layer films succeeded also in suppressing the
anisotropy of the SAF grown on Si/SiO${}_{\textrm{x}}$. As shall be explained
later, we can only give a semi-quantitative measurement the anisotropy field
$\mu_{0}H_{\textrm{k}}$ of the SAF, but its reduction (see Table 3) is almost
complete. The same trend is observed when the growth is performed on Z-cut
LiNbO3 (see Table 3).

However this quasi-suppression of the anisotropy is accompanied by an
evolution of the other magnetic properties. This can be seen by comparing the
frequencies of the experimental and simulated modes using the methodology
defined in ref. Mouhoub  _et al._ , 2022. Indeed the value of $f_{\text{opt}}$
at $H=0$ is essentially set by the interlayer coupling $J$. Annealing
obviously reduces it [compare Fig. 4(b) and (c)]. Besides, the curvature of
$f_{\text{opt}}$ versus $H$ is very sensitive to the ratio
$\frac{A_{\textrm{ex}}}{J}$: annealing obviously strongly affects this ratio.

The values of $A_{\textrm{ex}}$, $J$ that best fit the experimental data for
Si/SiO${}_{\textrm{x}}$ and Z-cut LiNbO3 substrates are listed in Table 3. The
experiment-to-micromagnetics agreement is excellent except in the small field
region for the acoustical spin wave, where micromagnetics systematically
underestimates the frequency of the acoustical mode [Fig. 4(b) and (c)]. The
same difficulty arises when attempting to account for the $\theta$-dependence
of $f_{\textrm{acou}}$ with micromagnetic simulations, as shown in Fig. 4(a).
The reason for this disagreement was not identified, but we believe that it
may arise from a gradient of the magnetic properties in the growth direction
which is not taken into account in the simulations. For this reason, we can
only give a semi-quantitative measurement the anisotropy field
$\mu_{0}H_{\textrm{k}}$. The anisotropy values in Table 3 are deduced from the
sole value of $f_{\text{acou}}$ at zero field.

Table 3: Material parameters of the synthetic antiferromagnet before and after annealing in a rotating field.  Substrate |  $\mu_{0}H_{k}$ (mT) |  $\mu_{0}M_{s}$ (T) |  $J$ (mJ/m2) |  $A_{ex}$ (pJ/m)
---|---|---|---|---
SiOx, as grown | 4.4 | 1.70 | -1.5 | 14.5
SiOx, 200∘C | 0.8 | 1.71 | -0.9 | 28.3
Z${}_{\textrm{LiNbO}_{3}}$, as grown | 3.8 | 1.70 | -1.7 | 15.5
Z${}_{\textrm{LiNbO}_{3}}$, 200∘C | 0.5 | 1.70 | -1.1 | 21

Upon annealing, $J$ reduces from -1.5 mJ/m2 to -0.9 mJ/m2 upon annealing, as
observed for our SAF grown on Si/SiO${}_{\textrm{x}}$. The atomic mobility
enabled by the annealing probably reduces the sharpness of the interfaces of
the Ru spacer, thereby decreasing $J$. The evolution of the local order within
the CoFeB material is also evident from the evolution of its exchange
stiffness $A_{\textrm{ex}}$, which undergoes a very substantial increase from
14.5 pJ/m to 28.3 pJ/m upon annealing. It is noteworthy that the as-grown
value of $A_{\textrm{ex}}$ is comparable to literature values in the amorphous
state for our composition, which are found to be Mouhoub  _et al._ (2022); Cho
_et al._ (2013); Choi (2020) in the range from 10 to 14 pJ/m. The exchange
stiffness is also known to increase substantially when the layer get either
crystalline or simply more dense Kim  _et al._ (2022).

##  V Conclusion

We have studied the impact of annealing on the magnetic properties of CoFeB
films and synthetic antiferromagnets. We identified the different
contributions to the uniaxial anisotropy in CoFeB single films by performing
various in-field thermal treatments for films grown on different substrates.
The anisotropy field of CoFeB can be increased when the annealing is performed
in samples grown on substrates whose surfaces have an anisotropic thermal
expansion. In this case the likely scenario is a full stress relaxation
occurring during the annealing, followed by the creation of a biaxial strain
in the CoFeB upon cooling, which induces a strong magneto-elastic anisotropy.
Anisotropy fields up to 11 mT can be induced when extremely anisotropic
substrates like Y-cut LiNbO3 are used. Conversely, the anisotropy field can be
decreased to below 1 mT when using substrates whose surface is quasi-
isotropic. In this case the anisotropy is controlled by the history of the
magnetic field applied during annealing. In particular, sequences of
orthogonal fields are very efficient in suppressing the anisotropy. This
method was applied to obtain isotropic CoFeB/Ru/CoFeB synthetic
antiferromagnets; however the annealing also affects the exchange interactions
within the stack.

###### Acknowledgements.

We acknowledge discussions with S. Margueron and A. Bartasyte. This work was
supported by a public grant overseen by the French National Research Agency
(ANR) as part of the “Investissements d’Avenir” program (Labex NanoSaclay,
reference: ANR-10-LABX-0035, project SPICY). R. L. S and F. M. acknowledge the
French National Research Agency (ANR) under Contract No. ANR-20-CE24-0025
(MAXSAW).

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